\documentclass[11pt,twoside]{article}\makeatletter \IfFileExists{xcolor.sty}% {\RequirePackage{xcolor}}% {\RequirePackage{color}} \usepackage{colortbl} \usepackage{wrapfig} \usepackage{ifxetex} \ifxetex \usepackage{fontspec} \usepackage{xunicode} \catcode`⃥=\active \def⃥{\textbackslash} \catcode`❴=\active \def❴{\{} \catcode`❵=\active \def❵{\}} \def\textJapanese{\fontspec{Noto Sans CJK JP}} \def\textChinese{\fontspec{Noto Sans CJK SC}} \def\textKorean{\fontspec{Noto Sans CJK KR}} \setmonofont{DejaVu Sans Mono} \else \IfFileExists{utf8x.def}% {\usepackage[utf8x]{inputenc} \PrerenderUnicode{–} }% {\usepackage[utf8]{inputenc}} \usepackage[english]{babel} \usepackage[T1]{fontenc} \usepackage{float} \usepackage[]{ucs} \uc@dclc{8421}{default}{\textbackslash } \uc@dclc{10100}{default}{\{} \uc@dclc{10101}{default}{\}} \uc@dclc{8491}{default}{\AA{}} \uc@dclc{8239}{default}{\,} \uc@dclc{20154}{default}{ } \uc@dclc{10148}{default}{>} \def\textschwa{\rotatebox{-90}{e}} \def\textJapanese{} \def\textChinese{} \IfFileExists{tipa.sty}{\usepackage{tipa}}{} \fi \def\exampleFont{\ttfamily\small} \DeclareTextSymbol{\textpi}{OML}{25} \usepackage{relsize} \RequirePackage{array} \def\@testpach{\@chclass \ifnum \@lastchclass=6 \@ne \@chnum \@ne \else \ifnum \@lastchclass=7 5 \else \ifnum \@lastchclass=8 \tw@ \else \ifnum \@lastchclass=9 \thr@@ \else \z@ \ifnum \@lastchclass = 10 \else \edef\@nextchar{\expandafter\string\@nextchar}% \@chnum \if \@nextchar c\z@ \else \if \@nextchar l\@ne \else \if \@nextchar r\tw@ \else \z@ \@chclass \if\@nextchar |\@ne \else \if \@nextchar !6 \else \if \@nextchar @7 \else \if \@nextchar (8 \else \if \@nextchar )9 \else 10 \@chnum \if \@nextchar m\thr@@\else \if \@nextchar p4 \else \if \@nextchar b5 \else \z@ \@chclass \z@ \@preamerr \z@ \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi} \gdef\arraybackslash{\let\\=\@arraycr} \def\@textsubscript#1{{\m@th\ensuremath{_{\mbox{\fontsize\sf@size\z@#1}}}}} \def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}} \def\abbr{} \def\corr{} \def\expan{} \def\gap{} \def\orig{} \def\reg{} \def\ref{} \def\sic{} \def\persName{}\def\name{} \def\placeName{} \def\orgName{} \def\textcal#1{{\fontspec{Lucida Calligraphy}#1}} \def\textgothic#1{{\fontspec{Lucida Blackletter}#1}} \def\textlarge#1{{\large #1}} \def\textoverbar#1{\ensuremath{\overline{#1}}} \def\textquoted#1{‘#1’} \def\textsmall#1{{\small #1}} \def\textsubscript#1{\@textsubscript{\selectfont#1}} \def\textxi{\ensuremath{\xi}} \def\titlem{\itshape} \newenvironment{biblfree}{}{\ifvmode\par\fi } \newenvironment{bibl}{}{} \newenvironment{byline}{\vskip6pt\itshape\fontsize{16pt}{18pt}\selectfont}{\par } \newenvironment{citbibl}{}{\ifvmode\par\fi } \newenvironment{docAuthor}{\ifvmode\vskip4pt\fontsize{16pt}{18pt}\selectfont\fi\itshape}{\ifvmode\par\fi } \newenvironment{docDate}{}{\ifvmode\par\fi } \newenvironment{docImprint}{\vskip 6pt}{\ifvmode\par\fi } \newenvironment{docTitle}{\vskip6pt\bfseries\fontsize{22pt}{25pt}\selectfont}{\par } \newenvironment{msHead}{\vskip 6pt}{\par} \newenvironment{msItem}{\vskip 6pt}{\par} \newenvironment{rubric}{}{} \newenvironment{titlePart}{}{\par } \newcolumntype{L}[1]{){\raggedright\arraybackslash}p{#1}} \newcolumntype{C}[1]{){\centering\arraybackslash}p{#1}} \newcolumntype{R}[1]{){\raggedleft\arraybackslash}p{#1}} \newcolumntype{P}[1]{){\arraybackslash}p{#1}} \newcolumntype{B}[1]{){\arraybackslash}b{#1}} \newcolumntype{M}[1]{){\arraybackslash}m{#1}} \definecolor{label}{gray}{0.75} \def\unusedattribute#1{\sout{\textcolor{label}{#1}}} \DeclareRobustCommand*{\xref}{\hyper@normalise\xref@} \def\xref@#1#2{\hyper@linkurl{#2}{#1}} \begingroup \catcode`\_=\active \gdef_#1{\ensuremath{\sb{\mathrm{#1}}}} \endgroup \mathcode`\_=\string"8000 \catcode`\_=12\relax \usepackage[a4paper,twoside,lmargin=1in,rmargin=1in,tmargin=1in,bmargin=1in,marginparwidth=0.75in]{geometry} \usepackage{framed} \definecolor{shadecolor}{gray}{0.95} \usepackage{longtable} \usepackage[normalem]{ulem} \usepackage{fancyvrb} \usepackage{fancyhdr} \usepackage{graphicx} \usepackage{marginnote} \renewcommand{\@cite}[1]{#1} \renewcommand*{\marginfont}{\itshape\footnotesize} \def\Gin@extensions{.pdf,.png,.jpg,.mps,.tif} \pagestyle{fancy} \usepackage[pdftitle={A Critical Performance Evaluation of Classification Methods with Modified JPEG Decompressed Multiband Images}, pdfauthor={}]{hyperref} \hyperbaseurl{} \paperwidth210mm \paperheight297mm \def\@pnumwidth{1.55em} \def\@tocrmarg {2.55em} \def\@dotsep{4.5} \setcounter{tocdepth}{3} \clubpenalty=8000 \emergencystretch 3em \hbadness=4000 \hyphenpenalty=400 \pretolerance=750 \tolerance=2000 \vbadness=4000 \widowpenalty=10000 \renewcommand\section{\@startsection {section}{1}{\z@}% {-1.75ex \@plus -0.5ex \@minus -.2ex}% {0.5ex \@plus .2ex}% {\reset@font\Large\bfseries}} \renewcommand\subsection{\@startsection{subsection}{2}{\z@}% {-1.75ex\@plus -0.5ex \@minus- .2ex}% {0.5ex \@plus .2ex}% {\reset@font\Large}} \renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% {-1.5ex\@plus -0.35ex \@minus -.2ex}% {0.5ex \@plus .2ex}% {\reset@font\large}} \renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}% {-1ex \@plus-0.35ex \@minus -0.2ex}% {0.5ex \@plus .2ex}% {\reset@font\normalsize}} \renewcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}% {1.5ex \@plus1ex \@minus .2ex}% {-1em}% {\reset@font\normalsize\bfseries}} \def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{1.0em plus 1pt} \@tempdima 1.5em \begingroup \parindent \z@ \rightskip \@pnumwidth \parfillskip -\@pnumwidth \bfseries \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}\par \endgroup} \def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}} \def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}} \def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}} \def\l@subparagraph{\@dottedtocline{5}{10em}{5em}} \@ifundefined{c@section}{\newcounter{section}}{} \@ifundefined{c@chapter}{\newcounter{chapter}}{} \newif\if@mainmatter \@mainmattertrue \def\chaptername{Chapter} \def\frontmatter{% \pagenumbering{roman} \def\thechapter{\@roman\c@chapter} \def\theHchapter{\roman{chapter}} \def\thesection{\@roman\c@section} \def\theHsection{\roman{section}} \def\@chapapp{}% } \def\mainmatter{% \cleardoublepage \def\thechapter{\@arabic\c@chapter} \setcounter{chapter}{0} \setcounter{section}{0} \pagenumbering{arabic} \setcounter{secnumdepth}{6} \def\@chapapp{\chaptername}% \def\theHchapter{\arabic{chapter}} \def\thesection{\@arabic\c@section} \def\theHsection{\arabic{section}} } \def\backmatter{% \cleardoublepage \setcounter{chapter}{0} \setcounter{section}{0} \setcounter{secnumdepth}{2} \def\@chapapp{\appendixname}% \def\thechapter{\@Alph\c@chapter} \def\theHchapter{\Alph{chapter}} \appendix } \newenvironment{bibitemlist}[1]{% \list{\@biblabel{\@arabic\c@enumiv}}% {\settowidth\labelwidth{\@biblabel{#1}}% \leftmargin\labelwidth \advance\leftmargin\labelsep \@openbib@code \usecounter{enumiv}% \let\p@enumiv\@empty \renewcommand\theenumiv{\@arabic\c@enumiv}% }% \sloppy \clubpenalty4000 \@clubpenalty \clubpenalty \widowpenalty4000% \sfcode`\.\@m}% {\def\@noitemerr {\@latex@warning{Empty `bibitemlist' environment}}% \endlist} \def\tableofcontents{\section*{\contentsname}\@starttoc{toc}} \parskip0pt \parindent1em \def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}} \newenvironment{reflist}{% \begin{raggedright}\begin{list}{} {% \setlength{\topsep}{0pt}% \setlength{\rightmargin}{0.25in}% \setlength{\itemsep}{0pt}% \setlength{\itemindent}{0pt}% \setlength{\parskip}{0pt}% \setlength{\parsep}{2pt}% \def\makelabel##1{\itshape ##1}}% } {\end{list}\end{raggedright}} \newenvironment{sansreflist}{% \begin{raggedright}\begin{list}{} {% \setlength{\topsep}{0pt}% \setlength{\rightmargin}{0.25in}% \setlength{\itemindent}{0pt}% \setlength{\parskip}{0pt}% \setlength{\itemsep}{0pt}% \setlength{\parsep}{2pt}% \def\makelabel##1{\upshape ##1}}% } {\end{list}\end{raggedright}} \newenvironment{specHead}[2]% {\vspace{20pt}\hrule\vspace{10pt}% \phantomsection\label{#1}\markright{#2}% \pdfbookmark[2]{#2}{#1}% \hspace{-0.75in}{\bfseries\fontsize{16pt}{18pt}\selectfont#2}% }{} \def\TheFullDate{2013-01-15 (revised: 15 January 2013)} \def\TheID{\makeatother } \def\TheDate{2013-01-15} \title{A Critical Performance Evaluation of Classification Methods with Modified JPEG Decompressed Multiband Images} \author{}\makeatletter \makeatletter \newcommand*{\cleartoleftpage}{% \clearpage \if@twoside \ifodd\c@page \hbox{}\newpage \if@twocolumn \hbox{}\newpage \fi \fi \fi } \makeatother \makeatletter \thispagestyle{empty} \markright{\@title}\markboth{\@title}{\@author} \renewcommand\small{\@setfontsize\small{9pt}{11pt}\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@ \belowdisplayskip \abovedisplayskip \abovedisplayshortskip \z@ plus2\p@ \belowdisplayshortskip 4\p@ plus2\p@ minus2\p@ \def\@listi{\leftmargin\leftmargini \topsep 2\p@ plus1\p@ minus1\p@ \parsep 2\p@ plus\p@ minus\p@ \itemsep 1pt} } \makeatother \fvset{frame=single,numberblanklines=false,xleftmargin=5mm,xrightmargin=5mm} \fancyhf{} \setlength{\headheight}{14pt} \fancyhead[LE]{\bfseries\leftmark} \fancyhead[RO]{\bfseries\rightmark} \fancyfoot[RO]{} \fancyfoot[CO]{\thepage} \fancyfoot[LO]{\TheID} \fancyfoot[LE]{} \fancyfoot[CE]{\thepage} \fancyfoot[RE]{\TheID} \hypersetup{citebordercolor=0.75 0.75 0.75,linkbordercolor=0.75 0.75 0.75,urlbordercolor=0.75 0.75 0.75,bookmarksnumbered=true} \fancypagestyle{plain}{\fancyhead{}\renewcommand{\headrulewidth}{0pt}} \date{} \usepackage{authblk} \providecommand{\keywords}[1] { \footnotesize \textbf{\textit{Index terms---}} #1 } \usepackage{graphicx,xcolor} \definecolor{GJBlue}{HTML}{273B81} \definecolor{GJLightBlue}{HTML}{0A9DD9} \definecolor{GJMediumGrey}{HTML}{6D6E70} \definecolor{GJLightGrey}{HTML}{929497} \renewenvironment{abstract}{% \setlength{\parindent}{0pt}\raggedright \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}} \vskip16pt \textcolor{GJBlue}{\large\bfseries\abstractname\space} }{% \vskip8pt \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}} \vskip16pt } \usepackage[absolute,overlay]{textpos} \makeatother \usepackage{lineno} \linenumbers \begin{document} \author[1]{Ch. Ramesh} \author[2]{Dr. N.B. Venkateswarlus} \author[3]{Dr. J.V.R. Murthy} \affil[1]{ Aditya Institute of Technology and Management/JNTUK} \renewcommand\Authands{ and } \date{\small \em Received: 15 December 2012 Accepted: 1 January 2013 Published: 15 January 2013} \maketitle \begin{abstract} Effective utilization of bandwidth andstorage space is important in imaging applicationsincluding remote sensing. Remote sensingapplications use multi-sensory, multi-band, multiresolution images. Usually, remote sensingapplications uses image classification results fortheir analysis and decision making. In this paper wepropose a new JPEG based image compressionalgorithm based on filters. Proposed algorithmperformance is evaluated in relation to conventionalJPEG algorithm. In order to envisage the effect ofcompression on classification performance, MaximumLikelihood, Mahalanobis and Euclidean distanceclassifiers performance is evaluated with originalimage data, conventional JPEG compressed data andthe compressed image data with the proposedmethod. Experiments are carried out with manymulti-band images. Our experiments supports thatthe classification accuracies of compressed imagesare at par with original image data. \end{abstract} \keywords{joint photo experts group (jpeg), filters, maximum likelihood, mahalanobis, euclidean, confusion matrix, kappa coefficient.} \begin{textblock*}{18cm}(1cm,1cm) % {block width} (coords) \textcolor{GJBlue}{\LARGE Global Journals \LaTeX\ JournalKaleidoscope\texttrademark} \end{textblock*} \begin{textblock*}{18cm}(1.4cm,1.5cm) % {block width} (coords) \textcolor{GJBlue}{\footnotesize \\ Artificial Intelligence formulated this projection for compatibility purposes from the original article published at Global Journals. However, this technology is currently in beta. \emph{Therefore, kindly ignore odd layouts, missed formulae, text, tables, or figures.