COLOR IMAGE QUANTIZATION USING WEIGHTED DISTORTION MEASURE OF HVS COLOR ACTIVITY

Transcription

1 COLOR IMAGE QUANTIZATION UING WEIGHTED DITORTION MEAURE OF HV COLOR ACTIVITY yeong Man im, Chae oo Lee, Eung Joo Lee, and Yeong Ho Ha Deparmen of Elecronic Engineering, yungpoo Naional Universiy, Taegu 70-70, orea ABTRACT Color quanizaion is o design a color palee having almos no noiceably perceived difference beween original and quanized images. In his paper, o design such a palee, he color quanizaion algorihm is considered in wo pars: he selecion of a proper disorion measure and he design of an opimal palee. The proper selecion of disorion measure in he quanizaion is imporan o image qualiy. ince he human eye is he final judge of image qualiy, i is desirable o use a percepion-based disorion measure. Thus we developed an aciviy-weighed disorion measure considering color visual sensiiviy and absorbance of human visual sysem(hv) depending on each color componen in he local region of image. Then using he disorion measure, a hierarchical quanizaion algorihm is proposed. The algorihm consiss of iniial and subdivision seps boh o reduce compuaion ime and o minimize he disorion based on spaial masing effec of HV. The experimenal resuls show ha he proposed algorihm shows beer visual qualiy and less compuaion ime comparing o he convenional algorihms.. INTRODUCTION Video monior displays color image by modulaing he inensiy of hree primary colors(red, green, and blue) a each pixel of he color image. In a digiized image, each primary color is usually quanized wih 8 bis of resoluion in order o eliminae disinguishable quanizaion seps in ri-chromaic specificaion (luminance, hue, and sauraion). Thus, full-color digial display sysems use 4 bis o specify he color of each pixel on he screen. However, he cos of high-speed memory needed o suppor such display on he high-resoluion monior maes many applicaions impracical. An alernaive approach in many currenly available displays is o provide a limied number of bi, such as 8 bis, for specifying he color a each pixel. Each of hese 8 values is hen used as an index ino user-defined able of color, i.e., color palee. Each enry in he able conains a 4- bi value ha specifies each primary componen of he color image. In his way, he user is allowed o selec a small subse of color palee from he full range of 4 colors. The drawbac of his scheme is ha i resrics he number of colors ha may be simulaneously displayed [-7]. ince naural images ypically conain a large number of disinguishable colors, displaying such images wih a limied palee is difficul. everal echniques exis for color quanizaion, some of which are based on a more general class of vecor quanizaion(vq) echniques. One approach involves he ieraive refinemen of an iniially seleced palee. Variaions on his idea include he manner in which he iniial palee is chosen and he color space in which he quanizaion is performed. The refinemen algorihm, commonly nown as he -means or Linde-Buzo-Gray(LBG) algorihm [], is a vecor exension of he Lloyd quanizer for scalars. I sees o reduce he oal squared error(te) beween he original and he quanized image a each ieraion unil a (local) minimum is found. This mehod yields high-qualiy images and, wih a properly chosen iniial palee, will resul in he lowes TE for a given palee size. I is, however, compuaionally inensive and is performance is sensiive o he choice of he iniial palee. Also here is a class of spliing algorihms [,3,6] ha divide he color space ino disjoin regions and pic a represenaive color from each region as a palee color. The algorihms vary according o he mehods used o spli he color space. As an example of such algorihm, he median-cu algorihm [] invened by Hecber was underaen as an alernaive o he populariy algorihm. The median-cu algorihm repeaedly subdivides he color space ino smaller recangular boxes unil he desired number of boxes is generaed. The spli poin is he median poin - he plane which divides he box ino wo halves so ha equal numbers of colors are on each

