(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, Image Compresson of MRI Image usng Planar Codng Laltha Y. S Department of Electroncs & Communcaton Engg. Appa Insttute of Engneerng & Technology Mrtyunjaya V. Latte Prncpal, JSS Academy of Techncal Educaton, Bangalore, Karnataa, Inda Gulbarga, Karnataa, Inda. Abstract-In ths paper a herarchcal codng technque for varable bt rate servce s developed usng embedded zero bloc codng approach. The suggested approach enhances the varable rate codng by zero tree based bloc-codng archtecture wth Context Modelng for low complexty and hgh performance. The proposed algorthm utlzes the sgnfcance state-table formng the context modelng to control the codng passes wth low memory requrement and low mplementaton complexty wth the nearly same performance as compared to the exstng codng technques. Keyword- mage codng; embedded bloc codng; context modelng; mult rate servces. I. INTRODUCTION Wth rapd development of heterogeneous servces n mage applcaton the future dgtal medcal mages and vdeo codng applcatons fnds varous lmtatons wth avalable resource. The tradtonal mult-bt stream approach to the heterogenety ssue s very constraned and neffcent under mult bt rate applcatons. The mult bt stream codng technques allow partal decodng at a varous resoluton and qualty levels. Several scalable codng algorthms have been proposed n the nternatonal standards over the past decade, but these former methods can only accommodate relatvely lmted decodng propertes. The rapd growth of dgtal magng technology n conjuncton wth the ever-expandng array of access technologes has led to a new set of requrements for mage compresson algorthms. Not only are hgh qualty reconstructed medcal mages requred at medum-low btrates, but also as the bt rate decreases, the qualty of the reconstructed MRI mage should degrade gracefully. The tradtonal mult-bt stream soluton to the ssue of wdely varyng user resources s both neffcent and rapdly becomng mpractcal. The bt level scalable codes developed for ths system allow optmum reconstructon of a medcal mage from an arbtrary truncaton pont wthn a sngle bt stream. For progressve transmsson, mage browsng, medcal mage analyss, multmeda applcatons, and compatble trans codng, n a dgtal herarchy of multple bt rates, the problem of obtanng the best MRI mage qualty and accomplshng t n an embedded fashon.e. all the encoded bts mang compatble to the target bt rate s a bottlenec tas for today s engneer. As medcal mages are of huge data set and encodng t for a lower bt rate results n loss of data, whch ntern results n very low mage qualty under compresson. Comng to the transmsson over a nosy channel ths problem becomes more effectve due to narrow bandwdth effect. Varous algorthms were proposed for encodng and compressng the MRI mage data before transmsson. These algorthms show hgh-end results under hgh bandwdth systems but show poor result under low data rate systems. The problem of transmsson of MRI mages over a low bt rate bandwdth can be overcome f the medcal mage data bts are such encoded and compressed that the data bt rate s made compatble to the provded low bt rate. Embedded zero tree wavelet algorthm s a proposed mage compresson algorthm whch encode the bt n the bt stream n the order of mportance whch embed the bt stream n herarchcal fashon. II. SYSTEM DESIGN Ths wor was motvated by success of two popular embedded codng technques: zero-tree/-bloc codng [1, 2, 3, 4] and context modelng of the sub band/wavelet coeffcents [5, 6, 7]. Zero-tree/-bloc codng taes advantage of the nature of energy clusterng of sub band/wavelet coeffcents n frequency and n space. These classes of coders apply a herarchcal set parttonng process to splt off sgnfcant coeffcents (wth respect to the threshold n the current bt plane codng pass), whle mantanng areas of nsgnfcant coeffcents. In ths way, a large regon of zero pxels can be coded nto one symbol. It provdes an effcent method to compactly represent a group of leadng zeros of sub band/wavelet coeffcents. The dstngushed compresson performances were demonstrated n [2, 3, 4]. Moreover, nstead of all pxels, only a small number of elements n lsts [2] needs to be processed n ndvdual bt plane codng passes. Thus, processng speed for ths class of coders s very fast. Hgh compresson effcency acheved wth context modelng was presented n [5, 6, 7]. In ths class of coders, ndvdual pxel of the DWT bt planes are coded usng context based arthmetc codng. Wth help of the context models, strong correlaton of sub band/wavelet coeffcents wthn and across sub bands can be effectvely utlzed. Although smple context modelng was also employed n [2, 3, 4], the lmted context nformaton n those algorthm were nsuffcent to accurately predct the status of the current node. Wth carefully desgned context models, some algorthms [6, 7] have been able to outperform the best zero-tree/bloc coders n PSNR performances. Nevertheless, unle zero-tree/-bloc coders, these algorthms needed to scan all sub band/wavelet coeffcents at least once to fnsh codng of a full bt plane, wth an mpled hgher computaton cost. To combne advantages of these two codng technques, e, low computaton complexty and effectve explotaton of correlaton of sub band coeffcents, we propose an embedded medcal mage codng algorthm usng Zero Blocs of sub band/ wavelet coeffcents and context modelng, or EZBC for ease of reference. Ths zero bloc codng www.jacsa.thesa.org 23 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, algorthm s also based on the set parttonng technque. We adopted the adaptve quad tree splttng method ntroduced n [3] to separate the sgnfcant coeffcents and code every bloc of zero pxels nto one symbol. In ths scheme, quad tree representatons of DWT coeffcents are frst establshed for ndvdual sub bands. The bottom level of the quad tree conssts of the sub band/wavelet