}} \end{textblock*} \let\tabcellsep& \section[{Introduction}]{Introduction}\par n the recent years use of remote sensingsatellite data for urban planning, military,weather forecast, robotics, automatednavigation system, remote surveillance hasincreased by many fold in addition toconventional applications such as naturalresources management. These applications involve acquisition, communication, storage and processing ofterrible number of images of earth surface.This situation is becoming more aggravatedbecause of increased pixel resolution, graylevel resolution, band resolutions and reducedrepetition cycle of satellite. All of these development demands more band width fordownlink lines of satellite in addition to moredisk space for storage.\par In communications, data compression techniques under the name hood of imagecoding are widely used to reduce thecommunication bandwidth bottlenecks duringdata communication. For instance, JPEGstandard is used for still image compression \hyperref[b0]{[1]}, MPEG is used for video compression \hyperref[b1]{[2]}. Also, while communicating data from satellites toground stations some compression methods areused \hyperref[b2]{[3]}.\par A typical image processing system isas shown in Figure \hyperref[fig_0]{1} that is commonlyemployed for remote sensing applications. It isvery common that most of the applicationscientists using original image data for theirprocessing. In majority of remote sensing applications, results of classification are theultimate interest \hyperref[b3]{[4]}.\par In this study, we propose to study howthe classification results will vary if we usecompressed image data instead of originalimage data. Usually applications such as landuse classifications assumes samples of a groupwill be having small random variations in theirpixel values while samples of different groupsto be having contrastingly different pixelvalues. Because of the increased pixel and graylevel resolutions, samples of a group may behaving similar pixel values. Moreover, they willbe having high level of spatial auto correlation.Evidently, majority of compression methods exploits this auto correlation to achieve highcompression ratios with acceptable PSNR (PeakSignal to Noise Ratio) values \hyperref[b4]{[5]}.\par Our proposed Algorithm is based onfiltering concept \hyperref[b5]{[6]}. In this Algorithm insteadof sending the original image, we send thefiltered image. In general, the number ofuseful DCT coefficients will become more if 8x8image blocks contain lot of variations in values,otherwise only few DCT coefficients will bemeaningful. If we apply filtering on image itgets smoothened, that is variation of the pixelvalues of a block reduces. It is attractive forpoint of view of compression as the number ofmeaningful DCT coefficients are going toreduce. Thus we are achieving compression benefit. We have compared the compression performance of our algorithm with conventional JPEG algorithm with variety ofmulti band images.\par Also in this study, we evaluate theclassification performance of popularclassification algorithms like Maximum Likelihood, Mahalanobis and Euclidian distanceby taking original image data, conventional Our paper work is organized as follows.Section II introduces the standard JPEGalgorithm. Section III explains proposedcompression algorithm. Section IV illustratesthe selected classification algorithms. Section Vincludes details about our experimentationsand results. Section VI contains conclusionsabout our research work II. \section[{Brief Overview of JPEG Encoding/ Decoding System}]{Brief Overview of JPEG Encoding/ Decoding System}\par JPEG is a well known standardized image compression technique. JPEG loses informationso the decompressed picture is not the same asthe original