diff --git a/.gitignore b/.gitignore index 5a310e3..a8109ae 100644 --- a/.gitignore +++ b/.gitignore @@ -1,5 +1,14 @@ # langserver .ccls-cache/ +.cache/ + +# gdb +.gdb_history + +*.ezw +perf/ +build/ +compile_commands.json # Prerequisites *.d diff --git a/.gitmodules b/.gitmodules new file mode 100644 index 0000000..b593b43 --- /dev/null +++ b/.gitmodules @@ -0,0 +1,3 @@ +[submodule "wavelib"] + path = wavelib + url = https://github.com/codepurble/wavelib.git diff --git a/2021-06-07-Note-19-23.xoj b/2021-06-07-Note-19-23.xoj new file mode 100644 index 0000000..ab6ec9f Binary files /dev/null and b/2021-06-07-Note-19-23.xoj differ diff --git a/CMakeLists.txt b/CMakeLists.txt new file mode 100644 index 0000000..d5b5dad --- /dev/null +++ b/CMakeLists.txt @@ -0,0 +1,27 @@ +cmake_minimum_required(VERSION 3.10) +project(libezw) + +set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -Wall") +set(CMAKE_C_FLAGS_DEBUG "${CMAKE_C_FLAGS_DEBUG} -Wall") +set(CMAKE_C_FLAGS_RELEASE "${CMAKE_C_FLAGS_RELEASE} -Wall") +set(SOURCE_DIR ${CMAKE_CURRENT_SOURCE_DIR}/src) +set(CMAKE_EXPORT_COMPILE_COMMANDS ON) + +add_subdirectory(wavelib) + +include_directories(include) +add_executable(main + ./src/ezw.c + ./src/main.c + ./src/utils.c + ./src/sbtree.c + ./src/smap.c + ./src/node.c + ./src/queue.c + ./src/stack.c + ./src/bitstream.c + ) + +target_link_libraries(main PUBLIC wavelib m) # "m" to link math.h +# target_link_libraries(main PUBLIC wavelib gsl gslcblas m) # "m" to link math.h + diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..256bf26 --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2022 Ramprakash + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md index 00d3130..6ab92bb 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,5 @@ # libezw C library for EZW based compression (WIP) + +## License +This code is under the [MIT License](https://github.com/CodePurble/libezw/blob/develop/LICENSE) diff --git a/docs/img/Jpeg2000_2-level_wavelet_transform-lichtenstein.png b/docs/img/Jpeg2000_2-level_wavelet_transform-lichtenstein.png new file mode 100644 index 0000000..53cd0df Binary files /dev/null and b/docs/img/Jpeg2000_2-level_wavelet_transform-lichtenstein.png differ diff --git a/docs/img/Lichtenstein_img_processing_test.png b/docs/img/Lichtenstein_img_processing_test.png new file mode 100644 index 0000000..e800ee7 Binary files /dev/null and b/docs/img/Lichtenstein_img_processing_test.png differ diff --git a/docs/img/Lichtenstein_img_processing_test_bw.png b/docs/img/Lichtenstein_img_processing_test_bw.png new file mode 100644 index 0000000..0ab9cc1 Binary files /dev/null and b/docs/img/Lichtenstein_img_processing_test_bw.png differ diff --git a/docs/img/New_NIE_Logo.png b/docs/img/New_NIE_Logo.png new file mode 100644 index 0000000..96ae4b1 Binary files /dev/null and b/docs/img/New_NIE_Logo.png differ diff --git a/docs/img/New_NIE_crest.png b/docs/img/New_NIE_crest.png new file mode 100644 index 0000000..299a2da Binary files /dev/null and b/docs/img/New_NIE_crest.png differ diff --git a/docs/img/block-diag.pdf b/docs/img/block-diag.pdf new file mode 100644 index 0000000..7dbe0bc Binary files /dev/null and b/docs/img/block-diag.pdf differ diff --git a/docs/img/block-diag.pdf_tex b/docs/img/block-diag.pdf_tex new file mode 100644 index 0000000..f5d6a98 --- /dev/null +++ b/docs/img/block-diag.pdf_tex @@ -0,0 +1,68 @@ +%% Creator: Inkscape 1.0.2 (e86c870879, 2021-01-15, custom), www.inkscape.org +%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 +%% Accompanies image file 'block-diag.pdf' (pdf, eps, ps) +%% +%% To include the image in your LaTeX document, write +%% \input{.pdf_tex} +%% instead of +%% \includegraphics{.pdf} +%% To scale the image, write +%% \def\svgwidth{} +%% \input{.pdf_tex} +%% instead of +%% \includegraphics[width=]{.pdf} +%% +%% Images with a different path to the parent latex file can +%% be accessed with the `import' package (which may need to be +%% installed) using +%% \usepackage{import} +%% in the preamble, and then including the image with +%% \import{}{.pdf_tex} +%% Alternatively, one can specify +%% \graphicspath{{/}} +%% +%% For more information, please see info/svg-inkscape on CTAN: +%% http://tug.ctan.org/tex-archive/info/svg-inkscape +%% +\begingroup% + \makeatletter% + \providecommand\color[2][]{% + \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% + \renewcommand\color[2][]{}% + }% + \providecommand\transparent[1]{% + \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% + \renewcommand\transparent[1]{}% + }% + \providecommand\rotatebox[2]{#2}% + \newcommand*\fsize{\dimexpr\f@size pt\relax}% + \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% + \ifx\svgwidth\undefined% + \setlength{\unitlength}{812.24998887bp}% + \ifx\svgscale\undefined% + \relax% + \else% + \setlength{\unitlength}{\unitlength * \real{\svgscale}}% + \fi% + \else% + \setlength{\unitlength}{\svgwidth}% + \fi% + \global\let\svgwidth\undefined% + \global\let\svgscale\undefined% + \makeatother% + \begin{picture}(1,0.31486612)% + \lineheight{1}% + \setlength\tabcolsep{0pt}% + \put(0,0){\includegraphics[width=\unitlength,page=1]{block-diag.pdf}}% + \put(0.78433979,0.19471835){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}Entropy\\Encoder\end{tabular}}}}% + \put(0,0){\includegraphics[width=\unitlength,page=2]{block-diag.pdf}}% + \put(0.21313016,0.17157899){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}Transformer\end{tabular}}}}% + \put(0,0){\includegraphics[width=\unitlength,page=3]{block-diag.pdf}}% + \put(0.48982453,0.17207761){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}Quantizer\end{tabular}}}}% + \put(0,0){\includegraphics[width=\unitlength,page=4]{block-diag.pdf}}% + \put(0.01307853,0.28974701){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}s(n1, n2)\end{tabular}}}}% + \put(0,0){\includegraphics[width=\unitlength,page=5]{block-diag.pdf}}% + \put(0.89707124,0.01156786){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}Bitstream\end{tabular}}}}% + 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+ diff --git a/docs/img/mapping.sddoc b/docs/img/mapping.sddoc new file mode 100644 index 0000000..b7aa323 Binary files /dev/null and b/docs/img/mapping.sddoc differ diff --git a/docs/img/packet.pdf b/docs/img/packet.pdf new file mode 100644 index 0000000..5b14c60 Binary files /dev/null and b/docs/img/packet.pdf differ diff --git a/docs/img/packet.svg b/docs/img/packet.svg new file mode 100644 index 0000000..04a76ea --- /dev/null +++ b/docs/img/packet.svg @@ -0,0 +1,154 @@ + + + + + + + + + + + + + + + + Threshold(t)(2 bytes) + Num of bytes(n)(4 bytes) + Symbols (packed into bytes)(n bytes) + + diff --git a/docs/img/sbtree.pdf b/docs/img/sbtree.pdf new file mode 100644 index 0000000..1616d63 Binary files /dev/null and b/docs/img/sbtree.pdf differ diff --git a/docs/img/sbtree.svg b/docs/img/sbtree.svg new file mode 100644 index 0000000..9635744 --- /dev/null +++ b/docs/img/sbtree.svg @@ -0,0 +1,289 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ROOT + LL + HL + HH + LH + + + diff --git a/docs/img/smap.pdf b/docs/img/smap.pdf new file mode 100644 index 0000000..647663b Binary files /dev/null and b/docs/img/smap.pdf differ diff --git a/docs/img/smap.svg b/docs/img/smap.svg new file mode 100644 index 0000000..2254914 --- /dev/null +++ b/docs/img/smap.svg @@ -0,0 +1,267 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/docs/img/subband1.pdf b/docs/img/subband1.pdf new file mode 100644 index 0000000..faa2f3a Binary files /dev/null and b/docs/img/subband1.pdf differ diff --git a/docs/img/subband2.pdf b/docs/img/subband2.pdf new file mode 100644 index 0000000..79ffe91 Binary files /dev/null and b/docs/img/subband2.pdf differ diff --git a/docs/img/subband2.svg b/docs/img/subband2.svg new file mode 100644 index 0000000..0745f7f --- /dev/null +++ b/docs/img/subband2.svg @@ -0,0 +1,192 @@ + +image/svg+xmlLLHLLHHHLLHLLHHHHLLHHH diff --git a/docs/img/wt1.pdf b/docs/img/wt1.pdf new file mode 100644 index 0000000..9b35908 Binary files /dev/null and b/docs/img/wt1.pdf differ diff --git a/docs/img/wt1.svg b/docs/img/wt1.svg new file mode 100644 index 0000000..3200c51 --- /dev/null +++ b/docs/img/wt1.svg @@ -0,0 +1,378 @@ + +image/svg+xml1.2.1ThetransformerThetransformerperformsamathematicaltransformonthesuppliedimage.Thetransformmustsatisfy2keyproperties,namely:•Fullinvertibility•SeparabilityAfewtransformsthatsatisfytheseconditionsaretheFouriertransform,thediscretecosinetransformandthewavelettransform.Wavelettransformisusedinthiscase,sinceitprovidesallthetoolsforperformingmulti-resolutionanalysis.WaveletsToovercometheshortcomingsoftraditionaltransformssuchastheDiscreteFourierTransform(DFT),DiscreteCosineTransform(DFT),ShortTimeFourierFourierTransform(STFT),andGa-borTransform,theneedforwaveletsarised.Thefourieranalysisprovideskeyinformationinthefrequencydomainwhilefailstoprovideanyinformationregardingthetimedomain.TheSTFTandtheGaborTransform(STFTwithGaussianwindowfunction)provideconcurrentinformationaboutbothtimeandfrequency,butthewindowsizeisimmutable.Essentially,itisnotpossibletoinfertheexactfrequencyandtheexacttimeofoccurenceofthatfrequencyinthesignal.Thereasonthatwaveletsarepreferredforimageanalysisisduetothefactthatitprovidesahierarchicalgradingofthetimeandfrequencyinformation.Thefactthatlowfrequencyinformationexistsforalongerperiodoftimeandthehighfrequencyinformationchangesrapidlywithtimeisexploitedinwaveletanalysis.Inthecaseofimageanalysis,timeisequivalenttospacialarea.Thephraselowfrequencycomponentsexistinlargerspacialareaindicatesthatthepixelvaluesinthatregiondonotchangesignifcantly.Similarly,highfrequencycomponentsreferstothefnerdetailswhichchangerapidlyinspace.Highertemporalaccuracyisrequiredtoobservethehighfrequencycomponentsandvice-versa.TimeFrequencyFigure1.2:MultiresolutionAnalysisPerformingwaveletanalysisbyutilizingascalableandmodulatedwindowtocalculatethespec-trumrepeatedlyprovidesthenecessarycollectionoftime-frequencyrepresentationsofthesignal.Inthiscontext,decreasingthescaleisequivalenttofocusingonhigherdetail.Scalingreferstoincreas-ingordecreasingthesizeofaportionofthesignalbyafactorandtranslationreferstoshiftingasignaltowardstherightortheleft.Thebasisfunctionwhichscalesandtranslatestoanalyzeothersignalsandgeneratewaveletsiscalledasthemotherwavelet.2 diff --git a/docs/pres/A14_pres.tex b/docs/pres/A14_pres.tex new file mode 100644 index 0000000..af9680e --- /dev/null +++ b/docs/pres/A14_pres.tex @@ -0,0 +1,365 @@ +\documentclass{beamer} +\usetheme{Antibes} +\usecolortheme{beaver} +% \setbeamertemplate{note page}[plain] +% \setbeameroption{show notes on second screen} +\usepackage{fontspec} % Set font families +\setmonofont{UbuntuMono Nerd Font Mono} +\graphicspath{{../img}} % Path to images +\usepackage{graphicx} +\usepackage{xcolor} % Colours +\usepackage{caption} % caption floats +\usepackage{tabularx} +\usepackage{float} +\usepackage[newfloat,outputdir=build]{minted} % source code blocks +\definecolor{codebg}{rgb}{0.9, 0.9, 0.9} +\usepackage{algorithm} +\usepackage{algpseudocode} +\usepackage{mathtools} +\usepackage{amsfonts} + +% \newenvironment{code}{\captionsetup{type=listing}}{} +% \SetupFloatingEnvironment{listing}{name=Listing} +% \newcommand\Smallfont{\fontsize{10}{7.2}\selectfont} + +\usepackage[backend=biber]{biblatex} +\addbibresource{/home/ramprakash/Documents/notes/bib/datacompr.bib} +\addbibresource{/home/ramprakash/Documents/notes/bib/wavelets.bib} + +\usepackage{csquotes} + +\logo{\includegraphics[height=0.6cm]{New_NIE_Logo.png}} + +\title{A Study \& Implementation of the Embedded Zerotree Wavelet Algorithm} +\author{ + C. Ramprakash (4NI18EC019) \\ Skanda Prasad (4NI18EC085) +} +\institute[NIE]{ + Under the guidance of Dr. Raghu J. Mandya \& Dr. Narasimha Kaulgud \\ + Department of ECE + \\ + The National Institute of Engineering, Mysuru +} +\date{August 2021} + +\begin{document} + +\maketitle + +\begin{frame}{Outline} + \tableofcontents +\end{frame} + + +\section{Background} +\begin{frame}{Data compression} + \begin{figure}[H] + \includegraphics[scale=0.4]{block-diag_shrunk.pdf} + \caption{Transform coder: Generalised \cite{shap1993}} + \end{figure} +\end{frame} + +\begin{frame}{Data compression} + A few notable transforms include: + \begin{itemize} + \item Discrete Fourier Transform (DFT) + \item Discrete Cosine Transform (DCT) + \item Discrete Wavelet Transform (DWT) + \end{itemize} +\end{frame} + +\begin{frame}{Why choose the DWT over others?} + \begin{itemize} + \item The ability to truncate (stop) the encoding of bits, without + significant loss of information + \item DWT is more resilient to artefact formation (e.g. box artefacts) + \end{itemize} +\end{frame} + +\begin{frame}{The embedded zerotree wavelet algorithm} + The algorithm is anchored on these key concepts: \cite{shap1993, sayood_datac} + \vspace{0.5cm} + + \begin{enumerate} + \item Decompose image into hierarchical sub-bands (using DWT) + \item Exploit the fact that a single coefficient in a smaller sub-band + may represent the same spatial location as multiple coefficients in + \textit{other sub-bands} + \item Successive-approximation quantization + \item Compression using an entropy coding technique that is lossless + such as adaptive arithmetic coding + \end{enumerate} +\end{frame} + +\begin{frame}{Limitations} + \begin{itemize} + \item Assumes that only a particular sub-band (\textit{LL}) is split iteratively + \item Incapable of exploiting spatial redundancies present in + coefficients \textit{within the same sub-band} + \end{itemize} +\end{frame} + +\section{Problem statement} +\begin{frame}{Problem statement} + To implement the \textit{Embedded Zerotree Wavelet} algorithm for image + compression as a C library, and study its performance under various + circumstances. +\end{frame} + +\section{Implementation} +\begin{frame}{Design Constraints} + \begin{itemize} + \item The images are assumed to be square in shape + \item The dimensions of the image are assumed to be exact powers of two + \item The images are in greyscale + \item The entropy encoder has been left out of our implementation for simplicity + \end{itemize} +\end{frame} +\begin{frame}{Software implementation: Wavelet transform} + \begin{itemize} + \item External library for computing DWT \cite{rpwavelib} + \item We have developed a quad-tree data-structure for ease of access + of coefficients at a particular level and sub-band. + \item We have also developed a hierarchical tree structure that + represents the significance-map. + \end{itemize} +\end{frame} + +\begin{frame}[fragile]{Software implementation: Sub-band tree} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{minted}[bgcolor=codebg, fontsize=\scriptsize]{c} +enum sb_type { + LL, + HL, + LH, + HH, + ROOT +}; +typedef struct SBtree_node { + struct SBtree_node *ll; + struct SBtree_node *hl; + struct SBtree_node *lh; + struct SBtree_node *hh; + double *coeffs; + enum sb_type type; +} SBtree_node; + \end{minted} + \end{column} + \begin{column}{0.5\textwidth} + \begin{figure}[H] + \centering + \includegraphics[scale=0.35]{sbtree.pdf} + \caption{Hierarchical sub-band tree} + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}[fragile]{Software implementation: Significance-map tree} + \begin{columns} + \begin{column}{0.6\textwidth} + \begin{minted}[bgcolor=codebg, fontsize=\scriptsize]{c} +enum smap_symbol { // significance map value + SP = 0, // Significant Positive + SN = 1, // Significant Negative + IZ = 2, // Isolated Zero + ZR = 3, // Zerotree Root + U = -1 // Unitialized +}; +typedef struct Smap_tree_node { + double coeff; + struct Smap_tree_node *parent; + struct Smap_tree_node *children[4]; + char isroot : 1; + enum smap_symbol type; + unsigned char not_available; +} Smap_tree_node; + \end{minted} + \end{column} + \begin{column}{0.4\textwidth} + \begin{figure}[H] + \centering + \includegraphics[scale=0.25]{smap.pdf} + \caption{Significance-map tree} + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{The dominant pass} + \begin{columns} + \begin{column}{0.8\textwidth} + \begin{algorithm}[H] + \caption{Dominant pass} + \label{alg:dompass} + \scriptsize + \begin{algorithmic} + \Require $smap\_tree\_root$ \Comment{Root of a significance map tree} + \Require $threshold \in \mathbb{Z}^+$ + \State $node \gets \text{NULL}$ + % \State $threshold \gets 2^{\lfloor\log_2{MAX(coefficients)}\rfloor}$\\ + \ForAll{$node \in \text{level order of } smap\_tree\_root$} + \State $check\_descendants(node, threshold)$ + \If{node is SP or SN or IZ} + \State $dominant\_list \gets (dominant\_list, current\_node)$ + \ElsIf{node is ZR} + \If{parent of node is not ZR or node is the root} + \State $dominant\_list \gets (dominant\_list, current\_node)$ + \EndIf + \EndIf + \EndFor + \end{algorithmic} + \end{algorithm} + \end{column} + \begin{column}{0.2\textwidth} + \begin{table}[H] + \centering + \scriptsize + \begin{tabular}{|c|c|} + \hline + \textbf{Symbol} & \textbf{Binary}\\ + \hline + SP & $00$\\ + SN & $01$\\ + IZ & $10$\\ + ZR & $11$\\ + \hline + \end{tabular} + \end{table} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{The subordinate pass} + \begin{columns} + \begin{column}{0.7\textwidth} + \begin{algorithm}[H] + \caption{EZW} + \label{alg:subpass} + \scriptsize + \begin{algorithmic} + \Require $dominant\_list$ + \Require $threshold \in \mathbb{Z}^+$ + \State $subordinate\_list \gets \text{NULL}$ + \State $node \gets \text{NULL}$ + \ForAll{$node \in dominant\_list$} + \State coeff $\gets$ coefficient of node + \If{node is SP or SN} + \If{$\lvert \text{coeff} \rvert > 1.5 \cdot t$} + \State Append a $1$ to $subordinate\_list$ + \Else + \State Append a $0$ to $subordinate\_list$ + \EndIf + \Else + \State Append a $0$ to $subordinate\_list$ + \EndIf + \EndFor + \end{algorithmic} + \end{algorithm} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{The compression algorithm} + \begin{columns} + \begin{column}{0.9\textwidth} + \begin{algorithm}[H] + \caption{EZW Compression} + \label{alg:ezwcomp} + \scriptsize + \begin{algorithmic} + \Require $smap\_tree\_root$ \Comment{Root of a significance map tree} + \Require $min\_threshold \ge 0$ + \State $node \gets \text{NULL}$ + \State $threshold \gets 2^{\lfloor\log_2{MAX(\text{coefficients of } smap\_tree\_root)}\rfloor}$ + \While{$threshold > min\_threshold$} + \State $dominant\_list \gets$ dominant\_pass(smap\_tree\_root, threshold) + \State $subordinate\_list \gets subordinate\_pass(dominant\_list, threshold)$ + \State Write data to file + \State $threshold \gets threshold/2$ + \EndWhile + \end{algorithmic} + \end{algorithm} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{The decompression algorithm} + \begin{columns} + \begin{column}{\textwidth} + \begin{algorithm}[H] + \caption{EZW Decompression} + \label{alg:ezwdecomp} + \scriptsize + \begin{algorithmic} + \Require $compressed\_file$ + \State $dominant\_list \gets \text{NULL}$ + \State $subordinate\_list \gets \text{NULL}$ + \ForAll{$dominant\_list, subordinate\_list$} + \State Approximate coefficients in $dominant\_list$ + \State Refine respective coefficients using $subordinate\_list$ + \State Write data to file + \EndFor + \end{algorithmic} + \end{algorithm} + \end{column} + \end{columns} +\end{frame} + +\section{Conclusion} +\subsection{Results} +\begin{frame} + \begin{table}[H] + \scriptsize + \begin{tabular}{|c|c|c|c|} + \hline + \textbf{Image} & \textbf{Original size (bytes)} & \textbf{Size after + compression (bytes)} & \textbf{Iterations}\\ + \hline + eggs8 & 64 & 46 & 4\\ + eggs8 & 64 & 70 & 5\\ + eggs8 & 64 & 216 & Max\\ + \hline + eggs16 & 256 & 153 & 6\\ + eggs16 & 256 & 257 & 7\\ + eggs16 & 256 & 621 & Max\\ + \hline + lichten & 262144 & 198751 & 14\\ + lichten & 262144 & 269263 & 15\\ + lichten & 262144 & 352671 & Max\\ + \hline + \end{tabular} +\end{table} + +\begin{block}{Note} + The maximum number of iterations for a given image is given by: + $$Max = \log_2{T_0}$$ +\end{block} +\end{frame} + +\subsection{Future work} +\begin{frame} + \begin{itemize} + \item Write the de-compressor + \item Include entropy encoder + \item A multi-core implementation of the algorithm + \item An FPGA-based hardware accelerator for the algorithm + \end{itemize} +\end{frame} + +\section{References} +\begin{frame} + \printbibliography +\end{frame} + +\section{End} +\begin{frame} + \centering + \huge{Thank You} + \par + \huge{Questions?} +\end{frame} + +\end{document} + diff --git a/docs/pres/notes.tex b/docs/pres/notes.tex new file mode 100644 index 0000000..d704393 --- /dev/null +++ b/docs/pres/notes.tex @@ -0,0 +1,129 @@ +\documentclass{beamer} +\usetheme{Antibes} +\usecolortheme{beaver} +\setbeameroption{show only notes} +\usepackage{graphicx} + +\usepackage[backend=biber]{biblatex} +\addbibresource{../../refs.bib} + +\usepackage{csquotes} + +\logo{\includegraphics[height=0.6cm]{../img/New_NIE_Logo.png}} + +\title{A Study \& Implementation of the Embedded Zerotree Wavelet Algorithm} +\author{ + C. Ramprakash (4NI18EC019) \\ Skanda Prasad (4NI18EC085) +} +\institute[NIE]{ + Under the guidance of Dr. Raghu J. Mandya \& Dr. Narasimha Kaulgud \\ + Department of ECE + \\ + The National Institute of Engineering, Mysuru +} +\date{May 2021} + +\begin{document} + +\maketitle + +\begin{frame}{Outline} + \tableofcontents +\end{frame} + + +\section{Background} +\begin{frame}{Data compression} + Any information is associated with a quantity called \textit{entropy} \cite{shan48}, given by: + \[H = -\sum\nolimits P_i \cdot \log_{b} P_i\] + + + \pause + + Compression schemes: + \begin{itemize} + \item Lossy + \item Lossless + \end{itemize} +\end{frame} + + +\note{bruh} +\begin{frame}{Data compression} + \begin{figure}[H] + \includegraphics[scale=0.2]{../img/block-diag.pdf} + \caption{Transform coder: Generalised \cite{shap93}} + \end{figure} + + \pause + + \[Quantizer \neq Quantizer\] +\end{frame} + +\begin{frame}{Data compression} + A few notable transforms include: + \begin{itemize} + \item Discrete Fourier Transform (DFT) + \item Discrete Cosine Transform (DCT) + \item Discrete Wavelet Transform (DWT) + \end{itemize} +\end{frame} + +\begin{frame}{Why choose the DWT over others?} + \begin{itemize} + \item The ability to truncate (stop) the encoding of bits, without + significant loss of information + \item DWT is more resilient to artefact formation (e.g. box artefacts) + \item Deals with multi-resolution processing with ease + \end{itemize} +\end{frame} + +\begin{frame}{The embedded zerotree wavelet algorithm} + An excerpt from the abstract of Shapiro's paper \cite{shap93} + \vspace{0.5cm} + + \begin{displayquote} + The EZW algorithm is based on four key concepts: + \begin{enumerate} + \item A discrete wavelet transform or hierarchical sub-band decomposition + \item Prediction of the absence of significant information across scales by exploiting the self-similarity inherent in images + \item Entropy-coded successive-approximation quantization + \item Universal lossless data compression which is achieved via adaptive arithmetic coding + \end{enumerate} + \end{displayquote} +\end{frame} + +\section{Problem statement} +\begin{frame}{Problem statement} + To implement the \textit{Embedded Zerotree Wavelet} algorithm for image + compression as a C library, and study its performance under various + circumstances. +\end{frame} + +\section{Implementation approach} +\begin{frame}{Software implementation} + \begin{itemize} + \item External library for computing DWT \cite{wavelib} + \item We implement the EZW algorithm on the transformed output + \end{itemize} +\end{frame} + +\section{Conclusion} +\subsection{Proposed outcomes} +\begin{frame} + A fully operative EZW coder, with data to support claims made earlier. +\end{frame} + +\subsection{Future work} +\begin{frame} + \begin{itemize} + \item A multi-core implementation of the algorithm + \item An FPGA-based hardware accelerator for the algorithm + \end{itemize} +\end{frame} + +\section{References} +\printbibliography + +\end{document} + diff --git a/docs/report/A14_Report.tex b/docs/report/A14_Report.tex new file mode 100644 index 0000000..a9aa143 --- /dev/null +++ b/docs/report/A14_Report.tex @@ -0,0 +1,116 @@ +\documentclass[a4paper,12pt]{report} + +\usepackage{fontspec} % Set font families +%\setmainfont{} +%\setsansfont{} +\setmonofont{UbuntuMono Nerd Font Mono} + +\usepackage[backend=biber]{biblatex} +\addbibresource{/home/ramprakash/Documents/notes/bib/datacompr.bib} +\addbibresource{/home/ramprakash/Documents/notes/bib/wavelets.bib} + +\usepackage{geometry} +\geometry{margin=1.5cm} + +\usepackage{tocloft} % toc, lof, lot, lol on same page by default +\usepackage{siunitx} % units +\usepackage{graphicx} % Images +\graphicspath{{../img}} % Path to images +\usepackage{xcolor} % Colours +\usepackage{caption} % caption floats +\usepackage{subcaption} +\usepackage{tabularx} +\usepackage{placeins} +\usepackage{float} +\usepackage[newfloat,outputdir=build]{minted} % source code blocks +\definecolor{codebg}{rgb}{0.9, 0.9, 0.9} +\usepackage{algorithm} +\usepackage{algpseudocode} +\usepackage{mathtools} +\usepackage{amsfonts} + +\usepackage{hyperref} % link crossrefs and toc +\hypersetup{ + colorlinks=true, + linkcolor=cyan, + filecolor=magenta, + urlcolor=cyan, + citecolor=black +} +\usepackage{subfiles} + +\newenvironment{code}{\captionsetup{type=listing}}{} +\SetupFloatingEnvironment{listing}{name=Listing} +\newcommand\Smallfont{\fontsize{10}{7.2}\selectfont} + +\begin{document} +\begin{titlepage} + \newgeometry{margin=2cm} + \begin{center} + \noindent + \makebox[0pt][l]{ + \begin{tabular}{@{}c@{}} + \includegraphics[scale=0.45]{New_NIE_crest.png} + \end{tabular} + }\hfill + \begin{tabular}{@{}c@{}} + \textbf{\Large The National Institute of Engineering} \\ + \textbf{\Large{Mysuru}} + \end{tabular} + \hfill + \makebox[0pt][r]{ + \begin{tabular}{@{}c@{}} + \includegraphics[scale=0.37]{ecelogo.png} + \end{tabular} + } \\ + \vspace{3.5cm} + {\huge Department of Electronics and Communication Engineering} \\ + \vspace{2cm} + \large{Mini Project Report} \\ + \large{EC6C06} \\ + \large{6\textsuperscript{th} Semester} \\ + \large{2020-21} \\ + \vspace{1cm} + \textbf{\huge A Study \& Implementation of the Embedded Zerotree + Wavelet Algorithm} \\ + \vspace{1cm} + \textbf{\underline{\large Submitted by:}} \\ + \vspace{0.5cm} + \begin{tabular}[H]{l l} + C. Ramprakash & 4NI18EC019 \\ + Skanda Prasad & 4NI18EC085 \\ + \end{tabular} + \\ + \vspace{1cm} + \textbf{\underline{\large Under the guidance of:}} \\ + \vspace{0.5cm} + \textbf{\large Dr. Narasimha Kaulgud} \\ + Professor and Head, Dept. of ECE \\ + \textbf{\large Dr. Raghu J. Mandya} \\ + Assistant Professor, Dept. of ECE \\ + \end{center} +\end{titlepage} +\clearpage +\restoregeometry + +\pagenumbering{roman} +\subfile{ack.tex} +\newpage +\tableofcontents +\newpage + +\listoffigures +\listoftables +\listoflistings +\newpage + +\pagenumbering{arabic} + +\subfile{introduction.tex} +\subfile{litsurvey.tex} +\subfile{impl.tex} +\subfile{conclusion.tex} +\printbibliography + +\end{document} + diff --git a/docs/report/ack.tex b/docs/report/ack.tex new file mode 100644 index 0000000..25be059 --- /dev/null +++ b/docs/report/ack.tex @@ -0,0 +1,24 @@ +\documentclass[./A14_Report.tex]{subfiles} + +\begin{document} +\newgeometry{margin=3cm} +\begin{center} + \huge \textbf{ACKNOWLEDGEMENT} +\end{center} +\vspace{3cm} +We are grateful to our dear Professor and Head, Department of Electronics and +Communication Engineering, NIE Mysuru, \textbf{Dr. Narasimha Kaulgud} for his +support and encouragement as it was his idea that inspired this endeavour. +\par +We sincerely extend our thanks to our guide \textbf{Dr. Raghu J. Mandya}, +Assistant Professor, Department of Electronics and Communication Engineering, +NIE Mysuru for his valuable guidance, constant assistance, and support for the +betterment of this project. +\\ +\begin{flushright} + \textbf{C. Ramprakash}\\ + \textbf{Skanda Prasad} +\end{flushright} +\restoregeometry +\end{document} + diff --git a/docs/report/conclusion.tex b/docs/report/conclusion.tex new file mode 100644 index 0000000..61e0d19 --- /dev/null +++ b/docs/report/conclusion.tex @@ -0,0 +1,53 @@ +\documentclass[./A14_Report.tex]{subfiles} + +\begin{document} +\chapter{Conclusion} +\section{Results} +The following results were obtained on applying the compression algorithm on +images of various sizes. Note that $Max = \log_2{T_0}$. +\begin{table}[H] +\centering +\begin{tabular}{|c|c|c|c|} + \hline + \textbf{Image} & \textbf{Original size (bytes)} & \textbf{Size after + compression (bytes)} & \textbf{Iterations}\\ + \hline + eggs8 & 64 & 46 & 4\\ + eggs8 & 64 & 70 & 5\\ + eggs8 & 64 & 216 & Max\\ + \hline + eggs16 & 256 & 153 & 6\\ + eggs16 & 256 & 257 & 7\\ + eggs16 & 256 & 621 & Max\\ + \hline + lichten & 262144 & 198751 & 14\\ + lichten & 262144 & 269263 & 15\\ + lichten & 262144 & 352671 & Max\\ + \hline +\end{tabular} +\caption{Data collected} +\label{tab:data} +\end{table} + +A key observation that can be made is that the algorithm produces files with +lower sizes than the originals only up to a certain maximum, after which the +algorithm generates files \textit{larger} than the original files. This is due +to redundancy that results from a very low threshold. Barring this, the +algorithm shows promising results for compression with minimum loss of data. + +\section{Remarks} +Undertaking this project has enabled us to explore the extensive research +conducted in the field of \textit{image compression}. We established an +understanding of the \textit{Discrete Wavelet Transform} and it's +immediate application in the Embedded Zerotree Wavelet Algorithm. We also +discovered the various aspects such as encoding schemes and quantization +methods that govern the EZW algorithm output. + +\section{Future work} +\begin{itemize} + \item Write the de-compressor + \item Include entropy encoder + \item A multi-core implementation of the algorithm + \item An FPGA-based hardware accelerator for the algorithm +\end{itemize} +\end{document} diff --git a/docs/report/impl.tex b/docs/report/impl.tex new file mode 100644 index 0000000..6539ab1 --- /dev/null +++ b/docs/report/impl.tex @@ -0,0 +1,380 @@ +\documentclass[./A14_Report.tex]{subfiles} + +\begin{document} +\chapter{Implementation} + +\section{Design constraints} +The following constraints were considered during the implementation process to +simplify the design: +\begin{itemize} + \item The images are assumed to be square in shape + \item The dimensions of the image are assumed to be exact powers of two + \item The images are in greyscale + \item The entropy encoder has been left out of our implementation for simplicity +\end{itemize} + +\section{The ``Transformer'' block} + +An external C library for performing wavelet transforms is used. It is fully +open source. We have modified the library, to suit it to our needs +\cite{rpwavelib}. The interface is straightforward, providing access to each +sub-band for a particular level. A snippet of the access is given below. + +\begin{code} + \begin{minted}[bgcolor=codebg]{c} + // Assume ROWS and COLS to be the dimensions of the image + wave_object obj; + wt2_object wt; + double *inp, *wavecoeffs, *cLL; + int N = ROWS*COLS; + int ir, ic; + char *name = "db2"; + obj = wave_init(name); // Initialize the wavelet + inp = (double*) calloc(N, sizeof(double)); + int J = 1; // decomposition level + wt = wt2_init(obj, "dwt", ROWS, COLS, J); + // Assume pix_arr is a row-major array of 8-bit pixel values + for (int i = 0; i < ROWS; ++i) { + for (int k = 0; k < COLS; ++k) { + inp[i*COLS + k] = (double) pix_arr[i*COLS + k]; + } + } + wavecoeffs = dwt2(wt, inp); + cLL = getWT2Coeffs(wt, wavecoeffs, 1, "A", &ir, &ic); + \end{minted} + \caption{\texttt{wavelib} LL sub-band extraction example \cite{libezw}} + \label{code:wavelibex} +\end{code} + +\pagebreak + +The sub-band coefficients are stored in a hierarchical tree-like structure for +easy access of coefficients. It is shown in the figure below. + +\begin{figure}[H] + \centering + \includegraphics{sbtree.pdf} + \caption{Sub-band tree \cite{libezw}} + \label{fig:sbtreediag} +\end{figure} + +The main root node is treated specially and does not contain any coefficients. +Every other node contains a row-major array of it's coefficients. It must also +be observed that only the \textit{LL} sub-bands have children. This is because +only the \textit{LL} sub-band is sub-divided further in our procedure. +\begin{code} +\begin{minted}[bgcolor=codebg]{c} +enum sb_type { + LL, + HL, + LH, + HH, + ROOT +}; +typedef struct SBtree_node { + struct SBtree_node *ll; + struct SBtree_node *hl; + struct SBtree_node *lh; + struct SBtree_node *hh; + double *coeffs; + enum sb_type type; +} SBtree_node; +\end{minted} +\caption{\texttt{C struct} representation of the tree shown in figure \ref{fig:sbtreediag} \cite{libezw}} + \label{code:sbtreedef} +\end{code} + +\section{The ``Quantizer'' block} +This block deals with the approximation and labelling of the coefficients as +one of four \textit{significance values}, to construct what is called a +\textit{significance map}. The significance map is also modelled as a tree +whose nodes contain the coefficients and all associated information. If we move +deeper into the tree, the level of decomposition \textbf{decreases}. Another +key point about the tree is that the first node (the \textit{LL} coefficient of +the highest level of decomposition) has only 3 children, while all others have +four. (see figure \ref{fig:subband2}) + +\begin{figure}[H] + \centering + \includegraphics{smap.pdf} + \caption{Significance map tree \cite{libezw}} + \label{fig:smaptreediag} +\end{figure} + +\begin{code} +\begin{minted}[bgcolor=codebg]{c} +enum smap_symbol { // significance map value + SP = 0, // Significant Positive + SN = 1, // Significant Negative + IZ = 2, // Isolated Zero + ZR = 3, // Zerotree Root + U = -1 // Unitialized +}; +typedef struct Smap_tree_node { + double coeff; + struct Smap_tree_node *parent; + struct Smap_tree_node *children[4]; + char isroot : 1; + enum smap_symbol type; + unsigned char not_available; +} Smap_tree_node; +\end{minted} +\caption{\texttt{C struct} representation of the tree shown in figure \ref{fig:smaptreediag} \cite{libezw}} + \label{code:sbtreedef} +\end{code} + +\subsection{The algorithms} +The algorithm used to assign the significance map values to the respective +coefficients are split into two steps or ``passes'', the \textit{dominant pass} +and the \textit{subordinate pass} that happen one after the other +\cite{shap1993}. Each set of passes depends on a threshold value, with which +coefficients are compared with to decide what value they are mapped to. +\par +\textbf{PTO} + +\begin{algorithm}[H] + \caption{Dominant pass} + \label{alg:dompass} + \begin{algorithmic} + \Require $smap\_tree\_root$ \Comment{Root of a significance map tree} + \Require $threshold \in \mathbb{Z}^+$ + \State $node \gets \text{NULL}$ + % \State $threshold \gets 2^{\lfloor\log_2{MAX(coefficients)}\rfloor}$\\ + \ForAll{$node \in \text{level order of } smap\_tree\_root$} + \State $check\_descendants(node, threshold)$ + \If{node is SP or SN or IZ} + \State $dominant\_list \gets (dominant\_list, current\_node)$ + \ElsIf{node is ZR} + \If{parent of node is not ZR or node is the root} + \State $dominant\_list \gets (dominant\_list, current\_node)$ + \EndIf + \EndIf + \EndFor + \end{algorithmic} +\end{algorithm} + +During the dominant pass, nodes in the tree (scanned breadth-first to get a +Morton scan) are compared with the current threshold, and assigned an +appropriate symbol. There are 4 possible symbols \cite{valezw1999}:\\ + +\begin{table}[H] + \centering + \begin{tabular}{|c|c|} + \hline + \textbf{Symbol} & \textbf{Binary Representation}\\ + \hline + Significant Positive (SP) & $00$\\ + Significant Negative (SN) & $01$\\ + Isolated Zero (IZ) & $10$\\ + Zerotree Root (ZR) & $11$\\ + \hline + \end{tabular} + \caption{Quantization symbols} + \label{tab:qsymbs} +\end{table} + +This assignment is handled by the \mintinline{c}{check_descendants()} routine +in algorithm \ref{alg:dompass}. Once that is done, the significant nodes are +put in a list and returned to be used in the subordinate pass. + +\begin{algorithm}[H] + \caption{Subordinate pass} + \label{alg:subpass} + \begin{algorithmic} + \Require $dominant\_list$ + \Require $threshold \in \mathbb{Z}^+$ + \State $subordinate\_list \gets \text{NULL}$ + \State $node \gets \text{NULL}$ + \ForAll{$node \in dominant\_list$} + \State coeff $\gets$ coefficient of node + \If{node is SP or SN} + \If{$\lvert \text{coeff} \rvert > 1.5 \cdot t$} + \State Append a $1$ to $subordinate\_list$ + \Else + \State Append a $0$ to $subordinate\_list$ + \EndIf + \Else + \State Append a $0$ to $subordinate\_list$ + \EndIf + \EndFor + \end{algorithmic} +\end{algorithm} + +In the subordinate pass, a refinement bit is added to help reconstruct the +coefficient when decoding. This also contributes to the quantization process, +along with the dominant pass. In this case, a $1$ is coded if the absolute +value of the coefficient of the node is greater than $1.5$ times the current +threshold, and a $0$ otherwise. These bits are filled in to a list and returned +for use later. + +\begin{algorithm}[H] + \caption{EZW Compression} + \label{alg:ezw} + \begin{algorithmic} + \Require $smap\_tree\_root$ \Comment{Root of a significance map tree} + \Require $min\_threshold \ge 0$ + \State $node \gets \text{NULL}$ + \State $threshold \gets 2^{\lfloor\log_2{MAX(\text{coefficients of } smap\_tree\_root)}\rfloor}$ + \While{$threshold > min\_threshold$} + \State $dominant\_list \gets$ dominant\_pass(smap\_tree\_root, threshold) + \State $subordinate\_list \gets subordinate\_pass(dominant\_list, threshold)$ + \State Write data to file + \State $threshold \gets threshold/2$ + \EndWhile + \end{algorithmic} +\end{algorithm} + +Finally, in the actual EZW algorithm, the initial threshold for a given set of +coefficients is calculated as the power of $2$ that is nearest to the largest +coefficient. Once this is done, the dominant and subordinate passes are called +in succession, while halving the threshold after each iteration. This increases +the amount of precision in the data every iteration. This is the successive +approximation quantization process, where the step-size of the quantizer is +decreased every iteration \cite{shap1993}. The information that is written to a +file must include the dominant and subordinate lists for each pass for correct +reconstruction. This information may be compressed even more using entropy +coding techniques. + +\begin{algorithm}[H] + \caption{EZW Decompression} + \label{alg:ezwdecomp} + \begin{algorithmic} + \Require $compressed\_file$ + \State $dominant\_list \gets \text{NULL}$ + \State $subordinate\_list \gets \text{NULL}$ + \ForAll{$dominant\_list, subordinate\_list$} + \State Approximate coefficients in $dominant\_list$ + \State Refine respective coefficients using $subordinate\_list$ + \State Write data to file + \EndFor + \end{algorithmic} +\end{algorithm} + +The decompression process is, by nature, the reverse of the compression +process. The steps involved in the approximation and refinement process are as +follows: +\begin{enumerate} + \item{Check the current symbol} + \item{If significant, assign it the value $1.5 \times T_i$} + \begin{enumerate} + \item{If the refinement bit is set, add $\frac{T_i}{4}$ to the + value set before, otherwise, subtract it.} + \item{If the symbol is labelled negative, multiply with $-1$} + \end{enumerate} + \item{Read next symbol} +\end{enumerate} + +The below code snippet shows how it is implemented. + +\begin{code} +\begin{minted}[bgcolor=codebg]{c} +switch(symbol) { + case SP: + { + if(lsb) { + curr_smap->coeff = (1.5*curr_threshold) + (curr_threshold/4.0); + } + else { + curr_smap->coeff = (1.5*curr_threshold) - (curr_threshold/4.0); + } + curr_smap->not_available = 1; + break; + } + case SN: + { + if(lsb) { + curr_smap->coeff = -((1.5*curr_threshold) + (curr_threshold/4.0)); + } + else { + curr_smap->coeff = -((1.5*curr_threshold) - (curr_threshold/4.0)); + } + curr_smap->not_available = 1; + break; + } + default: + { + curr_smap->coeff = 0.0; + break; + } +} +\end{minted} +\caption{Approximation of coefficients \cite{libezw}} + \label{code:sbtreedef} +\end{code} +\vspace{0.5cm} + +Consider the example shown in figure \ref{fig:exa} +\cite{sayood_datac}: + +\begin{figure}[H] + \begin{subfigure}[b]{0.5\textwidth} + \centering + \includegraphics[width=0.5\textwidth]{example1.pdf} + \caption{Original} + \label{fig:exa} + \end{subfigure} + \hfill + \begin{subfigure}[b]{0.5\textwidth} + \centering + \includegraphics[width=0.5\textwidth]{example2.pdf} + \caption{Reconstruction for first set of passes} + \label{fig:exb} + \end{subfigure} + \caption{Example decomposition} + \label{fig:ex} +\end{figure} + +\begin{displaymath} + T_0 = 2^{\lfloor\log_2{26}\rfloor} = 16 +\end{displaymath} +\begin{displaymath} + D = \{SP, ZR, ZR, ZR\}\\ +\end{displaymath} +\begin{displaymath} + S = \{1\}\\ +\end{displaymath} + +After the first round of reconstruction, we will get the decomposition shown in +figure \ref{fig:exb}. The value $28$ is found as follows: +\begin{displaymath} + T_0 = 16 +\end{displaymath} +\begin{displaymath} + Approx = 1.5 \times T_0 = 24 +\end{displaymath} +\begin{displaymath} + Refined = 24 + \frac{T_0}{4} = 28 +\end{displaymath} +This process is repeated until a limit (can be decided by user), as shown in +algorithm \ref{alg:ezw} to increase the accuracy of the reconstruction. + +\section{File format} +The output file consists of the symbols extracted during the dominant pass, +along with the refinement bits. The threshold value of each iteration and the +dimensions of the image are also part of the file. The binary file consists of +a \textit{main-header} and several \textit{mini-headers}, followed by the data. +The symbols are packed 2 at a time into bytes to save space. Entropy encoding +could have helped save even more space at this stage. The first byte of the +file is the power of $2$ that represents the dimensions of the image. So, if we +have a $d \times d$ image, the first byte will have the value $\log_2{d}$. The +packet format is specified in figure \ref{fig:packet}. There will be one packet +for every iteration of the algorithm. Assume there are $k$ symbols to be +written for the current iteration. Then- +\begin{displaymath} + t = \log_2{T_i} +\end{displaymath} +\begin{displaymath} + n = \frac{k}{2} + (k \bmod 2) +\end{displaymath} + +\begin{figure}[H] + \centering + \includegraphics{packet.pdf} + \caption{Packet format} + \label{fig:packet} +\end{figure} + +When reading the file, the information can be extracted by using bit-masks and +clever bitwise operations. + +\end{document} diff --git a/docs/report/introduction.tex b/docs/report/introduction.tex new file mode 100644 index 0000000..cdb453f --- /dev/null +++ b/docs/report/introduction.tex @@ -0,0 +1,210 @@ +\documentclass[./A14_Report.tex]{subfiles} + +\begin{document} +\chapter{Introduction} +\section{Overview} +\label{sec:overview} + +The project aims to implement the \textbf{Embedded Zerotree Wavelet} algorithm +as a C library. It employs the well known \textit{Discrete Wavelet Transform} +as a tool for compression. The algorithm will be studied under several +operating conditions and demands, such as varying levels of +compression,``bit-budget'', etc. + +\subsubsection{The Basics}% +\label{sec:the_basics} + +\textit{Data compression} is the science of representing any given information +in a compact form. A \textit{compression algorithm} by itself, refers to two +separate algorithms. \textit{A compression algorithm} (takes $\alpha$ and +generates $\alpha_c$) and a \textit{reconstruction algorithm} (takes $\alpha_c$ +and generates $\alpha$ or an approximation of $\alpha$), where $\alpha$ is a +symbol. The compression technique is said to be \textit{lossless} if the +reconstructed symbols are identical to the original symbols and it is said to +be \textit{lossy} if the reconstructed symbols are not identical to the +original symbols. + +\section{The transform