coeffcents. The sngle node at the top tree level, or the root node, just corresponds to the maxmum ampltude of the all DWT coeffcents. To start wth, the root s the only nsgnfcant node to process. Each quad tree node splts nto four nsgnfcant descendent nodes of the next lower level once t tests as sgnfcant aganst the threshold of the current bt plane codng pass. The same splttng process s recursvely appled to the ndvdual descendent nodes untl the bottom level of the quad tree s reached. In ths way, we can qucly zoom n to hgh-energy areas and regons of all zero pxels can be compactly represented. In EZBC, the context models were carefully desgned for codng quad tree nodes at dfferent tree levels and sub bands. Therefore, t retans the propertes of compactness and low complexty of the zero bloc coders, and adds context nformaton n an effectve way, whle the context nformaton s also made effectve use. Unle the zero tree structure, each zero bloc only represents pxels from one sub band. Hence, EZBC s nherently applcable to resoluton scalable applcatons. Wth the ad of nter band context, dependence of sub band/wavelet coeffcents across scales can stll be effectvely utlzed wthout havng zero trees spannng several sub bands. III. MEDICAL IMAGE CODING SYSTEM Image compresson addresses the problem of reducng the amount of data requred to represent a dgtal medcal mage. Compresson s acheved by the removal of one or more of three basc data redundances: (1) codng redundancy, whch s present when less than optmal (.e., the smallest length) code words are used; (2) nter pxel redundancy, whch results from correlatons between the pxels of an medcal mage; and/or (3) psycho vsual redundancy, whch s due to data that s gnored by the human vsual system (.e., vsually nonessental nformaton).in ths chapter We examne each of these redundances, descrbe a few of the many technques that can be used to explot them, and examne two mportant compresson standards JPEG and JPEG 2000. These standards unfy the concepts by combnng technques that collectvely attac all three data redundances. Medcal Image compresson systems are composed of two dstnct structural blocs: an encoder and a decoder. Image f ( x, y ) s fed nto the encoder, whch creates a set of symbols from the nput data and uses them to represent the medcal mage. If we let n and 1 n denote the number of nformaton carryng unts (usually 2 bts) n the orgnal and encoded medcal mages, respectvely, the compresson that s acheved can be quantfed numercally va the compresson rato n1 CR (1) n 2 To vew and/or use a compressed (.e., encoded) medcal mage, t must be fed nto a decoder (see Fg.2.1), where a reconstructed output medcal mage, (x,y), s generated. In general, (x,y) may or may not be an exact representaton of. If t s, the system s called error free, nformaton preservng, or lossless; f not, some level of dstorton s present n the reconstructed medcal mage. In the latter case, whch s called lossy compresson, we can defne the error f x,y between fˆ f x,y and fˆ (x,y), for any value of x and x,y fˆ x,y f x,y e (2) so that the total error between the two medcal mages s f M 1 N1 x,y f x,y y x0 y0 and the rms (root-means-square) error x,y fˆ (3) erms y e x,y as between and (x,y) s the square root of the squared error averaged over the M N array, or e rms fˆ 1 MN M 1 N1 x0 y0 y x,y f x, y 2 1/ 2 In the frst stage of the encodng process, the mapper transforms the MRI nput mage nto a (usually nonvsual) format desgned to reduce nter pxel redundances. The second stage, or quantzer bloc, reduces the accuracy of the mapper s output n accordance wth a predefned fdelty Crteronattemptng to elmnate only psycho vsually redundant data. Ths operaton s rreversble and must be omtted when errorfree compresson s desred. In the thrd and fnal stage of the process, a symbol coder creates a code (that reduces codng redundancy) for the quantzer output and maps the output n accordance wth the code. IV. BIT PLANE CODING Wavelet coeffcent bt plane codng n EZBC follows a smlar procedure to those adopted n other quad tree-based set parttonng coders. However, specal care s gven to lst management and bt stream organzaton, whch sgnfcantly nfluence effcency of context modelng and code stream embeddng, and scalable functonalty of the resultng code stream. The EZW encoder s based on two mportant observatons: 1) Natural MRI mages n general have a low pass spectrum. When a medcal mage s wavelet transformed the energy n the sub bands decreases as the scale decreases (low scale means hgh resoluton), so the wavelet coeffcents wll, on average, be smaller n the hgher sub bands than n the lower sub bands. Ths shows that progressve encodng s a very natural choce for compressng wavelet transformed medcal mages, snce the hgher sub bands only add detal. 2) Large wavelet coeffcents are more mportant than small wavelet coeffcents. (4) www.jacsa.thesa.org 24 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, These two observatons are exploted by encodng the wavelet coeffcents n decreasng order, n several passes. For every pass a threshold s chosen aganst whch all the wavelet coeffcents are measured. If a wavelet coeffcent s larger than the threshold t s encoded and removed from the mage, f t s smaller t s left for the next pass. When all the wavelet coeffcents have been vsted the threshold s lowered and the MRI mage s scanned agan to add more detal to the already encoded MRI mage. Ths process s repeated untl all the wavelet coeffcents have been encoded completely or another crteron has been satsfed (maxmum bt rate for nstance). The trc s now to use the dependency between the wavelet coeffcents across dfferent scales to effcently encode large parts of the MRI mages whch are below the current threshold. It s here where the zero tree enters. So, let me now add some detal to the foregong. (As most explanatons, ths