Radiometric Compensation of Images Projected on Non-White Surfaces by Exploiting Chromatic Adaptation and Perceptual Anchoring

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1 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < Rdiometric Compenstion of Imges Projected on Non-White Surfces by Exploiting Chromtic Adpttion nd Perceptul Anchoring Ti-Hsing Hung, Ting-Chun Wng, nd Homer H. Chen, Fellow, IEEE Abstrct Flt surfces in our living environment to be used s replcements of projection screen re not necessrily white. We propose perceptul rdiometric compenstion method to counterct the effect of color projection surfces on imge ppernce. It reduces color clipping while preserving the hue nd brightness of imges bsed on the nchoring property of humn visul system. In ddition, it considers the effect of chromtic dpttion on perceptul imge qulity nd fixes the color distortion cused by non-white projection surfces by properly shifting the color of the imge pixels towrd the complementry color of the projection surfce. User rtings show tht our method outperforms existing methods in 974 out of 020 subjective tests. Index Terms Rdiometric compenstion, procm, Vsrely illusion, chromtic dpttion, CIECAM02, Humn visul system. U I. INTRODUCTION BIQUITOUS projection, mening being ble to project n imge nywhere, is no longer fiction due to the minituriztion of projectors. With n embedded projector, mobile or werble devices cn project n imge on ny nerby surfce such s wll, desktop, floor, clothes, or plm. However, most flt surfces in our living environment re not conditioned for imge projection. Besides geometric deformtion, color distortion is inevitbly introduced to the projected imge. For exmple, when n imge is projected on wood-top desk, the grin pttern of the wood would blend with the imge nd ffect the imge ppernce. Similrly, s shown in Fig., when the projection surfce is non-white, the color of the surfce would ffect the imge ppernce. This work investigtes how to combt such color distortion by rdiometric compenstion. Mnuscript received October 22, 204. This work ws supported in prt by grnt from the Ministry of Science nd Technology of Tiwn under Contrct E MY3 nd grnt from Ntionl Tiwn University under Contrct 04R T.-H Hung is with the Grdute Institute of Communiction Engineering, Ntionl Tiwn University, Tipei 067, Tiwn, R.O.C (e-mil: tshung983@gmil.com). T.-C Wng is with the Deprtment of Electricl Engineering, Ntionl Tiwn University, Tipei 067, Tiwn, R.O.C (e-mil: tcwng0509@gmil.com). H. H. Chen is with the Deprtment of Electricl Engineering, Grdute Institute of Communiction Engineering, nd Grdute Institute of Networking nd Multimedi, Ntionl Tiwn University, Tipei 067, Tiwn, R.O.C (e-mil: homer@ntu.edu.tw). Fig.. Color blending is inevitble for non-white projection surfce. Appernce of n imge projected on white projection surfce nd blue projection surfce. Rdiometric compenstion cn be relized by dding digitl cmer to the projector s visul feedbck. The resulting system is clled procm, which works by first projecting one or sequence of clibrtion ptterns to the projection surfce. The clibrtion imges cptured by the cmer re nlyzed to identify the chrcteristics of the projection surfce. Then the imge to be displyed is compensted ccordingly to counterct the effect of non-white projection surfce on imge ppernce. In prctice, the imge, the projector, the cmer, nd the projection surfce ll hve limited dynmic rnge nd gmut. Furthermore, the dynmic rnges nd gmuts of the components of procm my not be comptible with ech other. Such limittions nd incomptibility ffect the performnce of procm. For exmple, when the color of the compensted imge extends beyond the projector s gmut, color clipping is bound to occur. How to overcome such limittions for rdiometric compenstion nd preserve the perceptul ppernce of n imge is n importnt issue. Besides the physicl properties of color signl, the perceptul properties of humn visul system (HVS) hve to be considered to bridge the gp between mchine perception nd humn vision [35]. Most rdiometric compenstion methods ssume tht two physiclly different color signls would pper different. This ssumption, however, is not necessrily true. It is well known tht, due to the chromtic dpttion property of HVS, n object tht gives the senstion of white under dylight still ppers white under n incndescent light, lthough the dylight is bluer thn the incndescent light. The fct tht our eyes utomticlly dpt to the disply environment unfortuntely hs flip side for the problem