coder} +\label{sec:the_transform_coder} + +\begin{figure}[h] + \centering + \includegraphics[scale=0.5]{block-diag_shrunk.pdf} + \caption{Transform coder: Generalised \cite{shap1993}} + \label{fig:tcoder} +\end{figure} + +A step-wise approach towards implementing this algorithm is taken, where each +step is represented by a block in figure \ref{fig:tcoder}. + +\pagebreak + +\subsection{The transformer} +\label{sec:the_transformer} + +The transformer performs a mathematical transform on the supplied image. The +transform must satisfy 2 key properties, namely: +\begin{itemize} + \item Full invertibility + \item Separability +\end{itemize} + +A few transforms that satisfy these conditions are the Fourier transform, the +discrete cosine transform and the wavelet transform. The wavelet transform is +used in this case, since it provides all the tools for performing +multi-resolution analysis. + +\subsubsection{Wavelets}% +\label{sec:theory_of_wavelets} + +To overcome the shortcomings of traditional transforms such as the Discrete +Fourier Transform (DFT), Discrete Cosine Transform (DFT), Short Time Fourier +Fourier Transform (STFT), and Gabor Transform, the need for \textit{wavelets} +arised. Fourier analysis provides key information in the frequency domain but +fails to provide any information regarding the time domain. The STFT and the +Gabor Transform (STFT with Gaussian window function) provide concurrent +information about both time and frequency, but the window size is immutable. +Essentially, it is not possible to infer the exact frequency and the exact time +of occurrence of that frequency in the signal. + +\par + +The reason that wavelets are preferred for image analysis is due to the fact +that it provides a hierarchical grading of the time and frequency information. +The fact that low frequency information exists for a longer period of time and +the high frequency information changes rapidly with time is exploited in +wavelet analysis. In the case of image analysis, \textit{time} is equivalent to +\textit{spacial area}. The phrase \textit{low frequency components exist in +larger spacial area} indicates that the pixel values in that region do not +change significantly. Similarly, \textit{high frequency components} refers to +the finer details which change rapidly in space. Higher temporal accuracy is +required to observe the high frequency components and vice-versa. + +\FloatBarrier +\begin{figure}[htpb] + \centering + \includegraphics[scale=0.3, width=0.5\linewidth]{wt1.pdf} + \caption{Multiresolution Analysis}% + \label{fig:multiresolution} +\end{figure} +\FloatBarrier + +\par + +Performing wavelet analysis by utilizing a scalable and modulated window to +calculate the spectrum repeatedly provides the necessary collection of +time-frequency representations of the signal. In this context, decreasing the +scale is equivalent to focusing on higher detail. \textit{Scaling} refers to +increasing or decreasing the size of a portion of the signal by a factor and +\textit{translation} refers to shifting a signal towards the right or the left. +The basis function which scales and translates to analyse other signals and +generate wavelets is called as the \textit{mother wavelet}. + +\par + +There are numerous choices of wavelets that are available, for example, +\textit{Haar, Daubechies, Coiflet, Gaussian, etc.} for performing wavelet +analysis of images. + +\subsubsection{The Wavelet Transform}% +\label{sec:the_wavelet_transform} + +The \textit{Continuous Wavelet Transform} (CWT) is mathematically represented +by the equation given below. + +\[\gamma(s, \tau) = \int f(t)\cdot\psi^{*}_{s, \tau}(t)dt\] + +\(f(t)\) is the signal to be decomposed into a set of basis functions +\(\psi_{s,\tau}(t)\) called the \textit{wavelets}. The new variables \(s\) and +$\tau$ are the scale and translation respectively. The wavelets generated by +scaling and translating the mother wavelet can now be mathematically +represented as + +$$\psi_{s,\tau}(t)=\frac{1}{\sqrt{s}}\cdot\psi \left (\frac{t-\tau}{s} \right)$$ + +The mother wavelet is scaled and translated to realize more orthogonal +wavelets. The issue with the CWT is that it brings in redundancy, and it's +computation is time consuming. To address these issues, the \textit{Discrete +Wavelet Transform} was developed, which computes the transforms at various +discrete samples. + +Mathematically, + +$$\psi_{j,k}(t) = \frac{1}{\sqrt{s_{0}^j}} \cdot \psi \left (\frac{t - k \tau_{0}s_{0}^j}{s_{0}^j} \right )$$ + +The wavelet transform is computed by calculating the inner product of the +function with a wavelet (mother wavelet after scaling and translating). An +important aspect here is that the DWT is not discrete in time, but the scale +and translation parameters are incremented/decremented in steps +\cite{valwav1999}. Further, it can be proved that implementing the wavelet +transform as an iterative digital filter bank enables the sub-sampling property. +This means that the signal is decomposed using filter banks, downsampled, +quantized and encoded. + +\par + +Applying the DWT on the images is equivalent to dividing the image into four +different \textit{sub-bands}. That is to say that, the wavelet based coding +divides the image into hierarchical sub-bands critically sub-sampled. Each +sub-band contains the wavelet coefficients and these coefficients interestingly +represent a spacial area in the higher levels of sub-bands. + +\FloatBarrier +\begin{figure}[htpb] + \centering + \includegraphics[scale=0.25, width=0.4\linewidth]{subband1.pdf} + \caption{Image decomposition}% + \label{fig:subband1} +\end{figure} +\FloatBarrier + +\pagebreak + +These four sub-bands are created by applying the digital filters in both the +horizontal and vertical directions. +\begin{itemize} + \item LL Sub-band: Realized by low pass filtering the image in both + horizontal and vertical directions. + \item HL Sub-band: Realized by high pass filtering the image in horizontal + direction low pass filtering in vertical direction. + \item LH Sub-band: Realized by low pass filtering the image in horizontal + direction high pass filtering in vertical direction. + \item LL Sub-band: Realized by high pass filtering the image in both + horizontal and vertical directions. +\end{itemize} + +These sub-bands are successively quantized for further compression. It is +important to note that every sub-band consists one-fourth of the total samples +of a certain level of decomposition. This process of successively decomposing +the LL sub-band for image analysis is known as \textit{dyadic partitioning}. +Each of the sub-images obtained in this manner can be filtered and sub-sampled +until the desired sub-band structure is obtained. + +\FloatBarrier +\begin{figure}[htpb] + \centering + \includegraphics[scale=0.5, width=0.4\linewidth]{subband2.pdf} + \caption{Multilevel sub-band decomposition}% + \label{fig:subband2} +\end{figure} +\FloatBarrier + +It is to be noted that when images are decomposed in this manner, most of the +information or the energy is concentrated in the lower sub-band (mostly LL +sub-band), which confirms that low frequency components contain the maximum +information of that spacial area. Generally the LL sub-band is a low resolution +and inexpensive approximation of the original image, while the other sub-bands +contain the finer details (horizontal, vertical, and diagonal) that can be +added. + +\subsection{The quantizer} +\label{sec:the_quantizer} + +The wavelet transformed coefficients are to be quantized to produce the +\textit{bitstream}. All information loss happens during the quantization +stage. The coefficients are passed through a mid-tread quantizer to obtain the +initial reconstructed value of the coefficient, which is $\pm 1.5$ times the +initial threshold value. To achieve higher precision of reconstructed values, +refinement is done by encoding the quantized difference value of the +coefficient and it's reconstructed value and using it for final reconstruction. +\end{document} diff --git a/docs/report/litsurvey.tex b/docs/report/litsurvey.tex new file mode 100644 index 0000000..62cbe23 --- /dev/null +++ b/docs/report/litsurvey.tex @@ -0,0 +1,63 @@ +\documentclass[./A14_Report.tex]{subfiles} + +\begin{document} +\chapter{Literature Survey} + +\section{The Embedded Zerotree Wavelet Algorithm}% +\label{sec:the_embedded_zerotree_wavelet_algorithm} + +The EZW algorithm generates a transformed and compressed bit-stream (embedded +coding) which is just enough to distinguish the compressed image with a null +image \cite{shap1993}. It ensures that the "important" bits are embedded at the +beginning of bit-stream i.e. low-frequency sub-bands contain the bulk of the +information. The sole purpose of this technique is to provide a reasonable +amount of image information for recovery after compression, at lower magnitudes +of bit-budget. + +\par + +EZW accomplishes this task by applying the \textit{Discrete Wavelet Transform} +on the individual rows and column of the digital image and in turn, dividing +the samples into various frequency sub-bands (LL, HL, LH, HH) in a hierarchical +manner. The transform on the image outputs the decorrelated wavelet +coefficients (i.e. there exists no dependencies between the samples of image) +which is the input for the EZW algorithm. + +\par + +In an abstract view, the EZW algorithm (a multi-pass algorithm) takes the +transformed image coefficients and compares it with a threshold value. The +binary decision taken here, at every pass, entitles the coefficient as either +\textit{significant} or \textit{insignificant} which expectantly gives rise to +the \textit{nascent zero-tree}. The threshold value is readjusted at every pass +to improve the quality of the compressed image. The algorithm also makes use of +(lossy) entropy-encoded successive approximation quantization to eliminate the +psycho-visual redundancies present in the image and regularizes the pixels +present to an extent. Further lossless data compression is achieved by the +adaptive arithmetic coding (uses precision available within an interval of +numbers rather than multiple numbers themselves) at the encoder. + +\par + +The EZW algorithm has an upper hand over compression techniques like Discrete +Cosine Transform (employed in JPEG algorithm where no prioritization of +coefficients exists). It also has its limitations however, for example, it +presumes that only the LL sub-band is split iteratively and it is also +incapable of exploiting the redundancy present in the neighbourhood +coefficients. + +The \textit{Set Partitioning in Hierarchical Trees} (SPIHT) is a revised version +of the EZW algorithm. It is much more efficient due to the fact that it +exploits the inherent similarities across the sub-bands in a wavelet +decomposition of an image. \cite{sayood_datac} + +\par + +Also, the EZW allows truncation of bits in the case of bit-budget exhaustion +but at points close to the truncation, some information is lost. This problem +is addressed by the \textit{Embedded Block Coding with Optimized Truncation} of +the embedded bit-stream (EBCOT) which specifies certain points at which +truncation can be performed to avoid loss of information. The famous +\textit{JPEG-2000} uses the EBCOT in it's image compression algorithm. +\cite{sayood_datac} +\end{document} diff --git a/include/bitstream.h b/include/bitstream.h new file mode 100644 index 0000000..95e2193 --- /dev/null +++ b/include/bitstream.h @@ -0,0 +1,28 @@ +#ifndef BITSTREAM_H +#define BITSTREAM_H +#include +#include "queue.h" + +// 0b00111000 +#define SYMB_MASK 0x38 + +typedef struct { + unsigned short threshold_pow; + unsigned int num_bytes; + unsigned char *bytes; +} mini_header; + +enum file_op_mode { + A, // append + W // write +}; + +// OPTIMIZE: Maybe pass by reference? Soo many copies!! +// OPTIMIZE: Maybe pass by const reference when not mutating? + +mini_header *create_mini_header(unsigned int threshold, Queue *symbols); +void write_bitstream_file(const char* filename, enum file_op_mode mode, + mini_header *m_hdr, unsigned int dim); +Queue* read_bitstream_file(const char* filename, Queue *header_queue, unsigned char *dim_pow); + +#endif diff --git a/include/bitstream.h.old b/include/bitstream.h.old new file mode 100644 index 0000000..7738f16 --- /dev/null +++ b/include/bitstream.h.old @@ -0,0 +1,48 @@ +#ifndef BITSTREAM_H +#define BITSTREAM_H +#include "queue.h" + +// TODO: +// A bitstream is a main header followed by groups of "mini-headers" and +// symbols packed into bytes +// Operations that need to be implemented: +// * Initialise bitstream +// * Close bitstream +// * Pack symbols into bytes +// * Create header and mini-headers +// * Write next set of symbols +// * Read next set of symbols + +// WARNING: +// The __packed__ attribute will result in unsafe behaviour on non x86 +// systems. Use this code with care. +// ref: https://stackoverflow.com/a/8568441 +// +// Group 10 symbols together to save space +// +// Change of plans....... no more structs +// Just fall back to 2 symbols per byte, 2 MSBs are discarded +// I just want to finish this.... +struct __attribute__((__packed__)) symbols_group { + unsigned char s0 : 3; + unsigned char s1 : 3; + unsigned char s2 : 3; + unsigned char s3 : 3; + unsigned char s4 : 3; + unsigned char s5 : 3; + unsigned char s6 : 3; + unsigned char s7 : 3; + unsigned char s8 : 3; + unsigned char s9 : 3; +}; + +struct symbol_set { + unsigned short threshold; + unsigned int size; + struct symbols_group *symbols; +}; + +void symbol_set_init(struct symbol_set *s_set, unsigned short threshold, unsigned int size); +void symbol_group_insert(struct symbols_group *s_grp, int count, unsigned char symbol); + +#endif diff --git a/include/ezw.h b/include/ezw.h new file mode 100644 index 0000000..5414882 --- /dev/null +++ b/include/ezw.h @@ -0,0 +1,19 @@ +#ifndef EZW_H +#define EZW_H +#include "smap.h" + +// OPTIMIZE: Maybe pass by reference? Soo many copies!! +// OPTIMIZE: Maybe pass by const reference when not mutating? + +void check_descendants(Smap_tree_node *parent, int threshold); +enum smap_symbol encode_coeff(float coeff, int threshold); +Queue *dominant_pass(Smap_tree_node *smap_root, int threshold); +Queue *subordinate_pass(Queue *dominant_list, int threshold); +// void ezw(Smap_tree_node *smap_root, unsigned char iter); +void ezw(const char *filename, Smap_tree_node *smap_root, int rows, int cols, unsigned int iter); +Smap_tree_node* reconstruct(unsigned char dim_pow, Queue *header_q); + +// NOTE: when decoding, just do morton scan, but replace coeff with decoded +// NOTE: approximation only if the current node coeff is zero + +#endif // EZW_H diff --git a/include/node.h b/include/node.h new file mode 100644 index 0000000..5ac719b --- /dev/null +++ b/include/node.h @@ -0,0 +1,12 @@ +#ifndef NODE_H +#define NODE_H + +typedef struct Node { + void *data; + struct Node *next; +} Node; + +Node *create_node(void *data); +void free_node(Node *n); + +#endif // NODE_H diff --git a/include/queue.h b/include/queue.h new file mode 100644 index 0000000..01c018e --- /dev/null +++ b/include/queue.h @@ -0,0 +1,30 @@ +#ifndef QUEUE_H +#define QUEUE_H +#include "node.h" + +// head is first, head->next is next in queue +// tail->next will always be NULL +// head->a->b->...