explanaton s a progressve one.) The EZW encoder explots the zero tree based on the observaton that wavelet coeffcents decrease wth scale. It assumes that there wll be a very hgh probablty that all the coeffcents n a quad tree wll be smaller than a certan threshold f the root s smaller than ths threshold. If ths s the case then the whole tree can be coded wth a sngle zero tree symbol. Now f the MRI mage s scanned n a predefned order, gong from hgh scale to low, mplctly many postons are coded through the use of zero tree symbols. Of course the zero tree rule wll be volated often, but as t turns out n practce, the probablty s stll very hgh n general. The prce to pay s the addton of the zero tree symbol to our code alphabet. Quad tree Structure The bt plane codng process begns wth establshment of the quad tree representatons for the ndvdual sub bands. The value of a quad tree (a) Quadtree buldup (b) Quadtree splttng node Q l (, ) j at poston (, j), quad tree level l and subband s defned by Q 0 (, j) c (, j), and Q l(, j) max{ Q [ l 1](2,2 j), Q [ l 1](2,2 j 1), Q [ l 1](2 1,2 j), Q [ l 1](2 1,2j 1)} Where c (, j) s the subband coeffcent at poston (, j), subband. That s, each bottom quadtree node s assgned to the magntude of the subband coeffcent at the same poston. The quadtree node at the next hgher level s then set to the maxmum of the four correspondng nodes at the current level, as llustrated n Fg. 1 (a). By recursvely groupng each 2 2 vector ths way, the complete quad tree s bult up for the ndvdual subbands. The top quad tree node Q [ D 1](0,0) s just equal to the maxmal magntude of all subband coeffcents { c (, j)},j from subband, where D s the quadtree depth for subband., Fg. 1 Illustraton of quad tree buld up and decomposton. Smlar to the conventonal btplane coders, we progressvely encode subband coeffcents from the MSB toward the LSB. The ndvdual btplane codng pass n encodes bt n of all coeffcents. The subband coeffcents are thus effectvely quantzed by a famly of embedded quantzers wth a (dead-zone) quantzaton threshold n= 2 n for btplane level n. We defne that a quadtree node Q tests sgnfcant wth respect to a quantzaton threshold f Q. A quadtree Q s defned to be a sgnfcant node durng the current btplane pass n f - Q n 1 Q[ n, n 1), or - and Q has been tested, and an nsgnfcant node otherwse. It should be noted that s stll consdered as an nsgnfcant node n the btplane pass n untl t has been coded/tested. A sgnfcant pxel (coeffcent) s located by the testng and splttng operaton recursvely performed on the sgnfcant nodes up to the pxel (bottom) level of a quadtree, as shown n Fg. 1 (b). Gven the coded quadtree splttng decsons, the decoder can duplcate the quadtree decomposton steps and the related sgnfcance nformaton. Q[ n, n 1) A parent-chld relatonshp s defned n the quadtree structure. As opposed to the classc zerotree structure, ths relatonshp s between nodes across the quadtree levels (rather than across resoluton scales), as llustrated n Fg. 3.5. Each parent has four chldren from the same 2 2 bloc at the next lower quadtree level,. These four chld nodes are consdered as sblngs of each other. All the descendants of can be recursvely traced from one quadtree level to the next lower n a smlar way up to the pxel level. Q [ ](, ) l j Q [ ](, ) l j Every quadtree node Q plays a dual role: It s an element wth the value defned by (3.1) subjected to sgnfcance test. The establshed quadtree representaton provdes an addtonal www.jacsa.thesa.org 25 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, pyramdal descrpton of the transformed medcal mage. The strong statstcal dependences among quadtree nodes, can be exploted to mprove the performance of condtonal entropy codng. Once a node Q tested nsgnfcant, t ndcates that all ts descendants are nsgnfcant, too. Hence, t also serves as a zero set defned n the conventonal set parttonng coder and contans all ts descendent coeffcents as members. Each nsgnfcant quadtree node Q [l ] (, j) thus effectvely groups 2 l x 2 l nsgnfcant coeffcents together. The herarchcal set parttonng wth respect to a gven test threshold s accomplshed va recursve quadtree splttng. Smlar to other herarchcal coders, we utlze the ordered lsts for tracng the sgnfcance status of the ndvdual subband coeffcent. LSP (lst of sgnfcant pxels) contans a full lst of sgnfcant pxels n subband. All the nsgnfcant coeffcents are compactly gathered n the quadtree nodes whch are mantaned n arrays of the LINs (lst of nsgnfcant nodes). LIN [l ], l = 0,, -1, contans a lst of nsgnfcant nodes from quadtree level l, subband. A node (, j) n LIN [l ] thus ndcates that 2 L x 2 L subband coeffcents {{ D c ( 2, 2 ) l j l l l c ( 2, j 2 2 1) l l l c ( 2 1, j 2 2 1) l, l l c ( 2, j 2 1) },{ },,,, l l c ( 2 1, j 2 ),, l l l c ( 2 2 1, j 2 ) l l l l c ( 2 2 1, j 2 2 1) }} (5),, are all nsgnfcant. Unle other earler set parttonng coders such as EZW, SPIHT and SPECK, the lsts here are mantaned separately for the ndvdual subbands and quadtree levels. Ths strategy can effectvely mprove performance of context modelng and codestream embeddng. Moreover, t s essental for effcent accommodaton of resoluton-scalable codestreams. Btplane Processng and Codng Intally, LIN [D -1] contans the sngle node from the top quadtree level and the other LIN lsts and LSP are just empty for each subband. It ndcates that all the subband coeffcents are nsgnfcant before the frst btplane codng pass starts. The codng process begns wth the MSB plane wth the bt ndex gven by n where log (max{ c (, j)}) max 2 (,, j ) (6) returns the largest ntegral value not greater than the nput. Because the quantzaton threshold s halved from btplane to btplane, more and more coeffcents becomes sgnfcant as the btplane codng process proceeds. Two tass are performed n each btplane pass n: 1) 1. Reveal the new sgnfcant coeffcents, {c c [ n 1 2,2 n )} wth respect to the current threshold ; 2) 2. Refne the old sgnfcant coeffcents, {c c collected from the prevous btplane passes. n 2 n 2 n1 }, Snce all the nsgnfcant coeffcents wth respect to the n 2 n1 prevous test threshold = were already compactly grouped by the quadtree nodes mantaned n the LINs, the new sgnfcant coeffcents can be fast located by sgnfcance test of the ndvdual nodes from the LINs. If a node s tested nsgnfcant, t remans n the same LIN. Otherwse, t splts nto four chldren and each chld s further tested. Once a chld s tested nsgnfcant, t s added to the LIN at the next lower level. Otherwse, t further splts nto four grandchldren and each s tested n a smlar way. Ths testng and splttng procedure s recursvely performed on the sgnfcant descendants up to the pxel level. As soon as a pxel tested sgnfcant, t s appended to the LSP and ts sgn s encoded mmedately. The refnement of old sgnfcant coeffcents (socalled refnement pass) s smply accomplshed by codng bt n of each coeffcent n the LSPs gathered from the prevous btplane passes (not ncludng the new sgnfcant coeffcents from the current pass). The Boolean results of sgnfcance tests (true or false), the sgn bts, and the refnement bts are all the requred nformaton for decodng of btplane data. They are all encoded by context-dependent bnary arthmetc codng, to be presented shortly. The btplane codng process wll stop once the desred codng btrate or mage qualty s reached. The quadtree buld-up stage s not needed at the decoder as the sgnfcance nformaton s already contaned n the codestream. The btplane decoder bascally follows the same procedure as the btplane encoder. Gven the coded sequences of quadtree splttng decsons, the decoder can duplcate the quadtree decomposton steps taen by the encoder. The executon path wthn a subband for btplane encodng s requred to be strctly followed for btplane decodng. However, snce the quadtrees are ndependently establshed for the ndvdual subbands, the btplane decodng order among subbands s allow to be manpulated n varous ways for some scalable codng applcatons. In addton to the subband coeffcents, the proposed algorthm also needs to deal wth the quadtree nodes from the ndvdual quadtree levels. At frst loo, t appears that the data sze for processng and codng n each btplane pass has been sgnfcantly expanded. Nevertheless, none of these quadtree nodes wll be vsted untl ther parents s already tested sgnfcant, except for the top quadtree nodes whch do not have any parents. On the contrary, our expermental results show that the number of coded bnary symbols n EZBC s n fact even smaller than that of pxels n the nput medcal mage (at a typcal lossy codng btrate). That s, the average number of bnary codng operaton per pxel s less than one although the ndvdual subband coeffcent s encoded through multple quantzaton and codng stages. It partally explans the hgh speed performance of ths bloc-based set parttonng codng scheme. Stll, we need to vst every coeffcent once for establshment of the quadtree representatons of the decomposed medcal mage at the very begnnng of the btplane codng process. Nevertheless, our codng algorthm n fact s only concerned wth the MSB ndex of a quadtree node (rather than the actual value) for sgnfcance test. Ths www.jacsa.thesa.org 26 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, quadtree buldup step can thus be effcently mplemented by the smple btwse OR operaton. In order to have effcently embedded codestreams, t s essental that the code data n the compressed fle are ordered accordng to ther relatve effcences for dstorton reducton. Ths basc concept s commonly called embeddng prncple. In the proposed algorthm, a fxed path for encodng of wavelet coeffcent btplane data s chosen as follows: The codng process advances n a btplane-wse fashon from the most sgnfcant bt toward the least. In a gven btplane, the arrays of LINs are processed n an ncreasng order of quadtree level, as suggested by Islam and Pearlman n SPECK. That s, all the pxels n LIN[0] are processed frst and all the nodes n LIN[1] are then processed next, followed by the processng s of LIN[2], LIN[3], and so on. In ths way, the busy areas n the transformed medcal mage are updated earler va a few quadtree splttng and codng steps, resultng n a good ratedstorton performance. The refnement of the prevous sgnfcant coeffcents from LSP s executed at last. In a sgnfcance test pass of a gven quadtree level or a coeffcent refnement pass, the subbands are vsted from coarse to hgh resoluton Fg. 2 Illustraton of the herarchcal layout of a EZBC codestream. A herarchcal layout of a EZBC codestream s depcted n Fg. 2, where p n, denotes the btplane pass n, p nl the subbtplane pass for processng the nsgnfcant nodes n LIN [l] nd, max p (routne CodeLIN(, l)), and the sub-btplane pass for the refnement of the sgnfcant coeffcents n LSP (routne CodeLSP()). Smlar to the btplane de-nterleavng scheme wdely adopted n the sequental btplane coders, EZBC effectvely parttons each btplane nto multple sub-btplane nl, { p } passes n,l, for provdng an embedded codestream of fne granularty. However, unle the mult-pass approach proposed n, EZBC does not need to scan the ndvdual pxels more than once n each btplane pass because all the nvolved pxels for the ndvdual sub-pass were already organzed n separate lsts. Although our pre-defned data embeddng order s not optmzed for the best R-D performance (as compared to the algorthms), our emprcal data show the resultng relatve performance loss s mostly nsgnfcant. The effectveness of the proposed data embeddng strategy s further evdenced by the smooth R-D curves shown n our actual codng smulaton results It s worth mentonng that each btplane pass could have been dvded nto even more sub-btplane passes n our data embeddng scheme to further mprove the R-D performance of the resultng codestream. It s smply