2 side. The main advanage of he spli algorihm is ha i has a lower compuaional ime cos and space for he spaial sorage scheme-mosly because i is simple o compue he spli poin. There remain, however, a number of problems associaed wih his mehod. One of hose is ha pariioning a box by a plane passing hrough he median poin does no necessarily lead o a lower quanizaion error. As explained above, he convenional color quanizaion algorihms usually use he TE as he disorion measure [5,7]. This measure is, however, percepually insufficien when accuraely esimaing he percepual difference beween an original image and is quanized represenaion. I does no ae ino accoun he spaial correlaions ha lined percepually adjacen pixels. Wih such a measure we have no means o now wheher he observed degradaions are he resul of several paricularly noiceable degradaions. The measure mus be reconsidered, his ime, by duly inegraing he noion of locally observable errors. Thus, we propose o use a new disorion measure ha aes ino accoun he spaial aciviy in local region of inpu image. The aciviy is compued as mean of difference beween inpu and local mean color in 4 4 region, where he visual sensiiviy and absorbance of HV [-3] are considered. Therefore, he measured disorion value means he human perceived error. Then using he disorion measure, a hierarchical quanizaion algorihm is proposed by considering he spaial masing effec, [9,0] a characerisic of HV. The algorihm consiss of iniial and subdivision seps boh o reduce he compuaional ime and o minimize he measured disorion.. THE PROPOED DITORTION MEAURE AND QUANTIZATION ALGORITHM The color quanizaion is usually done by reaing hree color componens(red, green, and blue) independenly in RGB color space. Alhough hree color componens can be decorrelaed by ransforming he color space o YIQ, Lab or some oher uniform color spaces, independen quanizaion in hese spaces is inefficien because cerain porion of hese spaces lies ouside he RGB color space. In any even, color ransformaions are of lile use in quanizaion for display; heir proper place is in image compression sysems. Thus, we adoped o quanize he colors of original image ino (usually =56 or less) colors, called color palee, in he RGB color space. The color image is assumed o be on a recangular grid of N (= M M, M: image size) pixels. The se of all grid poins is denoed by and is members s may be explicily wrien as s = ( i, j), where i and j are he row and column indices, respecively ( 0 i, j M ). The color value of he pixel a grid c = r, g, b where he componens are poin s is denoed s [ s s s] he red, green, and blue risimulus values for he pixel in he RGB color space and superscrip means ranspose. And in designing he color palee, he -h cluser of colors is denoed by Ω ( ) and he cenroid of he cluser is denoed by µ = µ r, µ g, µ b which composes he color palee. The inpu image colors are mapped o he cenroid colors afer he quanizaion and he mapped colors are displayed on he monior simulaneously.. ACTIVITY-WEIGHTED DITORTION MEAURE In his paper, o design he color palee having almos no noiceably perceived difference beween he inpu image and he reconsruced image, he color quanizaion problem is considered in wo pars: he selecion of a proper disorion measure and he design of an opimal color palee using he disorion measure. A basic and imporan concep in he color quanizaion is he disorion measure used o measure he quanizaion errors beween inpu colors and palee colors. ince he human eye is he final judge of quanized image qualiy, i is desirable o use a percepion-based disorion measure. Thus, we develop an aciviy-weighed disorion measure based on he color change simuli of he HV according o each color componen in he local region of color image. In order o measure he percepion-based disorion, firs, he color aciviy is compuaed as mean of coefficien-weighed difference beween inpu color and local mean color ( clm = [ clmr, clmg, clmb] ) in 4 4 local region of he image, as given below. 6 A( c i, i: 6 ) = 6 ( ci, clm ) i= 6 = { ( cir clmr ) ( cig clmg ) ( cib clmb ) } 6 α + β + γ i= where c i c ir, c ig, c ib is he i-h inpu color in he local region = and he coefficiens ( α = , β = , and γ = 085. ) are normalized ( α + β + γ = ) sum of produc beween visual sensiiviy and absorbance [-3] of HV, shown in Fig. and Fig.. The coefficiens are calculaed as follows. and α = Rλ RAλ β = GλGAλ γ = Bλ BAλ α β γ α α β γ β α β γ γ α β γ () () (3)