->tail->NULL + +typedef struct Queue { + Node *head; + Node *tail; + int len; +} Queue; + +enum q_type { + SMAP_TREE_NODE, + MINI_HDR, + INT, + DOUBLE +}; + +// OPTIMIZE: Maybe pass by reference? Soo many copies!! + +Queue *enqueue(Queue *q, void *data); +Node *dequeue(Queue *q); +void free_queue(Queue *q); +void queue_pretty_print(Queue *q, enum q_type t); + +#endif // QUEUE_H + diff --git a/include/sbtree.h b/include/sbtree.h new file mode 100644 index 0000000..4afe401 --- /dev/null +++ b/include/sbtree.h @@ -0,0 +1,36 @@ +#ifndef SBTREE_H +#define SBTREE_H + +enum sb_type { + LL, + HL, + LH, + HH, + ROOT +}; + +typedef struct SBtree_node { + struct SBtree_node *ll; + struct SBtree_node *hl; + struct SBtree_node *lh; + struct SBtree_node *hh; + double *coeffs; + enum sb_type type; +} SBtree_node; + +// OPTIMIZE: Maybe pass by reference? Soo many copies!! + +SBtree_node* sb_tree_init_root(); +SBtree_node* sb_tree_insert(SBtree_node *root, enum sb_type t, double *coeffs); +SBtree_node* sb_treeify(int levels, double *input, int rows, int cols); +double* sb_tree_get_coeff(SBtree_node *root, enum sb_type t, int level); +void sb_tree_free(SBtree_node *root); +void sb_tree_print_preorder(SBtree_node *root); +// double* sb_tree_get_quad( +// SBtree_node *root, +// int block_num, +// int levels, +// int rows, +// int cols +// ); +#endif // SBTREE_H diff --git a/include/smap.h b/include/smap.h new file mode 100644 index 0000000..f30c467 --- /dev/null +++ b/include/smap.h @@ -0,0 +1,45 @@ +#ifndef SMAP_H +#define SMAP_H +#include "sbtree.h" +#include "queue.h" + +enum smap_symbol { // significance map value + SP = 0, // Significant Positive + SN = 1, // Significant Negative + IZ = 2,// Isolated Zero + ZR = 3, // Zerotree Root + U = -1, // Unitialized +}; + +enum print_conf { + COEFF, + TYPE, + ALL +}; + +typedef struct Smap_tree_node { + double coeff; + struct Smap_tree_node *parent; + struct Smap_tree_node *children[4]; + char isroot : 1; + enum smap_symbol type; + unsigned char not_available; +} Smap_tree_node; + +// OPTIMIZE: Maybe pass by reference? Soo many copies!! + +char* smap_symbol_to_str(enum smap_symbol s); + +void smap_tree_print_levelorder(Smap_tree_node *root, enum print_conf p); +void smap_tree_print_preorder(Smap_tree_node *root, enum print_conf p); +Smap_tree_node *smap_tree_init_node(double coeff); +Smap_tree_node *smap_tree_init_root(double val, + double c1val, + double c2val, + double c3val); + +Queue *smap_tree_insert_quad(Queue *q, double *cvals); +Smap_tree_node *smap_treeify(SBtree_node *sb_root, int levels); +Smap_tree_node* smap_tree_reset(Smap_tree_node *root); +double *smap2levelorder(Smap_tree_node *root, int rows, int cols); +#endif // SMAP_H diff --git a/include/stack.h b/include/stack.h new file mode 100644 index 0000000..0901c28 --- /dev/null +++ b/include/stack.h @@ -0,0 +1,22 @@ +#ifndef STACK_H +#define STACK_H +#include "node.h" + +// top is first, top->next is next in stack +// bottom->next will always be NULL +// top->a->b->...->bottom->NULL + +typedef struct Stack { + Node *top; + Node *bottom; +} Stack; + +// OPTIMIZE: Maybe pass by reference? Soo many copies!! + +Stack *push(Stack *st, void *data); +Node *pop(Stack *st); +void free_stack(Stack *st); +void stack_pretty_print(Stack *st); + + +#endif // STACK_H diff --git a/include/utils.h b/include/utils.h new file mode 100644 index 0000000..248e781 --- /dev/null +++ b/include/utils.h @@ -0,0 +1,89 @@ +#ifndef UTILS_H +#define UTILS_H +#include +#include "smap.h" + +static inline void BOLD_CYAN_FG(char *str) +{ + printf("\033[1;38;2;51;177;255m%s\033[0m", str); +} + +static inline void DEBUG_INT(char *str, int x) +{ + BOLD_CYAN_FG("[debug] "); + printf("%s:%d\n", str, x); +} + +static inline void DEBUG_DOUBLE(char *str, double x) +{ + BOLD_CYAN_FG("[debug] "); + printf("%s:%f\n", str, x); +} + +static inline void DEBUG_STR(char *str, char *x) +{ + BOLD_CYAN_FG("[debug] "); + printf("%s:%s\n", str, x); +} + +static inline void DEBUG_UINT_PAIR(char *str, unsigned int *x) +{ + BOLD_CYAN_FG("[debug_uint_pair] "); + printf("%s:(%u %u)\n", str, x[0], x[1]); +} + +static inline void DEBUG_ARR_BYTE(unsigned char *x, int len) { + BOLD_CYAN_FG("[debug_arr_byte] "); + for(int i = 0; i < len; i++) { + printf("%x ", x[i]); + } + printf("\n"); +} + +static inline void DEBUG_ARR_F_1(double *x, int len) { + BOLD_CYAN_FG("[debug_arr_f_1] "); + for(int i = 0; i < len; i++) { + printf("%f ", x[i]); + } + printf("\n"); +} + +static inline void DEBUG_ARR_F_2(double **x, int r, int c) { + for(int i = 0; i < r; i++) { + BOLD_CYAN_FG("[debug_arr_f_2] "); + for(int j = 0; j < c; j++) { + printf("%f ", x[i][j]); + } + printf("\n"); + } +} + +static inline void DEBUG_ARR_INT(int *x, int r) { + BOLD_CYAN_FG("[debug_arr_int] "); + for(int i = 0; i < r; i++) { + printf("%d ", x[i]); + } +} + +static inline void DEBUG_SMAP_NODE(Smap_tree_node *n) { + if(n) { + DEBUG_DOUBLE("coeff", n->coeff); + } + else { + DEBUG_STR("coeff", "NULL"); + } +} + +#define DEBUG_BLANK DEBUG_STR("", "") + +void read_binary_file(FILE *infile, unsigned char *dest_arr, int rows, int cols); +void write_binary_file(FILE *outfile, unsigned char *src_arr, int rows, int cols); +void double_to_uchar(double *src, unsigned char* dest, int rows, int cols); +double max_double(double *arr, int len); +double** quads_from_arr(double *arr, int rows, int cols); +double* gsl_swap(double *unswapped, int rows, int cols); + +double* smap2arr(Smap_tree_node* smap_root, int rows, int cols); +unsigned int* morton_decode(unsigned int morton, unsigned int *inds); + +#endif // UTILS_H diff --git a/papers/WaveletTutorial.pdf b/papers/WaveletTutorial.pdf deleted file mode 100644 index 04f0f88..0000000 Binary files a/papers/WaveletTutorial.pdf and /dev/null differ diff --git a/papers/Zerotree_Approach.pdf b/papers/Zerotree_Approach.pdf new file mode 100644 index 0000000..b249f9c Binary files /dev/null and b/papers/Zerotree_Approach.pdf differ diff --git a/papers/bams_79_01_0061.pdf b/papers/bams_79_01_0061.pdf new file mode 100644 index 0000000..6975002 Binary files /dev/null and b/papers/bams_79_01_0061.pdf differ diff --git a/src/bitstream.c b/src/bitstream.c new file mode 100644 index 0000000..e0e9df2 --- /dev/null +++ b/src/bitstream.c @@ -0,0 +1,86 @@ +#include +#include +#include "utils.h" +#include "bitstream.h" + +mini_header *create_mini_header(unsigned int threshold, Queue *symbols) +{ + mini_header *m_hdr = malloc(sizeof(mini_header)); + m_hdr->num_bytes = (unsigned int) (symbols->len / 2) + (symbols->len % 2); + unsigned char curr_byte = 0xff; + unsigned char *bytes = (unsigned char *) calloc(m_hdr->num_bytes, sizeof(unsigned char)); + + // NOTE: Do we really need this?? + Node *node_pair[2] = {NULL}; + + m_hdr->threshold_pow = (unsigned short) log2(threshold); + unsigned int ind = 0; + while(symbols->head) { + curr_byte = 0xff; + // Pack pairs of symbols into bytes + for(int i = 0; i < 2; i++) { + node_pair[i] = dequeue(symbols); + if(node_pair[i]) { + curr_byte = (curr_byte << 3) | *(unsigned char *) node_pair[i]->data; + } + } + bytes[ind] = curr_byte; + ind++; + } + m_hdr->bytes = bytes; + // DEBUG_INT("t", m_hdr->threshold_pow); + // DEBUG_INT("n", m_hdr->num_bytes); + // DEBUG_ARR_BYTE(m_hdr->bytes, m_hdr->num_bytes); + return m_hdr; +} + +void write_bitstream_file(const char* filename, enum file_op_mode mode, + mini_header *m_hdr, unsigned int dim) +{ + FILE *fptr = NULL; + unsigned char dim_pow = log2(dim); + // DEBUG_INT("num_bytes", m_hdr->num_bytes); + if(mode == A) { + fptr = fopen(filename, "ab"); + } + else if(mode == W) { + fptr = fopen(filename, "wb"); + if(fwrite(&dim_pow, sizeof(dim_pow), 1, fptr) != 1) { + fprintf(stderr, "Error while writing file: %s", filename); + exit(1); + } + } + if(fwrite(&m_hdr->threshold_pow, sizeof(m_hdr->threshold_pow), 1, fptr) != 1) { + fprintf(stderr, "Error while writing file: %s", filename); + exit(1); + } + // if(fwrite(&m_hdr->num_bytes, sizeof(m_hdr->num_bytes), 1, fptr) != 1) { + if(fwrite(&m_hdr->num_bytes, sizeof(unsigned int), 1, fptr) != 1) { + fprintf(stderr, "Error while writing file: %s", filename); + exit(1); + } + // DEBUG_ARR_BYTE(m_hdr->bytes, m_hdr->num_bytes); + if(fwrite(m_hdr->bytes, sizeof(m_hdr->bytes[0]), m_hdr->num_bytes, fptr) != m_hdr->num_bytes) { + fprintf(stderr, "Error while writing file: %s", filename); + exit(1); + } + fclose(fptr); +} + +Queue* read_bitstream_file(const char* filename, Queue *header_queue, unsigned char *dim_pow) +{ + FILE *fptr = fopen(filename, "rb"); + + fread(dim_pow, sizeof(unsigned char), 1, fptr); + + unsigned short threshold_pow; + while(fread(&threshold_pow, sizeof(unsigned short), 1, fptr) != 0) { + mini_header *curr_hdr = (mini_header *) malloc(sizeof(mini_header)); + curr_hdr->threshold_pow = threshold_pow; + fread(&curr_hdr->num_bytes, sizeof(unsigned int), 1, fptr); + curr_hdr->bytes = calloc(curr_hdr->num_bytes, sizeof(unsigned int)); + fread(curr_hdr->bytes, sizeof(unsigned char), curr_hdr->num_bytes, fptr); + header_queue = enqueue(header_queue, curr_hdr); + } + return header_queue; +} diff --git a/src/bitstream.c.old b/src/bitstream.c.old new file mode 100644 index 0000000..f88f1aa --- /dev/null +++ b/src/bitstream.c.old @@ -0,0 +1,45 @@ +#include "bitstream.h.old" +#include "smap.h" + +void symbol_set_init(struct symbol_set *s_set, unsigned short threshold, unsigned int size) +{ + s_set->threshold = threshold; + s_set->size = size; +} + +void symbol_group_insert(struct symbols_group *s_grp, int count, unsigned char symbol) +{ + switch(count) { + case 0: + s_grp->s0 = symbol; + break; + case 1: + s_grp->s1 = symbol; + break; + case 2: + s_grp->s2 = symbol; + break; + case 3: + s_grp->s3 = symbol; + break; + case 4: + s_grp->s4 = symbol; + break; + case 5: + s_grp->s5 = symbol; + break; + case 6: + s_grp->s6 = symbol; + break; + case 7: + s_grp->s7 = symbol; + break; + case 8: + s_grp->s8 = symbol; + break; + case 9: + s_grp->s9 = symbol; + break; + default: return; + } +} diff --git a/src/ezw.c b/src/ezw.c new file mode 100644 index 0000000..f86ca4f --- /dev/null +++ b/src/ezw.c @@ -0,0 +1,277 @@ +#include +#include +#include +#include "wavelib.h" +#include "utils.h" +#include "ezw.h" +#include "queue.h" +#include "stack.h" +#include "bitstream.h" + +enum smap_symbol encode_coeff(float coeff, int threshold) +{ + enum smap_symbol symbol; + if(fabs(coeff) >= threshold) { + if(coeff >= 0) { + symbol = SP; + } + else { + symbol = SN; + } + } + else { + symbol = IZ; + } + return symbol; +} + +void check_descendants(Smap_tree_node *parent, int threshold) +{ + unsigned char is_zr = 1; + if(!parent) { + is_zr = -1; + } + else { + Stack *backtrack = NULL; + Queue *q = NULL; + + q = enqueue(q, parent); + backtrack = push(backtrack, parent); + + Node *curr_node; + Smap_tree_node *curr_smap_node; + while(q->head) { + curr_node = dequeue(q); + curr_smap_node = (Smap_tree_node *) curr_node->data; + curr_smap_node->type = encode_coeff(curr_smap_node->coeff, threshold); + // DEBUG_DOUBLE("coeff", curr_smap_node->coeff); + // DEBUG_STR("type", smap_symbol_to_str(curr_smap_node->type)); + if(curr_smap_node->type == SP || curr_smap_node->type == SN) { + is_zr = 0; + break; + } + else { + for(int i = 0; i < 4; i++) { + if(curr_smap_node->children[i]) { + backtrack = push(backtrack, curr_smap_node->children[i]); + q = enqueue(q, curr_smap_node->children[i]); + } + } + } + } + + // Trace back the tree and encode them accordingly + // If zerotree is detected, then everything is a zerotree root + // otherwise, it is an isolated zero + while(backtrack->top) { + curr_node = pop(backtrack); + curr_smap_node = (Smap_tree_node *) curr_node->data; + if(is_zr) { + curr_smap_node->type = ZR; + } + else { + if(curr_smap_node->type == U || curr_smap_node->type == ZR) { + curr_smap_node->type = IZ; + } + } + // DEBUG_DOUBLE("backtracking coeff", curr_smap_node->coeff); + // DEBUG_STR("type", smap_symbol_to_str(curr_smap_node->type)); + // DEBUG_STR("", ""); + } + } +} + +// Valens EZW +Queue *dominant_pass(Smap_tree_node *smap_root, int threshold) +{ + Queue *q = NULL; + Queue *dominant_list = NULL; + Node *curr_queue_node = NULL; + Smap_tree_node *curr_smap_node = NULL; + + // Manually add first one + q = enqueue(q, smap_root); + + while(q->head){ + curr_queue_node = dequeue(q); + if(curr_queue_node) { + curr_smap_node = (Smap_tree_node *) curr_queue_node->data; + for(int i = 0; i < 4; i++) { + if(curr_smap_node->children[i]) { + q = enqueue(q, curr_smap_node->children[i]); + } + } + check_descendants(curr_smap_node, threshold); + switch(curr_smap_node->type) { + case SP: + case SN: + case IZ: + dominant_list = enqueue(dominant_list, curr_smap_node); + break; + case ZR: + { + if((curr_smap_node->parent + && curr_smap_node->parent->type != ZR) + || curr_smap_node->isroot) { + dominant_list = enqueue(dominant_list, curr_smap_node); + } + } + case U: + break; + } + } + } + return dominant_list; +} + +Queue *subordinate_pass(Queue *dominant_list, int threshold) +{ + Queue *bitstream_elements = NULL; + if(dominant_list) { + Node *curr_queue_node = dominant_list->head; + Smap_tree_node *curr_smap_node = NULL; + while(curr_queue_node) { + unsigned char *symbol = (unsigned char *) malloc(sizeof(unsigned char)); + curr_smap_node = (Smap_tree_node *) curr_queue_node->data; + if(curr_smap_node->type == SP || curr_smap_node->type == SN) { + curr_smap_node->not_available = 1; + // add the third bit to the symbol + // If 1, the coeff is > 1.5*t else, coeff is <= 1.5*t + if(fabs(curr_smap_node->coeff) > 1.5*threshold) { + *symbol = curr_smap_node->type << 1 | 0x1; + } + else { + *symbol = curr_smap_node->type << 1; + } + curr_smap_node->coeff = 0.0; + } + else { + *symbol = curr_smap_node->type << 1; + } + bitstream_elements = enqueue(bitstream_elements, symbol); + curr_queue_node = curr_queue_node->next; + } + } + return bitstream_elements; +} + +void ezw(const char *filename, Smap_tree_node *smap_root, int rows, int cols, unsigned int iter) +{ + // bitplane coding is adopted here + // https://en.wikipedia.org/wiki/Bit_plane + // bitplanes can be coded efficiently + unsigned int