accomplshed by parttonng of the exstng lsts nto smaller sub-lsts and then processng each sub-lsts va separate sub-btplane codng passes. The resultng computatonal and storage costs are stll the same because the total number of the nodes to be stored and processed n all the mantaned lsts s unchanged. For example, our emprcal data show that the refnement of the sgnfcant coeffcents from the prevous btplane codng pass reduces dstorton more effcently than the refnement of the sgnfcant coeffcents from the other earler btplane codng passes (f exst). The PSNR performance can thus be slghtly mproved by parttonng the exstng refnement pass nto multple subpasses, each for the refnement of the sgnfcant coeffcents from partcular btplane level(s). Nevertheless, t s observed that the granularty of the resultng codestream by the current algorthm s already fne enough n practcal medcal mage codng applcatons. A. Context-dependent entropy codng As opposed to the conventonal sequental btplane coder, the proposed algorthm EZBC s requred to process the btplanes assocated wth the ndvdual quadtree levels n each btplane codng pass. A dual herarchcal pyramdal descrpton, as prevously shown n Fg. 3.1, s thus gven by ths quadtree representaton of the decomposed medcal mages. Strong ntraband correlaton s clearly exhbted among quadtree nodes. The self-smlarty s demonstrated across both quadtree and resoluton levels. Such dverse statstcal dependences are exploted by context-dependent arthmetc codng n EZBC. Unle most former set-partton coders, the lsts n EZBC are separately mantaned for the ndvdual subbands and quadtree levels. Therefore, the ndependent probablty models are allowed to be bult up for sgnfcance codng of the nodes from dfferent subbands and quadtree levels. As such, the unque statstcal characterstcs of the source samples assocated wth dfferent subband orentatons, sub-samplng factors and ampltude dstrbutons wll not be mxed up n the accumulated probablty models. Four classes of bnary symbols are encoded n EZBC: 1) Sgnfcance test of a gven quadtree node from LIN (n routne CodeLIN), 2) Sgnfcance test of a chld (n routne Code Descendants) 3) Sgn bt of a newly sgnfcant coeffcent, and 4) Refnement bt of a gven coeffcent from LSP. These symbols are all encoded by context-based arthmetc codng wth the dstnct modelng strateges, to be respectvely descrbed n the followng. B. Sgnfcance codng Ths subsecton begns wth a bref dscusson that relates the proposed entropy codng algorthm to the APSG (alphabet parttonng and sample groupng) scheme. The utlzaton of nter- and ntra-band correlaton and dependence between subband levels n a subband-based quadtree representaton s then respectvely descrbed, followed by a descrpton of our context quantzaton/selecton scheme. www.jacsa.thesa.org 27 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, Sgnfcance codng n the proposed algorthm s condtoned on the sgnfcance map defned by 1, f node (, j ) s sgnfcant, j 0, otherwse Nevertheless, n contrast to the conventonal sequental pxel-wse btplane codng approach, sgnfcance codng of a quadtree node n EZBC jontly encodes a group of coeffcents from a bloc regon. The sgnfcance status of a contextual quadtree node compactly ndcates local actvty level n the correspondng bloc area. Hence, we can thn of EZBC as a condtonal bloc entropy coder that apples the APSG scheme on both source samples and modelng contexts. As such, bloc entropy codng and condtonal entropy codng can be combned to explot the strong subband dependency wthout sufferng the complexty dffcultes commonly assocated wth hgh-order source extenson and context modelng. Although from a pont of vew of the conventonal unversal source codng, t was argued that there s no addtonal compresson gan by blocng samples n condtonal entropy codng. However, our bloc codng method here does not nvolve complex codeboo desgn or any other computaton-ntensve procedures. On the contrary, the speed performance of the resultng codng system s substantally mproved by compact groupng of subband coeffcents. Besdes, arthmetc codng of large areas of zero coeffcents ndvdually n conventonal sequental btplane codng s assocated wth a hghly sew probablty dstrbuton, whch s nown to be penalzed by a hgh learnng cost. C. Contextual Regon In Fg. 3 (a), we show the neghborng nodes ncluded n the modelng contexts n our coder EZBC for sgnfcance codng. The eght spatal adjacent nodes from the same quadtree level are utlzed to explot ntraband correlaton. Such a contextual structure has been wdely employed n many conventonal btplane coders, for sgnfcance codng of subband coeffcents. The applcaton of ths model to sgnfcance codng of quadtree nodes s justfed by the strong spatal dependency exhbted n the example MSB map n Fg. 3 (b). To explot the subband correlaton across scales, we adopt the correspondng node from the next lower quadtree level (rather than from the current level) n the parent subband, ndcated by F n Fg. 3 (a). Ths choce s based on the fact that at a gven quadtree level the related dmenson n an nput medcal mage for a quadtree node s doubled n the parent subband, as a result of sub-samplng operaton n the subband transformaton stage. The nter-band nformaton s thus provded at the same spatal resoluton by the parent subband, as demonstrated n Fg. 3(b). D. Inter-/Intra- Band Modelng The mportance of the nter-band neghborng pxels les n ts ablty to provde non-causal contextual nformaton for condtonal entropy codng. Such nformaton s partcularly valuable for effcent compresson of the leadng btplanes snce most spatal neghborng coeffcents are stll (7) nsgnfcant. However, the complexty of the algorthm may be ncreased by a use of the nter-band neghbors for some magng applcatons. It has been argued that the ntra-band context model s capable of effectve explotaton of Fg. 3 Modelng contexts for condtonal entropy codng of sgnfcance