3 where he R λ, G λ and B are he visual sensiiviy, and he RA, GA λ BA λ each color componen a wavelengh λ coefficiens show he response rae of human eye(cone) o each color componen. Then he compued aciviy shows he degree hus, maes he proposed measure he percepion-based disorion measure. The aciviy value is samely assigned o all quanizaion error of color. The higher aciviy means ha he color is less sensiive o human vision whereas he lower aciviy effec, a characerisic of HV which means ha human vision is he edge region. And hen, using he compued aciviy, he proposed disorion D = D = = c s c s A c = Ω ( s ) = = c s Ω A( c s ) E q µ (4) where D is he disorion of -h color cluser, E q is he quanizaion error. As he inpu color is included in he -h cluser, he quanizaion error is divided by he aciviy value of he inpu color. If so, he disorion error is decreased by he aciviy. Therefore, if he inpu color is less sensiive color, he aciviy is much higher and he disorion error is relaively much decreased. And if he inpu color is more sensiive color, he aciviy is much lower and he disorin error is relaively less decreased. This characerisic shows he masing effec. Thus, using he disorion measure, he less sensiive color can be less quanized, whereas he more sensiive color can be more finely quanized.. HIERARCHICAL QUANTIZATION ALGORITHM Using he disorion measure, a hierarchical color quanizaion algorihm is proposed by considering he masing effec. The algorihm consiss of iniial and subdivision seps boh o reduce he compuaional ime and o minimize he quanizaion errors. In he iniial sep, he inpu colors are divided ino 8 iniial color clusers, and hen in he subdivision sep, he iniial color clusers are recursively divided ino (56 or less) color clusers using he proposed disorion measure. In boh seps, inercluser variance maximizaion mehod [8] is used o deermine he quanizaion hreshold level, whch is fas and efficien in hresholds calculaion. The proposed algorihm is shown in Fig. 3. Then, he inpu colors are mapped o he cenroids of he color clusers using he pairwise-neares neighbor mehod. The mapped colors compose he color palee and are reconsruced on he video monior simulaneously. 3. EXPERIMENT AND REULT To simulae he proposed quanizaion algorihm, Girl, Lena, Pepper and Zelda images are used. These images conain boh smooh and edge regions and we can see he effec of he aciviy. For he original image, he aciviy in each 4 4 local region is compued and he values are samely assigned o all he pixels in he region. Then we sar he hierarchical quanizaion algorihm. In he iniial quanizaion sep, hree hresholds are calculaed using he iner-cluser variance maximizaion mehod. The hree acquired hresholds for Girl image are shown in Fig. 4. Depending on he hresholds, 8 iniial clusers are decided using he following equaion. cluser : r < R, g < G, and b < B cluser : r < R, g < G, and b B cluser 3 : r < R, g G, and b < B cluser 4 : r < R, g G, and b B cluser 5 : r R, g < G, and b < B cluser 6 : r R, g < G, and b B cluser 7 : r R, g G, and b < B cluser 8 : r R, g G, and b B where r s, g s, and b s are inpu color componens of he pixel a grid poin s, and R T, G T, and B T are he calculaed hresholds. In he subdivision sep, he cluser disorions(d ) are compued using Eq. (). Then, a maximal disorion cluser is seleced and subdivided ino 8 clusers using he above mehod. This process is repeaed unil color clusers are acquired, as shown in Fig. 3. Fig. 5 shows he comparison of displayed image on he monior using he convenional