threshold = pow(2, (int) floor((int) log2(smap_root->coeff))); + + Queue *dominant_list = NULL; + Queue *symbols = NULL; + mini_header *m_hdr = NULL; + unsigned int i = 0; + while(i < iter) { + if(threshold > 0) { + dominant_list = dominant_pass(smap_root, threshold); + // queue_pretty_print(dominant_list, SMAP_TREE_NODE); + + symbols = subordinate_pass(dominant_list, threshold); + // queue_pretty_print(symbols, INT); + + m_hdr = create_mini_header(threshold, symbols); + if(i == 0) { + write_bitstream_file(filename, W, m_hdr, rows); + } + else { + write_bitstream_file(filename, A, m_hdr, rows); + } + threshold /= 2; + free_queue(symbols); + free(m_hdr); + } + else { + break; + } + i++; + } +} + +Smap_tree_node* reconstruct(unsigned char dim_pow, Queue *header_q) +{ + // initialise empty trees for filling in with approximations + double *zeros = (double *) calloc(pow(2, dim_pow), sizeof(double)); + SBtree_node *reconst_root = sb_treeify(dim_pow, zeros, pow(2, dim_pow), pow(2, dim_pow)); + Smap_tree_node *smap_root = smap_treeify(reconst_root, dim_pow); + + Smap_tree_node *curr_smap = NULL; + Queue *smap_q = NULL; + int curr_threshold = 0; + unsigned char lsb = 0; + if(header_q) { + while(header_q->head) { + Node *curr_hdr_node = dequeue(header_q); + mini_header *curr_hdr = (mini_header *) curr_hdr_node->data; + unsigned char curr_byte = 0; + unsigned char *symbols = calloc(2*curr_hdr->num_bytes, sizeof(unsigned char)); + for(int i = 0; i < 2*curr_hdr->num_bytes; i++) { + curr_byte = curr_hdr->bytes[i/2]; + + // NOTE: extract from MSB half first + // eg: 0b11111001 + // extracts 0b111 first, then 0b001, which is the order we want + symbols[i] = (((curr_byte << (i%2)*3) & SYMB_MASK) >> 3); + } + + smap_q = enqueue(smap_q, smap_root); + curr_threshold = pow(2, curr_hdr->threshold_pow); + for(int i = 0; i < 2*curr_hdr->num_bytes; i++) { + Node *curr_smap_node = dequeue(smap_q); + curr_smap = (Smap_tree_node *) curr_smap_node->data; + for(int i = 0; i < 4; i++) { + if(curr_smap->children[i]) { + smap_q = enqueue(smap_q, curr_smap->children[i]); + } + } + if(!curr_smap->not_available) { + lsb = symbols[i] & 1; + symbols[i] >>= 1; + switch(symbols[i]) { + case SP: + { + if(lsb) { + curr_smap->coeff = (1.5*curr_threshold) + (curr_threshold/4.0); + } + else { + curr_smap->coeff = (1.5*curr_threshold) - (curr_threshold/4.0); + } + curr_smap->not_available = 1; + break; + } + case SN: + { + if(lsb) { + curr_smap->coeff = -((1.5*curr_threshold) + (curr_threshold/4.0)); + } + else { + curr_smap->coeff = -((1.5*curr_threshold) - (curr_threshold/4.0)); + } + curr_smap->not_available = 1; + break; + } + default: + { + curr_smap->coeff = 0.0; + curr_smap->not_available = 1; + break; + } + } + } + } + // DEBUG_ARR_BYTE(symbols, 2*curr_hdr->num_bytes); + // smap_tree_print_preorder(smap_root, ALL); + // printf("\n"); + free(symbols); + free(smap_q); + smap_q = NULL; + } + } + free(zeros); + sb_tree_free(reconst_root); + return smap_root; +} diff --git a/src/main.c b/src/main.c new file mode 100644 index 0000000..874b47d --- /dev/null +++ b/src/main.c @@ -0,0 +1,316 @@ +#include +#include +#include +#include +#include "utils.h" +#include "wavelib.h" +#include "sbtree.h" +#include "smap.h" +#include "ezw.h" +#include "queue.h" +#include "bitstream.h" + +// #define L + +// #define GSLTEST +#if defined(GSLTEST) +int main() +{ + const int dim = 16; + // double arr[64] = { + // 1447.38,-136.375,-173,-329,-164,-132.5,-21.5,-189, + // 90.875,-16.875,24.75,-35,13.5,-54,-37.5,21, + // 65,-138.5,107.5,-108,-3,35.5,-1.5,-23.5, + // 34.75,5,-101.25,-7,3.5,3.5,2.5,5.5, + // 41,122.5,-21.5,-66,41,-81.5,21.5,-13, + // -58.5,35,-37.5,-17,27.5,37,-51.5,17, + // -65,34.5,-8.5,18.5,-32,-28.5,31.5,-15.5, + // 31.5,-5.5,6.5,8.5,-3.5,11.5,2.5,-10.5 + // }; + double arr[256] = { + 3248.88,-154.875,54.125,-136.375,91,88.25,-173,-329,-3,30.5,67,47.5,-164,-132.5,-21.5,-189, + 129.125,79.125,-2.125,-103.875,-22.75,-43.25,25.75,-35,33.5,-25,-15.5,28.5,13.5,-54,-37.5,21, + 57.625,90.875,19.625,-16.875,32.75,-12.5,-45,-63.5,-16.5,16.5,-10,34.5,-3,35.5,-1.5,-23.5, + 162.125,26.125,22.125,-46.625,-54.75,-39.75,-22.5,110.75,39,-49.5,-71.5,-39.5,3.5,3.5,2.5,5.5, + 75,-1.75,65,-138.5,-45.5,-17.75,107.5,-108,-27.5,4.5,71.5,-4,33,28,8,1, + 68.75,-31.25,34.5,5,-10.75,84.75,-101.25,-7,0,22.5,-8.5,0,405,-41.5,-43.5,-15.5, + 37.25,7,-3.5,-41,-63.25,22.5,114.5,82,0,-1.5,2,27.5,-37,17,-20.5,0, + 81.75,-11.25,3.5,58.25,60.75,44.75,-57.5,-107.75,-4,-27,-67,-57,3,-5,35.5,137.5, + 3,21.5,0,-15.5,41,122.5,-21.5,-66,3,-23.5,1,15.5,41,-81.5,21.5,-13, + 48.5,-20,-1.5,17.5,-58.5,35,-37.5,-17,-33.5,28,-3.5,0.5,27.5,37,-51.5,17, + 70.5,-19.5,4,29.5,-65,34.5,-8.5,18.5,4.5,19.5,-4,3.5,-32,-28.5,31.5,-15.5, + 1,30.5,-26.5,-25.5,31.5,-5.5,6.5,8.5,9,-4.5,19.5,-25.5,-3.5,11.5,2.5,-10.5, + -17.5,4.5,27.5,6,-31,-8,5,7,-20.5,-4.5,16.5,-3,42,-37,-3,47, + 0,68.5,-15.5,-12,-39.5,39.5,6.5,-14.5,0,5.5,-20.5,0,-1.5,39.5,-10.5,-18.5, + 0,65.5,-1,23.5,-66,32,-39.5,0,0,-19.5,12,-16.5,-17,-17,-6.5,4, + -2,27,-1,-27,2,67,-55.5,117.5,0,27,-12,-18,1,5,34.5,-32.5, + }; + + double *array = (double *) calloc(dim*dim, sizeof(double)); + array = gsl_swap(arr, dim, dim); + + for(int i = 0; i < dim; i++) { + for(int j = 0; j < dim; j++) { + printf("%0.2f\t", array[i*dim + j]); + } + printf("\n"); + } + return 0; + +} +#elif defined(MORTONTEST) +int main() +{ + unsigned int *inds = (unsigned int *) calloc(2, sizeof(unsigned int)); + for(int i = 0; i < 4; i++) { + inds = morton_decode(i, inds); + DEBUG_UINT_PAIR("inds", inds); + } + return 0; +} +#elif defined(STACKTEST) +#include "stack.h" +int main() +{ + Stack *st = NULL; + Node *n = NULL; + int arr[10]; + for(int i = 0; i < 10; i++) { + arr[i] = i; + st = push(st, &arr[i]); + } + stack_pretty_print(st); + for(int i = 0; i < 10; i++) { + n = pop(st); + DEBUG_INT("top", *(int *) n->data); + } + stack_pretty_print(st); + return 0; +} +#elif defined(QTEST) +#include "queue.h" +int main() +{ + Queue *q = NULL; + Node *n = NULL; + int arr[10]; + for(int i = 0; i < 10; i++) { + arr[i] = i; + q = enqueue(q, &arr[i]); + } + queue_pretty_print(q); + for(int i = 0; i < 10; i++) { + n = dequeue(q); + DEBUG_INT("head", *(int *) n->data); + } + queue_pretty_print(q); +} +#elif defined(SBTEST) +int main() +{ + double LL3 = 57.0; + double HL3 = -37.0; + double LH3 = -29.0; + double HH3 = 30.0; + double LL2[4] = { + 57.0, -37.0, + -29.0, 30.0 + }; + double HL2[4] = { + 39.0, -20.0, + -17.0, 33.0 + }; + double LH2[4] = { + 14.0, 6.0, + 10.0, 19.0 + }; + double HH2[4]= { + 15.0, 13.0, + -7.0, 9.0 + }; + double LL1[16] = { + 57.0, -37.0, 39.0, -20.0, + -29.0, 30.0, 17.0, 33.0, + 14.0, 6.0, 15.0, 13.0, + 10.0, 19.0, -7.0, 9.0, + }; + double HL1[16] = { + 3.0, 7.0, 9.0, 10.0, + 8.0, 2.0, 1.0, 6.0, + 9.0, -4.0, 2.0, 3.0, + -7.0, 14.0, 12.0, -9.0, + }; + double LH1[16] = { + 12.0, 15.0, 33.0, 20.0, + 0.0, 7.0, 2.0, 4.0, + 4.0, 1.0, 10.0, 3.0, + 5.0, 6.0, 0.0, 0.0, + }; + double HH1[16] = { + -2.0, 3.0, 1.0, 0.0, + 4.0, -1.0, 1.0, 1.0, + 2.0, 0.0, 1.0, 0.0, + 3.0, 1.0, 2.0, 1.0, + }; + SBtree_node *root = sb_tree_init_root(); + + // layer 1 + root = sb_tree_insert(root, LL, &LL3); + root = sb_tree_insert(root, HL, &HL3); + root = sb_tree_insert(root, LH, &LH3); + root = sb_tree_insert(root, HH, &HH3); + // layer 2 + root = sb_tree_insert(root, LL, &LL2[0]); + root = sb_tree_insert(root, HL, &HL2[0]); + root = sb_tree_insert(root, LH, &LH2[0]); + root = sb_tree_insert(root, HH, &HH2[0]); + // layer 3 + root = sb_tree_insert(root, LL, &LL1[0]); + root = sb_tree_insert(root, HL, &HL1[0]); + root = sb_tree_insert(root, LH, &LH1[0]); + root = sb_tree_insert(root, HH, &HH1[0]); + + sb_tree_print_preorder(root); + printf("\n"); + sb_tree_free(root); + return 0; +} +#else +void printhelp(unsigned char exit) +{ + FILE *f = stdout; + if(exit != 0) { + f = stderr; + } + fprintf(f, "USAGE:\n\tmain [options] imagefile\n\n"); + fprintf(f, "MANDATORY OPTIONS:\n\t-o output file\n\t-d image dimension\n\n"); + fprintf(f, "OPTIONAL OPTIONS:\n\t-i iterations (defaults to 3)\n\t-h show this help and exit\n\n"); + fprintf(f, "EXAMPLE:\n\tHere, assume img.png is a 16x16 image\n\t$ main -o compressed.ezw -d 16 img.png\n"); +} + +int main(int argc, char **argv) +{ + int opt, rows, cols; + int o_flag = -1; + const char *outputFile; + const char *inputFile; + char *end; + int iter = 3; + while((opt = getopt(argc, argv, "o:d:i::h")) != -1) { + switch(opt) { + case 'h': { + printhelp(0); + return 0; + break; + } + case 'o': { + outputFile = optarg; + o_flag = strtol(optarg, &end, 10); + break; + } + case 'd': { + rows = strtol(optarg, &end, 10); + cols = rows; + break; + } + case 'i': { + iter = strtol(optarg, &end, 10); + break; + } + case '?': { + if(optopt != 'o' && optopt != 'd') { + fprintf(stderr, "Unknown option -%c.\n\n", optopt); + printhelp(1); + return 1; + } + break; + } + } + } + + if(o_flag == -1) { + fprintf(stderr, "-o is a mandatory option\n\n"); + printhelp(1); + return 1; + } + if(rows == -1) { + fprintf(stderr, "-d is a mandatory option\n\n"); + printhelp(1); + return 1; + } + + if(optind < argc) { + inputFile = argv[optind]; + } + + FILE *img_bin = fopen(inputFile, "rb"); + unsigned char *pix_arr = calloc(rows*cols, 1); // array of 8 bit vals + + if(!img_bin) { + fprintf(stderr, "Unable to open file: %s\n", inputFile); + return 1; + } + else { + read_binary_file(img_bin, pix_arr, rows, cols); + fclose(img_bin); + } + + wave_object obj; + wt2_object wt; + double *inp, *oup, *inv_out; + int N = rows*cols; + + char *name = "haar"; + obj = wave_init(name);// Initialize the wavelet + inp = (double *) calloc(N, sizeof(double)); + oup = (double *) calloc(N, sizeof(double)); + inv_out = (double *) calloc(N, sizeof(double)); + + // number of decompositions = max possible for the given dimensions + int J = (int) log2(rows); + + wt = wt2_init(obj, "dwt", rows, cols, J); + + for (int i = 0; i < rows; ++i) { + for (int k = 0; k < cols; ++k) { + inp[i*cols + k] = (double) pix_arr[i*cols + k]; + oup[i*cols + k] = 0.0; + } + } + + SBtree_node *root = (SBtree_node *) malloc(sizeof(SBtree_node)); + Smap_tree_node *smap_root = (Smap_tree_node *) malloc(sizeof(Smap_tree_node)); + Smap_tree_node *smap_root_copy = (Smap_tree_node *) malloc(sizeof(Smap_tree_node)); + // Smap_tree_node *smap_root_approx = (Smap_tree_node *) malloc(sizeof(Smap_tree_node)); + root = sb_treeify(J, inp, rows, cols); + smap_root = smap_treeify(root, J); + smap_root_copy = smap_treeify(root, J); + ezw(outputFile, smap_root_copy, rows, cols, iter); + + // Queue *header_q = NULL; + // unsigned char dim_pow; + // header_q = read_bitstream_file(outputFile, header_q, &dim_pow); + // // queue_pretty_print(header_q, MINI_HDR); + // smap_root_approx = reconstruct(dim_pow, header_q); + // double *arr = smap2arr(smap_root_approx, rows, cols); + // for(int i = 0; i < rows; i++) { + // for(int j = 0; j < cols; j++) { + // printf("%.2f ", arr[i*cols + j]); + // } + // printf("\n"); + // } + // smap_tree_print_levelorder(smap_root, ALL); + // printf("\n"); + // smap_tree_print_levelorder(smap_root_approx, ALL); + + // clean up + sb_tree_free(root); + wave_free(obj); + wt2_free(wt); + free(inp); + free(oup); + free(pix_arr); + free(inv_out); + return 0; +} +#endif // WAVE diff --git a/src/node.c b/src/node.c new file mode 100644 index 0000000..725977e --- /dev/null +++ b/src/node.c @@ -0,0 +1,18 @@ +#include +#include "node.h" + +Node *create_node(void *data) +{ + Node *new_node = (Node *) malloc(sizeof(Node)); + new_node->data = data; + new_node->next = NULL; + return new_node; +} + +void free_node(Node *n) +{ + if(n->data) { + free(n->data); + } + free(n); +} diff --git a/src/queue.c b/src/queue.c new file mode 100644 index 0000000..33ef849 --- /dev/null +++ b/src/queue.c @@ -0,0 +1,112 @@ +#include +#include +#include "queue.h" +#include "node.h" +#include "smap.h" +#include "bitstream.h" +#include "utils.h" + +Queue *enqueue(Queue *q, void *data) +{ + // If no queue + if(!q) { + q = (Queue *) malloc(sizeof(Queue)); + q->head = NULL; + q->tail = NULL; + } + + Node *new_node = create_node(data); + + // Only for first element + if(!q->head) { + q->head = new_node; + q->tail = new_node; + } + else { + // add new node to linked-list, and + // move the tail + q->tail->next = new_node; + q->tail = new_node; + } + q->len++; + return q; +} + +Node *dequeue(Queue *q) +{ + Node *node = NULL; + if(q->head) { + node = q->head; // save the head + if(q->head == q->tail) { + // queue is empty + q->head = NULL; + q->tail = NULL; + } + else { + // move head to next in queue + q->head = q->head->next; + } + q->len--; + } + return node; +} + +void free_queue(Queue *q) +{ + while(q->head) { + free_node(dequeue(q)); + } + free(q); +} + +void queue_pretty_print(Queue *q, enum q_type t) +{ + if(q) { + Node *curr = q->head; + switch(t) { + case SMAP_TREE_NODE: { + Smap_tree_node *curr_smap_node = NULL; + while(curr) { + curr_smap_node = (Smap_tree_node *) curr->data; + printf("(%f %s) ", curr_smap_node->coeff, + smap_symbol_to_str(curr_smap_node->type)); + curr = curr->next; + } + break; + } + case MINI_HDR: { + mini_header *curr_hdr = NULL; + while(curr) { + curr_hdr = (mini_header *) curr->data; + printf("(%d %d)\n", curr_hdr->threshold_pow, curr_hdr->num_bytes); + DEBUG_ARR_BYTE(curr_hdr->bytes, curr_hdr->num_bytes); + printf("\n"); + curr = curr->next; + } + break; + } + case INT: { + int *val = NULL; + while(curr) { + val = (int *) curr->data; + printf("%d ", *val); + curr = curr->next; + } + break; + } + case DOUBLE: { + double *val = NULL; + while(curr) { + val = (double *) curr->data; + printf("%f ", *val); + curr = curr->next; + } + break; + } + } + printf("\n"); + } + else { + printf("Queue is empty\n"); + } +} diff --git a/src/sbtree.c b/src/sbtree.c new file mode 100644 index 0000000..bf3d9e5 --- /dev/null +++ b/src/sbtree.c @@ -0,0 +1,215 @@ +#include +#include +#include +#include "wavelib.h" +#include "sbtree.h" + +SBtree_node* sb_tree_init_root() +{ + SBtree_node* root = (SBtree_node *) malloc(sizeof(SBtree_node)); + root->ll = NULL; + root->hl = NULL; + root->lh = NULL; + root->hh = NULL; + root->coeffs = NULL; + root->type = ROOT; + return root; +} + +// Returns NULL if "root" is uninitialized +// Perform NULL check before using +SBtree_node* sb_tree_insert(SBtree_node *root, enum sb_type t, double *coeffs) +{ + if(root) { + SBtree_node *curr = root; + SBtree_node *new = (SBtree_node *) malloc(sizeof(SBtree_node)); + new->type = t; + new->coeffs = coeffs; + new->ll = NULL; + new->hl = NULL; + new->lh = NULL; + new->hh = NULL; + + // Move to next level only if all subbands in current level are filled + while(curr && curr->ll && curr->hl && curr->lh && curr->hh) { + curr = curr->ll; + } + switch(t) { + case LL: + curr->ll = new; + break; + case HL: + curr->hl = new; + break; + case LH: + curr->lh = new; + break; + case HH: + curr->hh = new; + break; + case ROOT: + // do nothing + break; + } + return root; + } + else { + return NULL; + } +} + +// Returns NULL if a set of subband coeffs is not found +// Remember to check for NULL when using +double* sb_tree_get_coeff(SBtree_node *root, enum sb_type t, int level) +{ + if(level > 0) { + SBtree_node *curr = root; + for(int i = 1; i < level; i++) { + if(curr) { + curr = curr->ll; + } + else { + return NULL; + } + } + switch(t) { + case LL: + return(curr->ll->coeffs); + break; + case HL: + return(curr->hl->coeffs); + break; + case LH: + return(curr->lh->coeffs); + break; + case HH: + return(curr->hh->coeffs); + break; + case ROOT: + return NULL; + break; + default: + return NULL; + break; + } + } + else { + return NULL; + } +} + +SBtree_node* sb_treeify(int levels, double* input, int rows, int cols) +{ + SBtree_node *root = sb_tree_init_root(); + wave_object w_obj; + w_obj = wave_init("haar"); + wt2_object* wt2_arr = (wt2_object *) calloc(sizeof(wt2_object), levels); + double *subcoeffs_A; // LL + double *subcoeffs_H; // HL + double *subcoeffs_V; // LH + double *subcoeffs_D; // HH + double *curr_wavecoeffs; + int sub_r, sub_c; + + for(int i = 0; i < levels; i++) { + wt2_arr[i] = wt2_init(w_obj, "dwt", rows, cols, i+1); + } + + /* for(int i = 0; i < levels; i++) { */ + /* curr_wavecoeffs = dwt2(wt2_arr[i], input); */ + /* subcoeffs_A = getWT2Coeffs(wt2_arr[i], curr_wavecoeffs, i+1, "A", &sub_r, &sub_c); */ + /* subcoeffs_H = getWT2Coeffs(wt2_arr[i], curr_wavecoeffs, i+1, "H", &sub_r, &sub_c); */ + /* subcoeffs_V = getWT2Coeffs(wt2_arr[i], curr_wavecoeffs, i+1, "V", &sub_r, &sub_c); */ + /* subcoeffs_D = getWT2Coeffs(wt2_arr[i], curr_wavecoeffs, i+1, "D", &sub_r, &sub_c); */ + /* root = sb_tree_insert(root, LL, subcoeffs_A); */ + /* root = sb_tree_insert(root, HL, subcoeffs_H); */ + /* root = sb_tree_insert(root, LH, subcoeffs_V); */ + /* root = sb_tree_insert(root, HH, subcoeffs_D); */ + /* } */ + for(int i = levels; i > 0; i--) { + curr_wavecoeffs = dwt2(wt2_arr[i-1], input); + subcoeffs_A = getWT2Coeffs(wt2_arr[i-1], curr_wavecoeffs, i, "A", &sub_r, &sub_c); + /* dispWT2Coeffs(subcoeffs_A, sub_r, sub_c); */ + subcoeffs_H = getWT2Coeffs(wt2_arr[i-1], curr_wavecoeffs, i, "H", &sub_r, &sub_c); + /* dispWT2Coeffs(subcoeffs_H, sub_r, sub_c); */ + subcoeffs_V = getWT2Coeffs(wt2_arr[i-1], curr_wavecoeffs, i, "V", &sub_r, &sub_c); + /* dispWT2Coeffs(subcoeffs_V, sub_r, sub_c); */ + subcoeffs_D = getWT2Coeffs(wt2_arr[i-1], curr_wavecoeffs, i, "D", &sub_r, &sub_c); + /* dispWT2Coeffs(subcoeffs_D, sub_r, sub_c); */ + root = sb_tree_insert(root, LL, subcoeffs_A); + root = sb_tree_insert(root, HL, subcoeffs_H); + root = sb_tree_insert(root, LH, subcoeffs_V); + root = sb_tree_insert(root, HH, subcoeffs_D); + } + + // clean up + wave_free(w_obj); + for(int i = 0; i < levels; i++) { + wt2_free(wt2_arr[i]); + } + free(wt2_arr); + return(root); +} + +/* double* sb_tree_get_quad( */ +/* SBtree_node *root, */ +/* int block_num, */ +/* int levels, */ +/* int rows, */ +/* int cols */ +/* ) */ +/* { */ +/* double quad[2][2]; */ +/* enum sb_type subbands[4] = {LL, HL, LH, HH}; */ +/* int maxlevels = log2(rows); */ +/* if(block_num < 0 || levels > maxlevels || levels <= 0) { */ +/* return NULL; */ +/* } */ +/* else { */ +/* SBtree_node *curr = root; */ +/* SBtree_node *refnode = root; */ +/* int currlevel = levels; */ +/* int curredge; */ +/* for(int i = 0; i < block_num; i++) { */ +/* curredge = rows / (pow(2, currlevel)); */ +/* } */ +/* } */ +/* } */ + +// Recursively delete tree +// Steps: +// Save LL subband of current node +// Delete all subbands except LL for current node +// Delete the current node +// Recursively call on saved LL band (the new "root") +void sb_tree_free(SBtree_node *root) +{ + if(root) { + SBtree_node *temp_ll = root->ll; + free(root->hl); + free(root->lh); + free(root->hh); + free(root); + sb_tree_free(temp_ll); + } +} + +// DOES NOT print newline at the end, leaves trailing whitespace +void sb_tree_print_preorder(SBtree_node *root) +{ + if(root && root->coeffs) { + printf("%f\n", root->coeffs[0]); + } + if(root->ll) { + sb_tree_print_preorder(root->ll); + } + if(root->hl) { + sb_tree_print_preorder(root->hl); + } + if(root->lh) { + sb_tree_print_preorder(root->lh); + } + if(root->hh) { + sb_tree_print_preorder(root->hh); + } +} diff --git a/src/smap.c b/src/smap.c new file mode 100644 index 0000000..a3a5ba6 --- /dev/null +++ b/src/smap.c @@ -0,0 +1,234 @@ +#include +#include +#include +#include "smap.h" +#include "utils.h" + +Smap_tree_node *smap_tree_init_node(double coeff) +{ + Smap_tree_node *new_node = (Smap_tree_node *) malloc(sizeof(Smap_tree_node)); + new_node->coeff = coeff; + new_node->type = U; + new_node->parent = NULL; + new_node->children[0] = NULL; + new_node->children[1] = NULL; + new_node->children[2] = NULL; + new_node->children[3] = NULL; + new_node->isroot = 0; + new_node->not_available = 0; + return new_node; +} + +Smap_tree_node *smap_tree_init_root(double val, + double c1val, + double c2val, + double c3val) +{ + Smap_tree_node *new_node = smap_tree_init_node(val); + Smap_tree_node *c2 = smap_tree_init_node(c1val); + Smap_tree_node *c3 = smap_tree_init_node(c2val); + Smap_tree_node *c4 = smap_tree_init_node(c3val); + new_node->parent = NULL; + new_node->children[1] = c2; + new_node->children[2] = c3; + new_node->children[3] = c4; + for(int i = 1; i < 4; i++) { + new_node->children[i]->parent = new_node; + } + new_node->isroot = 1; + return new_node; +} + +// Recursively "reset" all node types to U +Smap_tree_node* smap_tree_reset(Smap_tree_node *root) +{ + if(root) { + root->type = U; + } + if(root->children[0]) { + smap_tree_reset(root->children[0]); + } + if(root->children[1]) { + smap_tree_reset(root->children[1]); + } + if(root->children[2]) { + smap_tree_reset(root->children[2]); + } + if(root->children[3]) { + smap_tree_reset(root->children[3]); + } + return root; +} + +/** + * Assume the first 4 Smap_tree_nodes are already in the queue + * So the nodes given here: + * a + * | + * ----------- + * / | \ + * b c d + * should already be in the queue + * Maintain an external queue + * 'a' need not be in the queue as it is the first to be enqueued + * so, the intial queue must be like this: + * [b, c, d] + * + * Breadth first insertion: + * 1) Dequeued value is inserted into the Smap_tree + * 2) The newly added nodes are enqueued + * + * New quads are inserted as children to the head of the queue, which is + * then dequeued. The newly inserted nodes are enqueued in order. +**/ +Queue *smap_tree_insert_quad(Queue *q, double *cvals) +{ + int start = 0; + Node *head = dequeue(q); + Smap_tree_node *curr = (Smap_tree_node *) head->data; + // DEBUG_DOUBLE("inserting quad at", curr->coeff); + // DEBUG_ARR_F_1(cvals, 4); + // DEBUG_BLANK; + if(curr->isroot) { + start = 1; + } + for(int i = start; i < 4; i++) { + curr->children[i] = smap_tree_init_node(cvals[i]); + curr->children[i]->parent = curr; + q = enqueue(q, curr->children[i]); + } + // queue_pretty_print(q); + // printf("\n"); + return q; +} + +Smap_tree_node *smap_treeify(SBtree_node *sb_root, int levels) +{ + Queue *q = NULL; + Smap_tree_node *smap_root = smap_tree_init_root(sb_root->ll->coeffs[0], + sb_root->hl->coeffs[0], + sb_root->lh->coeffs[0], + sb_root->hh->coeffs[0]); + + // First level, enqueue the 3 valid children + for(int i = 1; i < 4; i++) { + q = enqueue(q, smap_root->children[i]); + } + + // Coeffs of all subbands in current level + double *curr_coeffs[3] = {NULL}; + int dim; + int num_quads = 0; + // Rest of the levels + for(int i = 2; i <= levels; i++) { + dim = pow(2, i-1); + num_quads = (dim*dim)/4; + double **quads = (double **) calloc(sizeof(double *), num_quads); + + curr_coeffs[0] = sb_tree_get_coeff(sb_root, HL, i); + curr_coeffs[1] = sb_tree_get_coeff(sb_root, LH, i); + curr_coeffs[2] = sb_tree_get_coeff(sb_root, HH, i); + + for(int k = 0; k < 3; k++) { + quads = quads_from_arr(curr_coeffs[k], dim, dim); + for(int j = 0; j < num_quads; j++) { + q = smap_tree_insert_quad(q, quads[j]); + } + } + free(quads); + } + free(q); + return smap_root; +} + +void smap_tree_print_levelorder(Smap_tree_node *root, enum print_conf p) { + Queue *q = NULL; + q = enqueue(q, root); + while(q->head) { + Node *qnode = dequeue(q); + Smap_tree_node *curr_smap = (Smap_tree_node *) qnode->data; + for(int i = 0; i < 4; i++) { + if(curr_smap->children[i]) { + q = enqueue(q, curr_smap->children[i]); + } + } + switch(p) { + case COEFF: + printf("%f\n", curr_smap->coeff); + break; + case TYPE: + printf("%s\n", smap_symbol_to_str(curr_smap->type)); + break; + case ALL: + printf("(%f, %s)\n", curr_smap->coeff, smap_symbol_to_str(curr_smap->type)); + break; + } + } +} + +double *smap2levelorder(Smap_tree_node *root, int rows, int cols) +{ + double *arr = (double *) calloc(rows*cols, sizeof(double)); + int i = 0; + Queue *q = NULL; + q = enqueue(q, root); + while(q->head) { + Node *qnode = dequeue(q); + Smap_tree_node *curr_smap = (Smap_tree_node *) qnode->data; + for(int i = 0; i < 4; i++) { + if(curr_smap->children[i]) { + q = enqueue(q, curr_smap->children[i]); + } + } + arr[i] = curr_smap->coeff; + i++; + } + return arr; +} + +void smap_tree_print_preorder(Smap_tree_node *root, enum print_conf p) +{ + if(root) { + switch(p) { + case COEFF: + printf("%f\n", root->coeff); + break; + case TYPE: + printf("%s\n", smap_symbol_to_str(root->type)); + break; + case ALL: + printf("(%f, %s)\n", root->coeff, smap_symbol_to_str(root->type)); + break; + } + } + if(root->children[0]) { + smap_tree_print_preorder(root->children[0], p); + } + if(root->children[1]) { + smap_tree_print_preorder(root->children[1], p); + } + if(root->children[2]) { + smap_tree_print_preorder(root->children[2], p); + } + if(root->children[3]) { + smap_tree_print_preorder(root->children[3], p); + } +} + +char* smap_symbol_to_str(enum smap_symbol s) +{ + switch(s) { + case SP: + return "SP"; + case SN: + return "SN"; + case IZ: + return "IZ"; + case ZR: + return "ZR"; + case U: + return "U"; + default: + return ""; + } +} diff --git a/src/stack.c b/src/stack.c new file mode 100644 index 0000000..c0a3daf --- /dev/null +++ b/src/stack.c @@ -0,0 +1,55 @@ +#include +#include +#include "stack.h" + +Stack *push(Stack *st, void *data) +{ + if(!st) { + st = malloc(sizeof(Stack)); + st->top = NULL; + st->bottom = NULL; + } + + Node *new_node = create_node(data); + + if(!st->top) { + st->top = new_node; + st->bottom = new_node; + } + else { + new_node->next = st->top; + st->top = new_node; + } + return st; +} + +Node *pop(Stack *st) +{ + Node *node = NULL; + if(st->top) { + node = st->top; + if(st->top == st->bottom) { + st->top = NULL; + st->bottom = NULL; + } + else { + st->top = st->top->next; + } + } + return node; +} + +/* void free_stack(Stack *st) */ +/* { */ +/* } */ +/* */ +void stack_pretty_print(Stack *st) +{ + Node *curr = st->top; + while(curr) { + printf("%d ", *(int *) curr->data); + curr = curr->next; + } + printf("\n"); +} + diff --git a/src/utils.c b/src/utils.c new file mode 100644 index 0000000..70b076a --- /dev/null +++ b/src/utils.c @@ -0,0 +1,144 @@ +#include +#include +#include "utils.h" + +void read_binary_file(FILE *infile, unsigned char *dest_arr, int rows, int cols) +{ + if(fread(dest_arr, 1, rows*cols, infile) != rows*cols) { + fprintf(stderr, "Error while reading binary file\n"); + exit(1); + } + else { + printf("Read binary file...\n"); + } +} + +void write_binary_file(FILE *outfile, unsigned char *src_arr, int rows, int cols) +{ + fwrite(src_arr, 1, rows*cols, outfile); + printf("Wrote binary file...\n"); +} + +void double_to_uchar(double *src, unsigned char* dest, int rows, int cols) +{ + for(int i = 0; i < rows; i++) { + for(int j = 0; j < cols; j++) { + dest[i*cols + j] = (unsigned char) src[i*cols + j]; + } + } +} + +double max_double(double *arr, int len) +{ + double max = 0.0; + for(int i = 0; i < len; i++) { + if(arr[i] > max) { + max = arr[i]; + } + } + return max; +} + +double** quads_from_arr(double *arr, int rows, int cols) +{ + int quadcount = (rows*cols)/4; + double **quads = (double **) calloc(sizeof(double *), quadcount); + + int count = 0; + int i = 0; + while(count < quadcount) { + double *temp = (double *) calloc(sizeof(double), 4); + temp[0] = arr[i]; + temp[1] = arr[i+1]; + temp[2] = arr[i+rows]; + temp[3] = arr[i+rows+1]; + quads[count] = temp; + if((count + 1) % (rows/2) == 0 && count != 0) { + i += (rows+2); + } + else { + i += 2; + } + count++; + } + return quads; +} + +// NOTE: decompose row and col of current element from Morton scan (level order) output +// NOTE: by "un-interleaving" the bits of the Morton index +// https://en.wikipedia.org/wiki/Z-order_curve +unsigned int* morton_decode(unsigned int morton, unsigned int *inds) +{ + const unsigned int EVEN_MASK = 2; + const unsigned int ODD_MASK = 1; + unsigned int row_bit = 0; + unsigned int col_bit = 0; + inds[0] = inds[1] = 0; + for(int i = 0; i < sizeof(morton)*4; i++) { + row_bit = (morton & EVEN_MASK) >> 1; + col_bit = morton & ODD_MASK; + row_bit <<= i; + col_bit <<= i; + inds[0] |= row_bit; + inds[1] |= col_bit; + morton >>= 2; + } + return inds; +} + +double* smap2arr(Smap_tree_node* smap_root, int rows, int cols) +{ + double *arr = (double *) calloc(rows*cols, sizeof(double)); + unsigned int *inds = calloc(2, sizeof(unsigned int)); + unsigned int i = 0; + Queue *q = NULL; + q = enqueue(q, smap_root); + while(q->head) { + Node *qnode = dequeue(q); + Smap_tree_node *curr_smap = (Smap_tree_node *) qnode->data; + for(int j = 0; j < 4; j++) { + if(curr_smap->children[j]) { + q = enqueue(q, curr_smap->children[j]); + } + } + inds = morton_decode(i, inds); + arr[inds[0]*cols + inds[1]] = curr_smap->coeff; + i++; + } + free_queue(q); + return arr; +} + +double* gsl_swap(double *arr, int rows, int cols) +{ + int *level_collection = (int *) calloc(rows, sizeof(int)); + + for(int i = 0; i < rows; i++) { + level_collection[i] = 1 + (int) log2(rows/(i+1)); + } + + level_collection[0] = log2(rows/(1)); + level_collection[1] = level_collection[0]; + + int ratio, swap_count; + double temp; + for(int i = 0; i < rows; i++) { + ratio = (rows/pow(2, level_collection[i])); + swap_count = ratio; + for(int j = 0; j < cols; j++) { + if(i == 0 || i == 1) { + break; + } + else { + if(swap_count) { + temp = arr[i*cols + j]; + arr[i*cols + j] = arr[(i - ratio)*cols + (j + ratio)]; + arr[(i - ratio)*cols + (j + ratio)] = temp; + swap_count--; + } + } + } + } + free(level_collection); + return arr; +} diff --git a/utils/eggs-16x16-coeffs-ref.txt b/utils/eggs-16x16-coeffs-ref.txt new file mode 100644 index 0000000..abec5e4 --- /dev/null +++ b/utils/eggs-16x16-coeffs-ref.txt @@ -0,0 +1,134 @@ + Level 4 + ------- + (LL) + MATRIX Order : 1 X 1 + +R0: 3248.88 :R0 + + (HL) + MATRIX Order : 1 X 1 + +R0: -154.875 :R0 + + (LH) + MATRIX Order : 1 X 1 + +R0: 129.125 :R0 + + (HH) + MATRIX Order : 1 X 1 + +R0: 79.125 :R0 +------------------------------------ + + Level 3 + ------- + (LL) + MATRIX Order : 2 X 2 + +R0: 1655.63 1447.38 :R0 +R1: 1722.38 1672.38 :R1 + + (HL) + MATRIX Order : 2 X 2 + +R0: 54.125 -136.375 :R0 +R1: -2.125 -103.875 :R1 + + (LH) + MATRIX Order : 2 X 2 + +R0: 57.625 90.875 :R0 +R1: 162.125 26.125 :R1 + + (HH) + MATRIX Order : 2 X 2 + +R0: 19.625 -16.875 :R0 +R1: 22.125 -46.625 :R1 +------------------------------------ + + Level 2 + ------- + (LL) + MATRIX Order : 4 X 4 + +R0: 893.5 816.25 692.5 618.5 :R0 +R1: 819.75 781.75 845.75 738 :R1 +R2: 952.25 768 774 794.5 :R2 +R3: 932.25 792.25 924.5 851.75 :R3 + + (HL) + MATRIX Order : 4 X 4 + +R0: 91 88.25 -173 -329 :R0 +R1: -22.75 -43.25 24.75 -35 :R1 +R2: 32.75 -12.5 -45 -63.5 :R2 +R3: -54.75 -39.75 -22.5 110.75 :R3 + + (LH) + MATRIX Order : 4 X 4 + +R0: 75 -2.75 65 -138.5 :R0 +R1: 68.75 -31.25 34.75 5 :R1 +R2: 37.25 7 -3.5 -41 :R2 +R3: 81.75 -11.25 3.5 58.25 :R3 + + (HH) + MATRIX Order : 4 X 4 + +R0: -45.5 -17.75 107.5 -108 :R0 +R1: -10.75 84.75 -101.25 -7 :R1 +R2: -63.25 22.5 114.5 82 :R2 +R3: 60.75 44.75 -57.5 -107.75 :R3 +----------------------------------- + + Level 1 + ------- + (LL) + MATRIX Order : 8 X 8 + +R0: 507 477.5 442 462.5 346 173.5 21.5 268 :R0 +R1: 461.5 341 371.5 356.5 411.5 454 458.5 489 :R1 +R2: 427.5 369.5 396 342.5 402 468.5 350.5 352.5 :R2 +R3: 461 381.5 354.5 470.5 478.5 342.5 392.5 380.5 :R3 +R4: 479.5 505.5 392.5 363 420 309 386 345 :R4 +R5: 510 409.5 382.5 398 350.5 468.5 367.5 490.5 :R5 +R6: 510 367.5 393 359.5 424 478 456.5 506 :R6 +R7: 504 483 388 444 504 443 453.5 287.5 :R7 + + (HL) + MATRIX Order : 8 X 8 + +R0: -3 30.5 67 47.5 -164 -132.5 -21.5 -189 :R0 +R1: 33.5 -25 -18.5 -28.5 13.5 -54 -37.5 21 :R1 +R2: -16.5 16.5 -10 34.5 -3 35.5 -1.5 -23.5 :R2 +R3: 39 -49.5 -71.5 -39.5 3.5 3.5 2.5 5.5 :R3 +R4: -27.5 4.5 71.5 -4 33 28 8 1 :R4 +R5: 0 22.5 -8.5 0 4.5 -41.5 -43.5 -15.5 :R5 +R6: 0 -1.5 2 27.5 -37 17 -20.5 0 :R6 +R7: -4 -27 -67 -57 3 -5 35.5 137.5 :R7 + + (LH) + MATRIX Order : 8 X 8 + +R0: 3 21.5 0 -15.5 41 122.5 -21.5 -66 :R0 +R1: 48.5 -20 -1.5 17.5 -58.5 35 -37.5 -17 :R1 +R2: 70.5 -19.5 4 29.5 -65 34.5 -8.5 18.5 :R2 +R3: 1 30.5 -26.5 -25.5 31.5 -5.5 6.5 8.5 :R3 +R4: -17.5 4.5 27.5 6 -31 -8 5 7 :R4 +R5: 0 68.5 -15.5 -12 -39.5 39.5 6.5 -14.5 :R5 +R6: 0 65.5 -1 23.5 -66 32 -39.5 0 :R6 +R7: -2 27 -1 -27 2 67 -55.5 117.5 :R7 + + (HH) + MATRIX Order : 8 X 8 + +R0: 3 -23.5 1 15.5 41 -81.5 21.5 -13 :R0 +R1: -33.5 28 -3.5 0.5 27.5 37 -51.5 17 :R1 +R2: 4.5 19.5 -4 3.5 -32 -28.5 31.5 -15.5 :R2 +R3: 9 -4.5 19.5 -25.5 -3.5 11.5 2.5 -10.5 :R3 +R4: -20.5 -4.5 16.5 -3 42 -37 -3 47 :R4 +R5: 0 5.5 -20.5 0 -1.5 39.5 -10.5 -18.5 :R5 +R6: 0 -19.5 12 -16.5 -17 -17 -6.5 4 :R6 +R7: -2.02061e-14 27 -12 -18 1 5 34.5 -32.5 :R7 diff --git a/utils/eggs-8x8-coeffs-ref.txt b/utils/eggs-8x8-coeffs-ref.txt new file mode 100644 index 0000000..30c40a4 --- /dev/null +++ b/utils/eggs-8x8-coeffs-ref.txt @@ -0,0 +1,83 @@ + Level 3 + ------- + (LL) + MATRIX Order : 1 X 1 + +R0: 1447.38 :R0 + + (HL) + MATRIX Order : 1 X 1 + +R0: -136.375 :R0 + + (LH) + MATRIX Order : 1 X 1 + +R0: 90.875 :R0 + + (HH) + MATRIX Order : 1 X 1 + +R0: -16.875 :R0 +------------------------------------ + + Level 2 + ------- + (LL) + MATRIX Order : 2 X 2 + +R0: 692.5 618.5 :R0 +R1: 845.75 738 :R1 + + (HL) + MATRIX Order : 2 X 2 + +R0: -173 -329 :R0 +R1: 24.75 -35 :R1 + + (LH) + MATRIX Order : 2 X 2 + +R0: 65 -138.5 :R0 +R1: 34.75 5 :R1 + + (HH) + MATRIX Order : 2 X 2 + +R0: 107.5 -108 :R0 +R1: -101.25 -7 :R1 +----------------------------------- + + Level 1 + ------- + (LL) + MATRIX Order : 4 X 4 + +R0: 346 173.5 21.5 268 :R0 +R1: 411.5 454 458.5 489 :R1 +R2: 402 468.5 350.5 352.5 :R2 +R3: 478.5 342.5 392.5 380.5 :R3 + + (HL) + MATRIX Order : 4 X 4 + +R0: -164 -132.5 -21.5 -189 :R0 +R1: 13.5 -54 -37.5 21 :R1 +R2: -3 35.5 -1.5 -23.5 :R2 +R3: 3.5 3.5 2.5 5.5 :R3 + + (LH) + MATRIX Order : 4 X 4 + +R0: 41 122.5 -21.5 -66 :R0 +R1: -58.5 35 -37.5 -17 :R1 +R2: -65 34.5 -8.5 18.5 :R2 +R3: 31.5 -5.5 6.5 8.5 :R3 + + (HH) + MATRIX Order : 4 X 4 + +R0: 41 -81.5 21.5 -13 :R0 +R1: 27.5 37 -51.5 17 :R1 +R2: -32 -28.5 31.5 -15.5 :R2 +R3: -3.5 11.5 2.5 -10.5 :R3 diff --git a/utils/eggs_16x16_wavelet_decomposition_with_tree.xopp b/utils/eggs_16x16_wavelet_decomposition_with_tree.xopp new file mode 100644 index 0000000..566e2c2 Binary files /dev/null and b/utils/eggs_16x16_wavelet_decomposition_with_tree.xopp differ diff --git a/utils/eggs_16x16_wavelet_decomposition_with_tree.xopp~ b/utils/eggs_16x16_wavelet_decomposition_with_tree.xopp~ new file mode 100644 index 0000000..05b7f28 Binary files /dev/null and b/utils/eggs_16x16_wavelet_decomposition_with_tree.xopp~ differ diff --git a/utils/eggs_wavelet_decomposition - 16x16.csv b/utils/eggs_wavelet_decomposition - 16x16.csv new file mode 100644 index 0000000..5780615 --- /dev/null +++ b/utils/eggs_wavelet_decomposition - 16x16.csv @@ -0,0 +1,16 @@ +3248.88,-154.875,54.125,-136.375,91,88.25,-173,-329,-3,30.5,67,47.5,-164,-132.5,-21.5,-189 +129.125,79.125,-2.125,-103.875,-22.75,-43.25,25.75,-35,33.5,-25,-15.5,28.5,13.5,-54,-37.5,21 +57.625,90.875,19.625,-16.875,32.75,-12.5,-45,-63.5,-16.5,16.5,-10,34.5,-3,35.5,-1.5,-23.5 +162.125,26.125,22.125,-46.625,-54.75,-39.75,-22.5,110.75,39,-49.5,-71.5,-39.5,3.5,3.5,2.5,5.5 +75,-1.75,65,-138.5,-45.5,-17.75,107.5,-108,-27.5,4.5,71.5,-4,33,28,8,1 +68.75,-31.25,34.5,5,-10.75,84.75,-101.25,-7,0,22.5,-8.5,0,405,-41.5,-43.5,-15.5 +37.25,7,-3.5,-41,-63.25,22.5,114.5,82,0,-1.5,2,27.5,-37,17,-20.5,0 +81.75,-11.25,3.5,58.25,60.75,44.75,-57.5,-107.75,-4,-27,-67,-57,3,-5,35.5,137.5 +3,21.5,0,-15.5,41,122.5,-21.5,-66,3,-23.5,1,15.5,41,-81.5,21.5,-13 +48.5,-20,-1.5,17.5,-58.5,35,-37.5,-17,-33.5,28,-3.5,0.5,27.5,37,-51.5,17 +70.5,-19.5,4,29.5,-65,34.5,-8.5,18.5,4.5,19.5,-4,3.5,-32,-28.5,31.5,-15.5 +1,30.5,-26.5,-25.5,31.5,-5.5,6.5,8.5,9,-4.5,19.5,-25.5,-3.5,11.5,2.5,-10.5 +-17.5,4.5,27.5,6,-31,-8,5,7,-20.5,-4.5,16.5,-3,42,-37,-3,47 +0,68.5,-15.5,-12,-39.5,39.5,6.5,-14.5,0,5.5,-20.5,0,-1.5,39.5,-10.5,-18.5 +0,65.5,-1,23.5,-66,32,-39.5,0,0,-19.5,12,-16.5,-17,-17,-6.5,4 +-2,27,-1,-27,2,67,-55.5,117.5,0,27,-12,-18,1,5,34.5,-32.5 \ No newline at end of file diff --git a/utils/eggs_wavelet_decomposition-16x16.pdf b/utils/eggs_wavelet_decomposition-16x16.pdf new file mode 100644 index 0000000..4af43c1 Binary files /dev/null and b/utils/eggs_wavelet_decomposition-16x16.pdf differ diff --git a/utils/eggs_wavelet_decomposition-8x8.pdf b/utils/eggs_wavelet_decomposition-8x8.pdf new file mode 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new file mode 100644 index 0000000..6021a41 Binary files /dev/null and b/utils/eggs_wavelet_decomposition-8x8_with_tree_sp.xopp~ differ diff --git a/utils/get_gscale_raw.py b/utils/get_gscale_raw.py new file mode 100755 index 0000000..227ec5b --- /dev/null +++ b/utils/get_gscale_raw.py @@ -0,0 +1,28 @@ +#!/usr/bin/env python3 +from PIL import Image +from sys import argv + +ifname = argv[1] +ofname = ifname + ".bin" + +img = Image.open(ifname).convert('L') +WIDTH, HEIGHT = img.size + +data = list(img.getdata()) +data_bytes = bytes(img.getdata()) +# data = [data[offset:offset+WIDTH] for offset in range(0, WIDTH*HEIGHT, WIDTH)] + +with open(ofname, "wb") as f: + f.write(data_bytes) +# for row in data: +# for value in row: +# # print(' '.join('{:3}'.format(value)), end='') +# print(str(value) + ',', end='') +# print() + +# chars = '@%#*+=-:. ' # Change as desired. +# scale = (len(chars)-1)/255. +# for row in data: +# for value in row: +# print(chars[int(value*scale)], end='') +# print() diff --git a/utils/gimp/eggs-16x16.xcf b/utils/gimp/eggs-16x16.xcf new file mode 100644 index 0000000..22aa9c4 Binary files /dev/null and b/utils/gimp/eggs-16x16.xcf differ diff --git a/utils/gimp/eggs-8x8.xcf b/utils/gimp/eggs-8x8.xcf new file mode 100644 index 0000000..8c371c2 Binary files /dev/null and b/utils/gimp/eggs-8x8.xcf differ diff --git a/utils/gsl_swap.c b/utils/gsl_swap.c new file mode 100644 index 0000000..8977ba6 --- /dev/null +++ b/utils/gsl_swap.c @@ -0,0 +1,145 @@ +#include +#include +#include + +#define SIZE 16 +#define BASE 2 + +int level_collection[SIZE]; // Collection of decomposition levels of first element of each row +double new_2D_arr[SIZE][SIZE]; // 2D Array form of the original linear array +double final_2D_arr[SIZE][SIZE]; // Final array after swapping +double final_arr[SIZE * SIZE]; // Final swapped 1D array in row-major addressing + +// void swap_decision(int[], double[][], int); // Decides if the element has to be swapped or not and performs the swap if necessary +// void find_levels(double[], int); +// void row_majorize(double[][], int); + +// void swap_decision(int[], double[][SIZE], int); // Decides if the element has to be swapped or not and performs the swap if necessary +// void row_majorize(double[][], int); +// void find_levels(double[][], int); +/* + * Converts arr[SIZE * SIZE] into 2D array of SIZE x SIZE + * Assigns the level of decomposition of first element of each row + * */ + +double arr[SIZE * SIZE] = { + 3248.88,-154.875,57.625,90.875,75,-1.75,65,-138.5,3,21.5,0,-15.5,41,122.5,-21.5,-66, + 129.125,79.125,162.125,26.125,68.75,-31.25,34.5,5,48.5,-20,-1.5,17.5,-58.5,35,-37.5,-17, + 54.125,-136.375,19.625,-16.875,37.25,7,-3.5,-41,70.5,-19.5,4,29.5,-65,34.5,-8.5,18.5, + -2.125,-103.875,22.125,-46.625,81.75,-11.25,3.5,58.25,1,30.5,-26.5,-25.5,31.5,-5.5,6.5,8.5, + 91,88.25,-173,-329,-45.5,-17.75,107.5,-108,-17.5,4.5,27.5,6,-31,-8,5,7, + -22.75,-43.25,25.75,-35,-10.75,84.75,-101.25,-7,0,68.5,-15.5,-12,-39.5,39.5,6.5,-14.5, + 32.75,-12.5,-45,-63.5,-63.25,22.5,114.5,82,0,65.5,-1,23.5,-66,32,-39.5,0, + -54.75,-39.75,-22.5,110.75,60.75,44.75,-57.5,-107.75,-2,27,-1,-27,2,67,-55.5,117.5, + -3,30.5,67,47.5,-164,-132.5,-21.5,-189,3,-23.5,1,15.5,41,-81.5,21.5,-13, + 33.5,-25,-15.5,28.5,13.5,-54,-37.5,21,-33.5,28,-3.5,0.5,27.5,37,-51.5,17, + -16.5,16.5,-10,34.5,-3,35.5,-1.5,-23.5,4.5,19.5,-4,3.5,-32,-28.5,31.5,-15.5, + 39,-49.5,-71.5,-39.5,3.5,3.5,2.5,5.5,9,-4.5,19.5,-25.5,-3.5,11.5,2.5,-10.5, + -27.5,4.5,71.5,-4,33,28,8,1,-20.5,-4.5,16.5,-3,42,-37,-3,47, + 0,22.5,-8.5,0,405,-41.5,-43.5,-15.5,0,5.5,-20.5,0,-1.5,39.5,-10.5,-18.5, + 0,-1.5,2,27.5,-37,17,-20.5,0,0,-19.5,12,-16.5,-17,-17,-6.5,4, + -4,-27,-67,-57,3,-5,35.5,137.5,0,27,-12,-18,1,5,34.5,-32.5, + }; + + +//double arr[SIZE * SIZE] = { +// 1447.38,-136.375,65,-138.5,41,122.5,-21.5,-66, +// 90.875,-16.875,34.75,5,-58.5,35,-37.5,-17, +// -173,-329,107.5,-108,-65,34.5,-8.5,18.5, +// 24.75,-35,-101.25,-7,31.5,-5.5,6.5,8.5, +// -164,-132.5,-21.5,-189,41,-81.5,21.5,-13, +// 13.5,-54,-37.5,21,27.5,37,-51.5,17, +// -3,35.5,-1.5,-23.5,-32,-28.5,31.5,-15.5, +// 3.5,3.5,2.5,5.5,-3.5,11.5,2.5,-10.5, +// }; + +void find_levels(double arr[] /*,int size*/) +{ + printf("This is the original 2D array\n\n"); + + for(int i = 0; i < SIZE; i++) + { + level_collection[i] = 1 + log2(SIZE/(i+1)); + } + + level_collection[0] = log2(SIZE/(1)); + level_collection[1] = level_collection[0]; + + printf("\n\n"); + for(int i = 0; i < SIZE; i++) + printf("%d\t", level_collection[i]); +} +// REFACTOR: +// + Remove globals and pass as parameters +// + Why do we have multiple copies of the ratio +void swap_decision(int level_collection[SIZE], double new_2D_arr[][SIZE], int size) +{ + int ratio, temp_ratio; + +// printf("This is the 2D array after swapping\n\n"); + + for(int i = 0; i < size; i++) + { + ratio = (SIZE/pow(2, level_collection[i])); + temp_ratio = ratio; + + for(int j = 0; j < SIZE; j++) + { + if(i == 0 || i == 1) + { + final_2D_arr[i][j] = new_2D_arr[i + ratio][j - ratio]; + } + else + { + if(ratio) + { + final_2D_arr[i][j] = new_2D_arr[i + ratio][j - ratio]; + ratio--; + } + else if(temp_ratio) + { + final_2D_arr[i][j] = new_2D_arr[i][j]; + temp_ratio--; + } + else + { + final_2D_arr[i][j] = new_2D_arr[i + ratio][j - ratio]; + } + } + printf("%.2f\t", final_2D_arr[i][j]); + } + /*final_2D_arr[0][0] = new_2D_arr[0][0];*/ + /*final_2D_arr[0][1] = new_2D_arr[0][1];*/ + /*final_2D_arr[1][0] = new_2D_arr[1][0];*/ + /*final_2D_arr[1][1] = new_2D_arr[1][1];*/ + printf("\n"); + } +} + +void row_majorize(double final_2D_arr[][SIZE], int size) +{ + printf("This is the final swapped 1D array printed as 2D array after converting to row-major\n\n"); + + for(int i = 0; i < size; i++) + { + for(int j = 0; j < SIZE; j++) + { + final_arr[i*size + j] = final_2D_arr[i][j]; + printf("%.2f\t", final_2D_arr[i][j]); + } + printf("\n"); + } +} + +int main() +{ + find_levels(arr/*,SIZE*/); + printf("\n\n"); + swap_decision(level_collection, new_2D_arr, SIZE); + printf("\n\n"); + row_majorize(final_2D_arr, SIZE); + printf("\n\n"); + + return 0; +} + diff --git a/utils/img/Lichtenstein_img_processing_test_bw.png b/utils/img/Lichtenstein_img_processing_test_bw.png new file mode 100644 index 0000000..0ab9cc1 Binary files /dev/null and b/utils/img/Lichtenstein_img_processing_test_bw.png differ diff --git a/utils/img/circles.svg b/utils/img/circles.svg new file mode 100644 index 0000000..033d2bc --- /dev/null +++ b/utils/img/circles.svg @@ -0,0 +1,109 @@ + + + + + + + + + + + + + + + diff --git a/utils/img/eggs-16x16.png b/utils/img/eggs-16x16.png new file mode 100644 index 0000000..e12ed7b Binary files /dev/null and b/utils/img/eggs-16x16.png differ diff --git a/utils/img/eggs-8x8.png b/utils/img/eggs-8x8.png new file mode 100644 index 0000000..bb45d54 Binary files 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b/utils/lichtenstein_gscale_raw.txt new file mode 100644 index 0000000..bf4ec2a --- /dev/null +++ b/utils/lichtenstein_gscale_raw.txt @@ -0,0 +1,512 @@ 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diff --git a/utils/notes.jpeg b/utils/notes.jpeg new file mode 100644 index 0000000..5670f9c Binary files /dev/null and b/utils/notes.jpeg differ diff --git a/utils/pywt_verif.py b/utils/pywt_verif.py new file mode 100644 index 0000000..1f33e2f --- /dev/null +++ b/utils/pywt_verif.py @@ -0,0 +1,22 @@ +#! /usr/bin/env python3 + +import numpy +import pywt +from pprint import pprint +arr = [] +i = 0 +with open("imgbin/eggs-8x8.png.bin", "rb") as f: + byte = f.read(1) + while byte: + arr.append(int.from_bytes(byte, "big")) + byte = f.read(1) + +# print(arr) + +arr1 = numpy.reshape(arr, (8,8)) +pprint(arr1) + +coeffs = pywt.wavedec2(arr1,'haar') +pprint(coeffs) + +f.close() diff --git a/wavelib b/wavelib new file mode 160000 index 0000000..c1f86a8 --- /dev/null +++ b/wavelib @@ -0,0 +1 @@ +Subproject commit c1f86a8b9c95749ef8a46a4593fad8241064b947