test. (a) Left: Neghbors ncluded n the modelng contexts. (b) Rght: Example MSB map of quadtree nodes from the decomposed MRI mage. Subband dependency combned wth some effcent zero codng schemes. EBCOT, for nstance, exhbts excellent compresson performance combnng quadtree decomposton, run-length codng wth conventonal context-based btplane codng. Smlar phenomenon was also observed durng the development of EZBC. Our expermental results show that no PSNR mprovement s made for sgnfcance codng of the ndvdual pxels from LIN by ncluson of nterband neghbors n the modelng context. The mprovement for sgnfcance codng of a chld pxel s also very lmted. It s expected because the current pxel for sgnfcance test often already has some neghborng pxels tested sgnfcant when the quadtree decomposton operaton proceeds to the bottom level. As a result, we only employ ntraband modelng for condtonal entropy codng of sgnfcance test at the pxel level. On the other hand, t was also observed n our expermental results that the spatal dependency among quadtree nodes s decreasng as we move toward the hgher quadtree levels. Recall that the value of a quadtree node s defned to be the maxmal ampltude of all subband coeffcents from ts correspondng bloc regon and the bloc sze grows exponentally wth the quadtree level. As s well nown, the pxels wth pea values are typcally related to sngularty n the nput MRI mage. Because of the energy clusterng nature of subband coeffcents, these medcal mage features are typcally easly notceable n the spatal contexts at the lower quadtree levels. Nevertheless, such clusterng s of hgh energy are restrcted to the local regon around the pea pxels. As the bloc sze grows (or the quadtree level ncreases), ths energy clusterng phenomenon n the current bloc wll become less lely reflected n the neghborng nodes f the pea pxel s not close to the bloc boundares. Nevertheless, such an anomaly n space remans seen from the same correspondng area n the parent subband. Snce the sgnfcance of a parent node s coded earler durng every btplane pass, we can say that the parent node provdes a loo-ahead functon nto the regon covered by the current node. In fact, our smulatons ndcate that the nterband-only context model (contanng a sngle neghborng node from the parent band) outperforms the www.jacsa.thesa.org 28 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, ntraband-only context model (contanng eght spatal neghborng nodes) at the 3rd level of the quadtree and hgher. The use of nter-band modelng s only optonal n EZBC. An example applcaton desrable for ntraband modelng s hghly scalable mage codng presented. E. Dependency between Quadtree Levels The correlaton between the adjacent quadtree levels s exploted to provde the nter-subband contextual nformaton at the same spatal resoluton. Wthn a gven subband, the dependency also exsts between the adjacent quadtree levels, drectly attrbuted to the two propertes assocated wth the basc mechansm of quadtree buld-up and splttng: 1) When a parent remans nsgnfcant, all ts chldren are also nsgnfcant; 2) After a parent tested sgnfcant, at least one of ts four chldren wll test sgnfcant n the subsequent descendant test Property () s already utlzed n a conventonal zerobloc coder to compactly represent large numbers of nsgnfcant pxels from bloc regons. Property () mples that the chance of beng testng sgnfcant s ncreasngly hgher for the next chld f none of ts sblngs have been tested sgnfcant yet. For example, wthout consderng other contextual nformaton, the probablty that the frst chld tests sgnfcant s no less than 0.25. Had none of the past three sblngs been tested sgnfcant, the fourth chld s sgnfcant for sure and no sgnfcance testng and codng s requred. Ths statstcal characterstc s exploted n our context modelng scheme detaled n the next secton. F. Context Selecton and Loo-up tables Although adaptve arthmetc codng s a unversal codng scheme whch allows the source statstcs to learn on the fly, the related learnng costs often turn out qute expensve for many practcal nstances. The compresson effcency can be substantally mproved f pror nowledge about the source s effectvely exploted n the context model desgn. Unle the conventonal sequental btplane coder whch encodes subband samples one by one n each btplane codng pass, EZBC processes coeffcents n groups and hence has fewer samples to encode. Context dluton thus becomes an ssue of great concern. Our context modelng scheme s based on the sgnfcance map whch allows context quantzaton to be mplctly carred out. Instead of treatng all the resultng context vectors (2 9 totally) as dfferent condtonal states, we carefully classfy them nto several model classes, smlar to the context selecton approach adopted n EBCOT and JPEG 2000. The loo-up tables are then establshed accordngly to fast map a gven context to the assgned model ndex. Ths strategy can further lower the model cost and enable the probablty models to fast adapt themselves to varyng local statstcs. The context classfcaton, based upon the confguratons of the sgnfcance map, s characterzed by: 1) Orentatons: dentfed by H = σ(w)+ σ(e), such that 0 H 2, V = σ(n) + σ(s), such that 0 V 2, HV = H + V, such that 0 HV 4, and D = σ(nw) + σ(ne) + σ(sw) + σ(se), such that 0 D 4 where the relatve postons of nodes W, E, N, S, NW, NE, SW, SW are shown n Fg. 3. 2) Inter-band dependency: dentfed by P = σ(f), such that, 0 p 1, where the poston of node F s shown n Fg. 3 3) Relatve poston ν: ndex of the current chld node as shown n Fg. 3. where v{00, 01, 10, 11}. 