2 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 Fig. 2. Illustrtion of the chromtic Vsrely illusion. A repeted gry cross-shped pttern is surrounded by uniform bckground of different color. The cross-shped pttern illusorily ppers to be yellow in nd blue in [22]. considered here in tht color would pper differently when it is surrounded by different color bckground. This perceptul property of HVS cn be best illustrted by the chromtic Vsrely illusion [22]. Only gry nd blue colors re used to generte the pttern shown in Fig. 2. But the HVS is tricked into seeing yellow (the complementry color of blue) in the gry crosses becuse the blue bckground ffects the color perception of HVS. Similrly, the gry cross-shped pttern in Fig. 2 illusorily ppers to be blue in yellow bckground. For non-white projection surfces, it is importnt to ddress the effect of color bckground on imge ppernce. This pper is different from our previous work [32] in tht the projection surfces re not limited to be uniform color. Our system cn del with texture surfces now (Section III), nd we include n nlysis of computtionl efficiency, ccurcy, nd optimiztion in Section V. The contributions of the pper re s follows: We propose n optimiztion method for rdiometric compenstion to reduce the clipping rtifct while preserving the photometric (lightness, hue, nd chrom) qulity of the imge. All prmeters of the method re determined through subjective tests to ensure tht the design is in conformnce with humn visul perception (Section III). Unlike most existing rdiometric compenstion methods, our method considers the effect of chromtic dpttion on ubiquitous projection nd yields more fithful color reproduction (Section III). We simplify the nonliner color trnsformtions of CIECAM02 [6] nd reduce the computtion time by 50% with only 2.3% pproximtion error (Section IV). The speedup is importnt for prcticl pplictions. II. REVIEW This section briefly reviews the rdiometric compenstion techniques, the chromtic dpttion property of HVS, the nchoring theory, the CIECAM02 model, nd the color clipping reduction techniques. A. Rdiometric Compenstion The procm model developed by Grossberg et l. [] hs been widely dopted to describe the color conversion process of procm nd relte the input intensity of the projector ll the wy to the output intensity of the cmer. A clibrtion procedure is required to determine the projector response function, the surfce reflectnce function, nd the cmer response function for the procm model. The first two re often combined into new function P( ) tht reltes the input intensity of the projector to the output irrdince of the projection surfce. The clibrtion for the idel white surfce nd the color projection surfce re performed seprtely. Given P( ), the rdiometric compenstion works by first computing the irrdince R of n input imge on the white screen from the imge intensity I, R P ( ), W I where the subscript W denotes white screen. Then the imge is compensted such tht the irrdince of the compensted imge on the color projection surfce is equl to tht of the imge on the white screen. Tht is, () P ( I) P ( I), (2) C where the subscript C denotes color projection surfce nd I denotes the compensted imge. Tking the inverse conversion on both sides of (2) yields W I P ( P ( I)). (3) C The bove procedure works under the idel condition with no limittion on the dynmic rnge nd gmut of ech procm component. We tke such limittion into considertion in Section III. Grossberg s model [] cnnot ccurtely describe the non-linerity of color mixing [] between the projector nd the cmer. A more ccurte model ws developed by Grundhöfer [34]. B. Anchoring Theory The nchoring theory of lightness perception suggests tht HVS tends to first identify the highest luminnce of n imge s the nchor nd then determine the ppernce of the imge with respect to the nchor [4]. In the context of color perception, the nchor refers to set of tristimulus vlues or chromticity coordintes tht define the white color of the imge. Anchoring is perceptul tendency tht ccounts for the chromtic dpttion property of HVS. Tke Fig. 2 s n exmple. When looking t the cross-shped pttern, our eyes tke slightly blue color s white becuse blue hs the highest dominnt brightness in the imge. As result, the ppernce of the imge would bis slightly towrd the complementry color of blue, which is yellow. This is why the gry cross-shped pttern ppers yellowish in Fig. 2. Likewise, the gry cross-shped pttern in Fig. 2 ppers bluish becuse our visul perception of the pttern is slightly shifted towrd the complementry color of yellow, which is blue. C. CIECAM02 Color Appernce Model CIECAM02 is the most recent color ppernce model rtified by the CIE Technicl Committee [6]. It provides mthemticl description of the reltionship between the W