quanizaion algorihms and he proposed algorihm. The proposed algorihm shows beer visual qualiy. And Table has he comparison of he PNR, quanizaion errors in uniform color coordinae sysem space, and compuaion ime using un parc Worsaion in each algorihm. In he able, he proposed algorihm aes a lile longer compuaion ime han he Hecber s algorihm bu i aes much shorer compuaion ime han LBG. 4. CONCLUION We have proposed an efficien color quanizaion algorihm for designing a color palee whch has almos no noiceably perceived error and achieves high visual qualiy. ince he human eye is he final judge of quanized image qualiy, he (5)

4 weighed disorion measure based on HV color aciviy was considered. Wih his measure, we could esimae he percepual difference beween inpu image and quanized represenaion as a degree of color change simuli on he human vision in he local region of an image. And he proposed hierarchical quanizaion algorihm could produce an improved color palee by recursively subdividing a color cluser having maximal quanizaion error compued by he proposed measure. The performance of our quanizaion algorihm is comparable o ha of he opimal LBG algorihm under PNR and RME of quanizaion error in he CIE uniform color space, bu i has much shorer compuaion ime. Anoher advanage of he proposed algorihm is ha i shows beer image qualiy wihou any pos-processing such as ordered dihering, error diffusion, or erosion mehods commonly used in oher algorihms. [] R.W.G. Hun, A Model of Color Vision for Predicing Color Appearance, COLOR research and applicaion, vol.7, no., pp. 95-, 98. [3] Guner Wyszeci and W.. iles, COLOR CIENCE: Conceps and Mehods, Quaniaive Daa and Formulae nd Ediion, John Wiley & ons, pp , Augus 98. REFERENCE [] Y. Linde, A. Buzo, and R. Gray, "An algorihm for vecor quanizer design," IEEE Transacions on Commun., vol. COM-8, no., pp , January 980. [] Paul. Hecber, " Color image quanizaion for frame buffer display," Compu. Graph., vol. 6, no. 3, pp , July 98. [3] Nafaly Goldber, "Color image quanizaion for high resoluion graphics display," Image and vision compuing, vol. 9, no. 5, Ocober 99. [4] Michael T. Ochard and Charles A. Bouman, "Color quanizaion of images," IEEE Transacions on ignal Processing, vol. 39, no., December 99. [5] A. Tremeau, M. Calonnier, and B. Lage, "Color quanizaion error in erms of perceived image qualiy," 994 ICAP. [6] Raja Balasubramanian, "Color-image quanizaion wih use of a fas binary spliing echniques," J. Op. oc. Am. A, vol., no., November 994. [7] Tsann-hyong Liu and Long-Wen Chang, "Fas color image quanizaion wih error diffusion and morphological operaions," ignal Processing 43, pp , 995. [8] N. Osu, "A hreshold selecion mehod for gray level hisograms," IEEE Transacions on ys. Man and Cybern., vol. MC-9, pp.6-66, Jan [9] A. Neravali and B. Prasada, "Adapive quanizaion of picure signals using spaial masing," Proc. of IEEE 65, pp , 977. [0] Arun N. Neravali and Barry G. Hasell, Digial Picures, Plenn Press New Yor and London, pp , 989. [] J. D. Mollon and L. T. harpe, COLOR VIION: Physiology and Psychophysics, Academic Press INC., 983. Fig.. Relaive visual sensiiviy of human vision(cone). Fig.. Relaive visual absorbance of human vision(cone). Fig. 3. The proposed hierarchical quanizaion algorihm considering he spaial masing effec of HV.

5 (a) red componen (a) Original image (b) green componen (c) blue componen (b) The resul of LBG algorihm Fig. 4. Aciviy disribuion in he inensiy level of each color componen and hree hresholds(r T, G T, and B T) acquired in he iniial sep of he proposed algorihm using Girl image. Table. The comparison of PNR, quanizaion errors(q e) in CIE(Lu*v*), and compuaion ime using un parc Worsaion in each algorihm Image Algorihm PNR [db] Q e in Lu*v* Time [sec] LBG Girl Hecber The proposed LBG Lena Hecber The proposed LBG Pepper Hecber The proposed LBG Zelda Hecber The proposed (c) The resul of Hecber algorihm (d) The resul of he proposed algorihm Fig. 5.The experimenal resuls using Girl image.