4) Sgnfcance of the past coded sblngs: 1, f v 0 and v sb 0, otherwse v1 0 0 Where ν s the ndex of the current chld node. The spatal correlaton among quadtree nodes s exploted by the eght frst order neghbors, as depcted n Fg.3. The structure features are summarzed n horzontal, vertcal and dagonal drectons, respectvely. It s well nown that the MRI mage attrbutes such as edges and corners are retaned along the drecton of lowpass flterng after subband transform. Hence, our context modelng scheme emphaszes the drectonal characterstcs n accordance wth the current subband orentaton. For nstance, the horzontal features are favored over the vertcal and dagonal ones n the LH subband (horzontal lowpass flterng followed by vertcal hghpass flterng). Snce the nter-band dependency s not as useful at lower quadtree levels, we restrct the modelng contexts to the ntraband neghbors for sgnfcance codng at the pxel quadtree level. It was mentoned that the codng statstcs for sgnfcance test of the ndvdual chld are poston-dependent. Hence, sgnfcance codng of each chld s addtonally condtoned on ts relatve poston, ν, and the sgnfcance status of ts past coded sblngs, σ sb. The loo-tables are respectvely desgned for the subbands of LH and HH orentatons. Followng the dea of EBCOT, the coeffcent matrx from the HL subband s transposed frst before the btplane codng process starts. In ths way, the same set of loo-up tables can be shared by both the HL and HL subbands. The transposton of the LH subband s avoded n the JPEG 2000 standard by transposng the loo-up tables for the LH subband nstead. G. Refnement of sgnfcant coeffcents The same contextual ntraband regon shown n Fg. 3 s utlzed for condtonal codng of the refnement of the sgnfcant coeffcents from LSP. The contextual nformaton s characterzed by sgnfcance map σ p (, j), the sgnfcance status wth respect to the quantzaton threshold at the prevous btplane level. H. Context-dependent de-quantzaton Ths secton presents a new de-quantzaton algorthm that features a context-dependent strategy for reconstructon of (8) www.jacsa.thesa.org 29 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, subband coeffcents. A smple source statstcal model s desgned for each context wth the model parameters estmated from the statstcs accumulated at the decoder. It s nown that the optmal representaton levels of a scalar quantzer should satsfy the followng centrod condton Where r d 1 * d r 1 d 1 d quantzaton nterval [ xf x fx x x dx dx (9) s the optmal reconstructon value for a gven d, d 1 ] and a probablty densty functon (pdf) fx ( x ). However, the reconstructon values for the decoded coeffcents are typcally set to the mdponts of the correspondng quantzaton ntervals n practce ether for smplcty of mplementaton or for lac of nowledge about the source statstcs. Such a choce s optmal for the source wth unform probablty dstrbuton over the ndvdual decson ntervals. For btplane codng n partcular, t s mplctly assumed that the postve and negatve coeffcents wthn the dead zone are equally lely and the reconstructed values of all the nsgnfcant pxels are set to zero as a result. The proposed de-quantzaton algorthm s based on the two expermental observatons: 1) Subband coeffcents exhbt strong spatal correlaton n both sgns and magntudes 2) The statstcs of btplane samples bear strong resemblances wthn and across btplane levels n a gven subband and gradually grow nto less sew probablty dstrbuton from btplane to btplane. Observaton () has been utlzed for context-based arthmetc codng of the subband coeffcents n EZBC. Smlarly, the coded sgnfcant pxels can provde contextual nformaton for reconstructon of ther neghborng coeffcents. Partcularly, the sgns of sgnfcant pxels are useful for predctng the sgns of ther neghborng nsgnfcant coeffcents whch are dstrbuted over the dead zone and are quantzed to the zero symbols. Combned wth observaton (), we can estmate the source statstcs on a gven context usng the related probablty tables accumulated durng the decodng process. I. Reconstructon of sgnfcant coeffcents A smple statstcal model s adopted for reconstructon of a sgnfcant subband coeffcent c [ x, x ) 0 0 n Fg. 4(a), where x s the decoded value of 0 quantzer step sze,, for c s gven by, as depcted c. The 2, f c has been coded durng the last pass n (10) a1 2, otherwse The estmated condtonal probablty pˆ pˆ c x0 c 2 0 r x0,x0 c (11) gven a context c s emprcally determned by the related probablty tables whch were already accumulated durng the decodng process. The defnton of the contexts s the same as the one used for refnement codng of the sgnfcant coeffcents. Unform dstrbuton s then assumed for each half of the quantzaton nterval. The resultng reconstructon level, r, s computed by x0 x0 xfˆ x x dx 2 pˆ 0 x0 2 1 pˆ 0 xdx x0 x0 x0 xdx / 2 3 1 3 1 x0 pˆ 0 x0 pˆ 4 2 4 2 0 (12) where represents the estmated condtonal probablty densty functon for the magntude of a sgnfcant coeffcent c. We note that the reconstructon value r approaches the mdpont of the quantzaton bn, the conventonal reconstructon value, as the probablty dstrbuton becomes less sew fˆx x pˆ 0 1/ 2 J. Reconstructon of nsgnfcant coeffcents Our statstcal model for reconstructon of nsgnfcant subband coeffcents 1,r 2 0 c, pˆ sp s depcted n Fg. 4 (b). The quantzaton threshold for c s equal to 2 n or 2 n+1, dependng upon whether c has been vsted durng the last btplane pass. The estmated condtonal probabltes pˆ pˆ pˆ c c, 2 0 r c sp pˆ r 1 c,, c and Fgure 4 : The assumed condtonal probablty densty functon (pdf) for the subband coeffcents. (a) Left: The condtonal pdf model for sgnfcant (b) for coeffcents c x, x. 0 0 Rght: The condtonal pdf model for nsgnfcant coeffcents c (, ). The rght half of the coordnate plane corresponds to = 1 (the sgn predcton s correct). The gven contexts C are emprcally decded by the accumulated probablty tables, where ζ denotes the correctness of sgn predcton for c. www.jacsa.thesa.org 30 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, pˆ sp The defntons of the contexts for estmaton of ˆp 0 and are the same as the ones employed n sgnfcance codng of pxels and sgn codng, respectvely. Further, we assume the events and c 2 1 c, c c,, c are