3 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 Fig. 3. Explntion of color clipping by the sptil reltion between the imge gmut nd the projection surfce gmut in 3D color spce. Since the gmut of the imge lies completely within the gmut of the idel white projection surfce, there is no color clipping. When the trget gmut is not entirely enclosed by the gmut of the color projection surfce, color clipping is bound to hppen. Fig. 4. Illustrtion of how imge gmut scling cn reduce the color clipping rtifct in 3D color spce. The sptil reltion between the imge gmut nd the projection surfce gmut is dopted from Fig. 3. The imge gmut is scled down to within the projection surfce gmut to void color clipping. A compensted imge thus obtined. physiclly mesurble quntities of stimuli nd the ttributes of visul senstion. Specificlly, it reltes the CIE tristimulus vlues [5] to six ttributes of visul senstion: brightness, lightness, colorfulness, chrom, hue, nd sturtion. CIECAM02 requires user-specified reference white s the nchor for computing the ppernce of n input color with respect to the reference white. The degree of chromtic dpttion is controlled by prmeter D rnging from 0 for no dpttion to for complete dpttion. The model cn be implemented in forwrd or bckwrd mnner. In the forwrd mnner, the model outputs the ppernce ttributes of color with respect to given reference white. In the bckwrd mnner, the model genertes color using the input ppernce ttributes nd the reference white. All the imge opertions described in Section III re bsed on CIECAM02. We dopt this color ppernce model in our method becuse of its ccurcy nd flexibility [33]. It hs the following dvntges over CIELAB nd CIELUV: Viewing condition prmeters cn be set to represent the disply s viewing conditions. Reference white cn be chnged over wide rnge relibly. They provide more numericl correltes for ll perceived ttributes of color (colorfulness, chrom, sturtion, hue, brightness, nd lightness) Numericl scles of these correltes correspond better to color perception thn CIELUV correltes. CIECAM02 is more uniform color spce for smll nd lrge color differences. D. Color Clipping Artifct Whether the imge color cn be properly displyed on projection surfce hs to do with the gmut of the imge with respect to the gmut of the projection surfce. If the imge gmut is not entirely inside the gmut of the projection surfce, color clipping would occur nd result in noticeble rtifct. This is illustrted in Fig. 3. For ubiquitous projection, the gmut of the imge on n idel white screen serves s the trget gmut, which often flls outside or cross the gmut of the projection surfce. To reproduce the ppernce of n imge on color projection surfce with s little color clipping s possible, the imge gmut hs to be properly mnipulted with respect to the gmut of the projection surfce. The methods for reducing color clipping rtifct cn be divided into the multi-projector pproch [2][4] nd the single-projector pproch [5][3]. The former expnds the gmut of the projection surfce by superimposing the imges projected from number of projectors; color clipping rtifct is reduced t the expense of system complexity nd cost. The ltter involves scling opertion tht shrinks the imge gmut, s shown in Fig. 4, t the expense of imge brightness nd detils. In generl, rtifct is introduced s result of improper scling. Both heuristic nd perceptul metrics cn be used to quntify the effect of color clipping nd dimming on imge qulity. For exmple, root-men-squre error hs been dopted to mesure rdiometric distortion [23], nd perception-bsed error metric [24] tht considers contrst sensitivity [25] nd visul msking [26] of HVS hs been used to mesure the noticeble luminnce distortion [7]. Generlly, the qulity of error metric ffects the performnce of rdiometric compenstion method. III. PROPOSED METHOD Conventionl rdiometric compenstion ttempts to completely reproduce the color tone of n imge. However, due to the physicl limittion on the gmut of projector, the brightness nd color tone usully cnnot be perfectly recovered t the sme time by rdiometric compenstion. Therefore, trdeoff between brightness nd color tone hs to be mde. Fig. 5 illustrtes how the conventionl method works for single pixel in the liner RGB color spce. Suppose the color of the projection surfce is mgent nd the trget color is X 0. When X 0 is projected onto the mgent surfce, the complementry color of mgent which is green would be prtilly bsorbed by the projection surfce, nd the reflected color would be bised towrd mgent. To compenste for the bsorption of the green color, the conventionl method increses the intensity of the green chnnel from X 0 to X so tht, when projecting X onto the projection surfce, the reflected color would be exctly X 0. However, in prctice, this reflected color would pper greener thn X 0 due to the chromtic dpttion of HVS.