one. The main reason for use ofJPEG is to reduce the size of image files.Reducing image files is an important procedurefor transmitting files across networks orarchiving libraries. Usually JPEG can removethe less important data before thecompression; hence JPEG is able to compressimages meaningfully, which produces a hugedifference in the transmission time and the diskspace. Figure {\ref 2} shows the basic Architecture ofJPEG compression system. Here is a briefoverview of the JPEG compression system. \hyperref[b4]{[5]} The image is first subdivided into pixelblocks of size 8X8, which are processed left toright, top to bottom. As each 8X8 block or subimage is encountered, its 64 pixels are levelshifted by subtracting the quantity L/2, whereL is the Gray level resolution of the image . The2-D Forward Discrete Cosine Transform (FDCT)(Eq-1) \hyperref[b4]{[5]}of the block is then computed,quantized using 64 corresponding step sizevalues from the quantization table in Figure 3 \hyperref[b6]{[7]}. After quantization the DCT coefficientsare rearranged in a zigzag sequence order as shown in the Figure {\ref 4}. \hyperref[b6]{[7]} Since the one-dimensional reorderedarray generated under the zigzag pattern ofFigure 3 is qualitatively arranged according toincreasing spatial frequency, the JPEG codingprocedure is designed to take the advantage ofthe long runs of zeros that normally result fromthe reordering. In particular, the nonzero ACcoefficients (the term AC denotes all transformcoefficients with the exception of the zeroth orDC coefficient) are coded using a variablelengthcode that defines the coefficient's valueand number of preceding zeros. The DCcoefficient is difference coded relative to theDC coefficient of the previous sub image. The decompression process performs aninverse procedure. It decodes the Huffmancodes. Then, it makes the inversion of theQuantization step. In this stage, the decoderraises the small numbers by multiplying themby the quantization coefficients. The resultsare not accurate, but they are close to theoriginal numbers of the DCT coefficients. AnInverse Discrete Cosine Transform (IDCT) (Eq.4) \hyperref[b6]{[7]} is performed on the data received from theprevious step. Finally add L/2 to each subimage. Place the sub images in their correctpositions. \hyperref[b3]{(4)} The error between the original imageand reconstructed image is calculated in termsof Peak signal to noise ratio (PSNR) = 10 log10 Mean filtering [8] is a simple, intuitiveand easy to implement method of imagesmoothing i.e. reducing the amount of variationbetween one pixel and the next or surroundingpixels. It is often used to reduce noise inimage. The idea of mean filtering is simply toreplace each pixel in an image with the meanvalue of its neighbors including itself. This hasthe effect of eliminating pixel values which areunrepresentative of their surroundings. Usually,3x3 neighborhoods of pixels are consideredwhile calculating mean filtered value of anypixel.(L2/MSE) (5)\textbf{(6)}? = ? = ? ? ? ? ? ? + ? ? ? ? ? ? + = 1 0 1 0 2 ) 1 2 ( cos 2 ) 1 2 ( cos ) , ( ) ( ) ( ) , ( N x N y N v y N u x y x f v u v u C ? ? ? ? for u, v = 0, 1, 2, . . . . , N -1 ? ? ? > = = 0 / 2 0 / 1 ) ( u for N u for N u ? ? ? ? > = = 0 / 2 0 / 1 ) ( v for N v for N v ? ?? ? = ? = ? ? ? ? ? ? + ? ? ? ? ? ? + = 1 0 1 0 2 ) 1 2 ( cos 2 ) 1 2 ( cos ) , ( ) ( ) ( ) , ( ?N u N v N v y N u x v u C v u y x f ? ? ? ? [ ]\par Median filter [9] is normally used to reducenoise in an image like the mean filter.However, it often does a better job than themean filter in preserving useful detail in theimage. Like the mean filter, the median filterconsiders each pixel in the image in turn andlooks at its neighbors to decide whether or notits representative of its surroundings. Insteadof simply replacing the pixel value with themean of neighboring pixel values, it replaces itwith the median of those values.