statstcally ndependent so that pr c 1 c 2 pr c 2 pr c 2, c c, c c, c. 13) V. RESULTS The results at dfferent bpp are shown n Fgure 5. It s shown as the bt rate decreases, the qualty of the reconstructed MRI mage should degrade. The results are tabulated for two samples as n fgure 6 and 7. The PSNR values for dfferent bpp are shown n table 1. () Orgnal MRI Image sample2 () Recovered MRI mage at 0.9 bpp Fgure 5. Recovered mages wthdfferent Bts per pxel values. (b) Recovered MRI mage sample at 0.1 bpp (a) Orgnal MRI mage sample1 (d) Recovered MRI mage sample at 0.9 bpp (c) Recovered mage at 0.5 bpp () Recovered mage at 0.1 bpp www.jacsa.thesa.org 31 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, (v) Recovered MRI mage sample at 0.5 bpp Fg. 6 PSNR v/s bpp plot for the gven mage Fg. 7 PSNR v/s bpp plot for the gven mage TABLE 1 PSNR V/S BPP PLOT FOR THE GIVEN LEAF IMAGE VI. CONCLUSION Ths project mplements an enhanced mage codng system for medcal mage compresson compared to the exstng JPEG 2000 system. It s observed that EZW s able to acheve ts good performance wth a relatvely smple algorthm. EZW does not requre complcated bt allocaton procedures le subband codng does, t does not requre tranng or codeboo storage le vector quantzaton does, and t does not requre pror nowledge of the mage source le JPEG does (to optmze quantzaton tables). EZW also has the desrable property, resultng from ts successve approxmaton quantzaton. One desrable consequence of an embedded bt stream s that t s very easy to generate coded outputs wth the exact desred sze. Truncaton of the coded output stream does not produce vsual artfacts snce the truncaton only elmnates the least sgnfcant refnement bts of coeffcents rather than elmnatng entre coeffcents as s done n subband codng. From the obtaned results t s concluded that embedded zero tree wavelet codng taes comparatvely less(about 60%) tme then the JPEG codng system. The codng also shows less percentage of error n medcal mage compare to the exstng JPEG codng system. It s observed that mage coded wth embedded zerotree wavelet codng shows clearer mage than other codng system. REFERENCES [1] A. Sad Pearlman, A new, fast, and effcent mage codec based on set parttonng n herarchcal trees, IEEE Trans. Crcuts Syst. Vdeo Technol., vol.6, no.3,1996, pp.243-249. [2] D.Taubman, Hgh Performance scalable mage compresson wth EBCOT, IEEE Trans. Image processng, vol.9, no.7, 2000, pp. 1158-1170. [3] M.Rabban and R.Josh, An overvew of the JPEG 2000 stll mage compresson standard, Sgnal Processng: Image Communcaton, vol.17, no.1, 2002, pp.3-48. [4] S.-T. Hsang and J.W.Woods, Embedded mage codng usng zeroblocs and of subband/wavelet coeffcents and context modelng, Proc. IEEE ISCAS 00, vol.3, Geneva Swtzerland, may 2000, pp. 662-665. [5] J.M. Shapro, Embedded mage codng usng zerotrees of wavelet coeffcents, IEEE Trans. on sgnal processng.vol.41, Dec.1993, pp. 3445-3462. [6] G.K. Wallace, The JPEG stll pcture compresson standard, Communcatons of the ACM, vol. 34, Aprl 1991, pp.30-44. [7] W.P. Pennebaer and J.L. Mtchell. JPEG Stll Image Data Compresson Standard. New Yor: Van Nostrand Renhold [8] J.Woods. ed., Subband Image Codng. Kluwer Academc Publshers. 1991. [9] M.Vetterl and J. Kovacevc, Wavelets and Subband Codng. Englewood Clffs.NJ: Prentce-Hall, 1995. [10] M. Antonn.M. Barlaud, P. Matheu, and I. Daubeches, Image codng usng wavelet transform, IEE Trans. Image Processng, vol. 1, pp. 205-220, 1992 [11] S.-T. Hsang and J. W. Woods, Hghly scalable and perceptually tuned embedded subband/wavelet mage codng, n SPIE Conference on VsualCommuncatons and Image Processng, vol. 4671, (San Jose, CA), Jan. 2002, pp. 1153 1164. [12] N. S. Jayant and P. Noll, Dgtal Codng of Waveforms. Englewood Cl.s, NJ: Prentce-Hall, 1984. [13] A. K. Jan, Fundamentals of Dgtal Image Processng. Englewood Cl.s, NJ: Prentce-Hall, 1989. [14] S. Rane, A. Aaron, and B. Grod, Systematc Lossy Forward Error Protecton for Error Reslent Dgtal Vdeo Broadcastng, n Proc. VCIP 2004, San Jose, CA, USA. www.jacsa.thesa.org 32 P a g e
(IJACSA) Internatonal Journal of Advanced Computer Scence and Applcatons, [15] A. Sehgal, A. Jagmohan, and N. Ahuja, Wyner-Zv codng of vdeo: An error-reslent compresson framewor, IEEE Trans. Mult., vol. 6, no. 2, Apr. 2004, pp. 249 258. [16] C. Tller and B. Pesquet-Popescu, 3D, 3-Band, 3-Tap Temporal Lftng For Scalable Vdeo Codng, n Proc. ICIP 2003, Barcelona, Span, 2003,Sept. 14-17. [17] C. Tller, B. Pesquet-Popescu, and M. Van der Schaar, Multple Descrpton Scalable Vdeo Codng, n Proc. EUSIPCO 2004, Venna, Austra, 2004,Sept. 6-10. [18] C. Tller and B. Pesquet-Popescu, A New 3-band MCTF Scheme For Scalable Vdeo Codng, n Proc. PCS 2004, San Francsco, CA, USA, 2004, Dec. 15-17. [19] C. Brtes, J. Ascenso and F. Perera, Improvng Transform Doman Wyner-Zv Vdeo Codng Performance, n Proc. ICASSP 2006, Toulouse, France, 2006, May 14-19. AUTHORS PROFILE LalthaY.S was born on December 7, 1969 n Inda. She receved B.E degree n Electroncs and Communcaton Engneerng and M.E. degree n Power Electroncs from Gulbarga Unversty Gulbarga, Inda, n 1991 and 2002 respectvely. She s worng as Professor n Appa Insttute of Engneerng & Technology, Gulbarga, Inda. Her research nterests nclude mage Processng, Wavelet Transform codng. Mrtyunjaya V Latte was born on Aprl 25 th 1964 n Inda. He receved B.E. degree n electrcal Engneerng and M.E. degree n Dgtal electroncs from S.D.M. College of Engneerng & Technology, Dharwad, Inda n 1986 & 1995 respectvely. He was awarded Ph.D. degree n 2004 for hs wor n the area of dgtal sgnal processng. He s worng as Prncpal, JSS Academy of Techncal Educaton, Bangalore, Inda. Hs research nterests nclude codng, mage processng and multresoluton transforms. He receved a best paper award for hs paper n a natonal conference NCSSS -2002 held at Combatore, Inda. www.jacsa.thesa.org 33 P a g e