4 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 Fig. 5. The difference between the proposed method nd the conventionl method in rdiometric compenstion. However, the proposed method results in brighter imge thn the conventionl method. This is illustrted in Fig. 5, where X nd X 2, respectively, re the scled colors generted by the conventionl nd the proposed methods. Since L 2 (the distnce between nd the origin) is lrger thn L (the distnce X 2 between nd the origin), the imge generted by the proposed method is brighter thn tht generted by the conventionl method. When the color of the bckground surfce under white illumintion is not visible t ll, the mount of hue djustment would be very smll becuse the trget bckground color is nerly blck. For such cses, our lgorithm would not djust the color of the imge, similr to the conventionl rdiometric compenstion lgorithm. Bsed on the rdiometric compenstion procedure described in Section II. A, we propose n optimiztion method to reduce the color clipping rtifct while preserving the color ppernce of the compensted imge s much s possible. The block digrm of the proposed method is shown in Fig. 6. First, we dopt Grossberg s procm model [] described in Section II.A to compute the irrdince of n imge projected on white surfce vi P W( ). Then, brightness scling nd hue djustment opertion re pplied to the imge with optimized coefficients. Finlly, we perform rdiometric compenstion vi. The detils of our method re described s follows. P C () X Fig. 6. Block digrm of the proposed lgorithm. A. Clibrtion of the Procm Model The procm system considered in this work consists of projector (SANYO PLC-XW56) nd cmer (Cnon 40D). The experimentl setup nd the corresponding block digrm re shown in Fig. 7. The irrdince R of pixel locted t (x, y) of projected imge cn be modeled by R( x, y) P( I( x, y), r( x, y), ( x, y)), (4) p( I( x, y)) r( x, y) ( x, y) Fig. 7. Experimentl setup. The procm system consists of projector (SANYO PLC-XW56) nd cmer (Cnon 40D). The rchitecture of procm system. To compenste for the chromtic dpttion, we djust the projected color from X to less green color X 2. It should be noted tht X 0, X, nd X 2 would be colliner in most rel cses becuse the compenstion for the projection surfce color nd the compenstion for the chromtic dption re both bsed on the color of the projection surfce. The only difference between them is tht the former increses while the lter decreses the intensity of the green chnnel of X 0. Becuse the mount of color djustment due to chromtic dpttion is smller thn tht due to surfce color compenstion, X 2 would ly between X 0 nd X. The projected color my not ly inside the projector gmut. Like the conventionl method, our proposed method solves the problem by scling down the projected color long the line pssing through the origin to preserve the hue of the color t the cost of brightness (the distnce from color to the origin). where p( ) is the projector response function, r(x, y) is the reflectnce of the surfce, nd (x, y) is the irrdince contributed by the mbient light. To determine r(x, y) nd (x, y), we project two gry imges with different intensity levels I nd I 2 onto the projection surfce nd obtin the corresponding irrdinces R (x, y) nd R 2(x, y), respectively, s follows: Therefore, R ( x, y) p( I ) r( x, y) ( x, y). (5) R ( x, y) p( I ) r( x, y) ( x, y) 2 2 R( x, y) R2( x, y) r( x, y) p( I) p( I2). (6) R( x, y) R2( x, y) ( x, y) R2( x, y) p( I2) p( I) p( I2) Substituting (6) into (4) yields R( x, y) R2( x, y) R( x, y) R2( x, y) p( I( x, y)) p( I2). (7) p( I ) p( I ) 2