\par An outlier [10] is an observation that isnumerically distant from the rest of the data.In an image, a pixel value is very different fromits surrounding pixels, it can be called asoutlier.\par From basic statistics, we know that apopulations sample values with someconfidence level can be given as mean ± C*P, where C is weighing factor (critical value) and P is standard deviation of the population. Table-1 shows the commonly used ConfidenceLevels and Corresponding Critical Values \hyperref[b7]{[11]}.In our outlier based algorithms, we take thesesimple confidence limits of normal distributionin deciding whether a pixel is outlier or not. Ifthe pixel is observed to be outlier with thegiven confidence level, we may retain else wemay take its mean filtered or median filtered value. ? Apply mean filtering with a little variation tothe given original image using 3x3 window. Foreach pixel, calculate average and standarddeviation of its neighboring 3x3 pixels. If apixels value is observed to be outlier (not inthe range of Mean ± C*P) then its value is takenas itself else mean is taken as its filtered value. ? Apply DCT on the outliermean filteredimage. \section[{d) OutlierMedianDCT Algorithm}]{d) OutlierMedianDCT Algorithm}\par ? Apply median filtering with a little variationto the given original image using 3x3 window.For each pixel, calculate median and standarddeviation of its neighboring 3x3 pixels. If apixels value is observed to be outlier (not inthe range of Median ± C*P) then its value istaken as itself else median is taken as itsfiltered value. ? Apply DCT on the outliermedian filteredimage. \section[{IV.}]{IV.} \section[{Popular Classification Algorithms a) Maximum Likelihood Classifier}]{Popular Classification Algorithms a) Maximum Likelihood Classifier}\par Let w 1 ,w 2 , . . . , w m denote m distinctpopulations (classes) with known d-dimensionalprobability density functions p 1 (X), p 2 (X), . . . .. p m (X), respectively. The a priori probabilitiesthat an observation is selected frompopulations w 1 , w 2 , . . . ,w m are denoted by q l ,q 2 , . . . ., q m , respectively {\ref [12]}. According tothe Bayesian ML classification rule, assumingequal costs for misclassifications, a random ddimensional pixel vector X is classified as classw k \hyperref[b6]{(7)} Assuming equal a priori probabilities for all theclasses, decision rule (7) becomes:(8)\par In Equations ( {\ref 7}) and (8), the probability densityp k (X) will be given as: ( ) Year ) , ( ?y x f q k p k (X) = max\{q i P i (X)\} for i = 1, 2 . . . ., m. p k (X) = max\{p i (X)\}, i = 1, 2 , . . . , m 2 / 1 2 / ) 2 ( 1 ) ( ? = k d k X p ? ? ? ? ? ? 1 )]. ( ) .( 2 / 1 exp[ k k T k M X M X X b) Mahalanobis Classifier\textbf{37}\par According to this classifier a ddimensionalrandom pixel vector (X) will be assigned to thegroup to which it is nearest \hyperref[b8]{[13]}. Each group ischaracterized by its mean vector, which iscalculated from training data. Nearness isdetermined by the Mahalanobis distancebetween the group mean and X. Inmathematical terms, the same classificationrule can be represented as: {\ref (10)} where i = (1, 2, . . . C) groups if d i (X)OutlierMeanDCT (for C=1.28 to 2.58).As the value of C increases in the Outlier,Compression Benefit increases. For C=3.08 to3.27 Compression Benefit in MeanDCT andOutlierMeanDCT is almost same. PSNR in MeanDCTOutlierMedianDCT(for C=1.28 to 2.58). As}\\ \multicolumn{4}{l}{Median DCT algorithm. With all the images we found}\tabcellsep \multicolumn{6}{l}{the value of C increases in the Outlier,Compression}\\ \multicolumn{4}{l}{that Median DCT and Outlier Median DCTalgorithms}\tabcellsep \multicolumn{6}{l}{Benefit increases. For C=3.08 to 3.27 Compression}\\ \multicolumn{4}{l}{have better compression ratios as compared to}\tabcellsep \multicolumn{6}{l}{Benefit in MedianDCT andOutlierMedianDCT is same.}\\ \multicolumn{4}{l}{conventional JPEG coding. The PSNR loss in Median}\tabcellsep \multicolumn{6}{l}{PSNR in MedianDCT