5 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 5 Rewriting (4) by putting the non-liner terms together nd denote them by N( ), we hve p( I( x, y)) p( I ) R( x, y) R ( x, y) R ( x, y) R ( x, y). (8) 2 2 p( I) p( I2) R ( x, y) N( I( x, y)) R ( x, y) R ( x, y) 2 2 Note tht N( ) is independent of the reflectnce of the texture surfce becuse it is only relted to the input imge nd the projector s response function. On the other hnd, the terms R 2(x, y) nd (R (x, y) R 2(x, y)) implicitly represent the reflected irrdince of the mbient light nd the reflectnce of the textured surfce t (x, y). From (8), we hve R( x, y) R2 ( x, y) N( I( x, y)). (9) R ( x, y) R ( x, y) 2 Note tht since the vlue of I(x, y) is n integer rnging from 0 to 255, N( ) cn theoreticlly be obtined for ll 256 possible inputs. In prctice, since there re noises in the obtined irrdince dt, N( ) is determined by regression. Specificlly, we project clibrtion pttern with intensity levels uniformly distributed from 0 to 255 onto the texture surfce. From the cptured imge, we cn obtin multiple irrdince vlues corresponding to ech of the 256 possible inputs of N( ). Then N( ) is determined by regression. B. Color Mixing between Projector nd Cmer Grossberg s color decoupling method [] nd its corresponding clibrtion procedure re dopted in this work to del with the color mixing [] between projector nd cmer. Specificlly, the irrdince modeled by R cptured by the cmer is R VP, (0) where V is 3-by-3 mtrix, P is the irrdince of the projector, nd is the reflected irrdince of the mbient light. R, P, nd re 3-vectors. Grossberg et l. decompose V into the multipliction of two terms s follows: V V V V V V V V V V RR RG RB GR GG GB BR BG BB VRG VRBrR 0 0 VGR V GB 0 rg 0, () VBR VBG 0 0 r B Denoting the first term by V nd the second term by r yields VRG VRB rr 0 0 V VGR V GB 0 rg 0 V r, (2) V BR VBG 0 0 r B where V models the color mixing between projector nd cmer, nd r models the reflectnce of the projection surfce. Specificlly, in (), ech V CC 2models the contribution of the C chnnel of the projector to the C 2 chnnel of the cmer, nd r models the reflectnce of the projection surfce C corresponding to the C chnnel of the projector. Ech VCC 2 in () is determined seprtely by projecting two imges with intensity difference only in the C color chnnel of the projector nd normlizing the resulting irrdince difference in ech cmer chnnel. C. Brightness Scling We reduce the color clipping rtifct by shrinking the imge gmut while preserving the imge ppernce s much s possible. The ide is similr to tht illustrted in Fig. 5 except tht the opertion is performed in the 6D color-ppernce spce specified by CIECAM02 insted of 3D color spce. A mjor benefit of CIECAM02 is tht it llows us to incorporte the nchoring property of humn color perception nd preserve the reltive ttributes of lightness, chrom, nd hue of n imge cross different projection surfces. In ddition, the ccurcy of CIECAM02 hs been verified by rigorous test procedures [3]. There re two steps. In the first step, the ttributes of visul senstion of the imge re computed using CIECAM02, for which the reference white is set to the highest luminnce of the imge. In the second step, the luminnce of the reference white is scled down nd used s reference to trnsform the visul ttributes obtined in the previous step to the color spce of the imge. Since the color ppernce of the imge is to be preserved, we do not modify the visul ttributes. The detils of brightness scling re s follows. First, the intensities of the input imge re trnsformed to the luminnce vlues on the white surfce using the intensity-to-luminnce function P W ( ) described in Section II.A. Then, the luminnce vlues re normlized nd trnsformed to the XYZ tristimulus vlues. The lrgest tristimulus vlue T W is identified nd used s the reference white in the forwrd trnsformtion of CIECAM02 to relte ech tristimulus vlue to the six visul ttributes. Finlly, these visul ttributes re trnsformed bck to the luminnce vlues with respect to new white point αt W, where α is brightness scling fctor tht is determined through qulity optimiztion process described in Section III.E. D. Hue Adjustment The purpose of hue djustment is to compenste the effect of chromtic dpttion of HVS on the color ppernce of n imge. An illustrtion of the effect is shown in Fig. 8, where the bckground represents projection surfce nd the foreground represents n imge. The top blue imge block is projected on white surfce. The bottom row shows the scenrio where the sme blue imge block is projected on blue projection surfce. The trditionl rdiometric compenstion method would im for perfect restortion nd generte the bottom left blue imge. Apprently, even if the color of the compensted imge is physiclly restored, it ppers different from the top blue imge block. In contrst, our hue djustment opertion would mke the compensted imge block shown on the bottom right little bit bluer, nd hence the color ppernce of the resulting imge would be closer to the top imge block. Similr to the brightness scling opertion, the hue of n imge is djusted by mnipulting the color of the reference white of the CIECAM02 model. It involves severl steps. First,

6 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 optimiztion process. E. Qulity Optimiztion We find the optiml α nd D tht blnce the undesirble brightness reduction, hue distortion, nd color clipping in the compensted imge through the following optimiztion procedure: 2 2 D w w2d E D, rg min ( ) (, ),, D (3) Fig. 8. An illustrtion of the effect of hue djustment. The top hlf shows blue imge block projected on white surfce. The bottom hlf shows two imge blocks projected on blue surfce. The two imge blocks re generted from the top imge block in two different wys. The left one is physiclly the sme color s the top imge block, nd the right one is with hue djustment. It ppers tht the right imge block is perceptully more similr to the top imge block thn the left one. Fig. 9. Setup of the off-line subjective experiment. The left prt of the projection re is white nd the right prt is color surfce. The originl test imge is projected onto the white projection surfce, nd the compensted imge is projected onto the color projection surfce. The subject cn switch the imge on the color projection surfce between two compensted imges generted with different w nd w2 in ech tril. Fig. 0. The EMMens of the winning times of different combintions of w nd w2. the visul ttributes of the input imge re computed using the sme procedure for brightness scling. Next, P C ( ) is pplied to the lrgest intensity of the input imge to obtin its luminnce on the color surfce, which is then normlized nd trnsformed to obtin the tristimulus vlue T. Finlly, the color ppernce of W the input imge is trnsformed bck using T s the white point. W Recll tht the degree of chromtic dpttion is controlled in the CIECAM02 model through the chromtic dpttion degree D, which rnges from 0 for no dpttion to for complete dpttion. We use this prmeter to control the mount of hue djustment of color towrd T. The lrger the vlue of D, the W more hue djustment is performed. Similr to the brightness scling fctor α, D is lso determined through qulity where (-α) ccounts for the brightness reduction of the resulting imge, D ccounts for the mount of hue djustment, nd E ccounts for the mount of clipping rtifct in the compensted imge, which is clculted s follows: 2 (4) i i E(, D) l p (, D) U p (, D) U / I, i where l is n indictor function, p i is the luminnce vlue of pixel i in the compensted imge, U is the upper bound of the projector s dynmic rnge, nd I denotes the totl number of pixels in the imge. It should be noted tht p i is function of α nd D becuse the luminnce vlue of the compensted imge chnges whenever α or D chnges. The weightings w nd w 2 re determined through n off-line subjective experiment which ims t mking the optimiztion in conformnce with humn visul perception. The detils re described s follows. F. Off-Line Subjective Experiment A subjective test involving 0 mle nd 0 femle subjects ws conducted to determine w nd w 2 in (3). The ge of the subjects rnges from 2 to 26. Since it is infesible to test the infinitely mny possible vlues of w nd w 2, we empiriclly chose four cndidte vlues (3, 5, 0, nd 20) for w nd nother four vlues (0 4, 0 5, 5 0 5, nd ) for w 2 tht produce imges with better qulity (judged subjectively by the uthors). In the test, we used 0 test imges selected from three imge dt sets: Wterloo [8], Kodk [9], nd SIPI [20]. Ech test imge ws compensted using the (α, D) generted by the 6 combintions of the cndidte vlues of w nd w 2. This wy, we hd 6 compensted imges tht correspond to the 6 combintions of weights (w,w 2) for ech test imge. The experimentl setup is shown in Fig. 9. The tsk of the subjects ws to choose from the 6 compensted imges the one tht best mtches the originl imge projected on white surfce. The comprison proceeded in pir-wise mnner. Specificlly, in ech tril, subject ws presented two rndomly selected compensted imges projected on color surfce long with the originl imge projected on white surfce. The one tht is more similr to the originl imge ws kept, nd the other one ws substituted with nother rndomly selected compensted imge tht hs not yet been shown to the subject. This process repeted until ll compensted imges were tested. The experiment ws performed on mgent, yellow, nd blue projection surfces. We determined one set of weighting coefficients for ll color surfces. An ANOVA [2] of two fctors (w nd w 2) ws conducted on the totl number of times ech combintion won. The estimted mrginl mens (EMMEANS) re shown in Fig. 0. We cn see tht the best

7 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 7 following, we use the sme nottions s those in [6] nd only introduce the new nottions of the simplified model. ) Forwrd trnsformtion: We follow the originl model to trnsform n input color from the CIEXYZ spce to the CAT02 spce using the M CAT02 trnsformtion mtrix: R X X G M CAT 02 Y Y. (5) B Z Z Then, the chromtic dpttion trnsform for the R chnnel is pproximted by Fig.. Block digrm of the proposed lgorithm. performnce is chieved when w = 0 5 nd w 2 = 5. This weight combintion is dopted in our implementtion. IV. SIMPLIFICATION The brightness scling nd hue djustment opertions presented in Section III re computtionlly hevy becuse of the nonliner color trnsformtions of CIECAM02. To reduce the computtionl cost, two simplifictions re proposed: ) reducing the use of CIECAM02 by combining the brightness scling nd hue djustment opertions, nd 2) simplifying the CIECAM02 model. The detils of these two simplifictions re described in this section. A. Procedure Simplifiction The brightness scling nd hue djustment re combined into one trnsformtion. In this new trnsformtion, the luminnce vlues of the imge re trnsformed to ppernce vlues using T s the white point nd then trnsformed bck using α W T W s the white point. The overll block digrm of the simplified procedure is shown in Fig.. B. Model Simplifiction The forwrd nd bckwrd trnsformtions of the CIECAM02 model re time consuming due to the non-liner color trnsformtions. Becuse only the nchor is replced in the forwrd nd bckwrd trnsformtions, it is possible to simplify the entire process. CIECAM02 mkes use of the CAT02 spce [27] for the chromtic dpttion trnsform nd the Hunt-Pointer-Estevez spce [28] for computing perceptul ttribute correltes. The reder is referred to [6] for the detils of CIECAM02. In the Y w Rc D DR D R, Rw (6) where R c is the dpted R vlue of the input color, Y w nd R w, respectively, re the luminnce nd R vlues of the reference white, nd D is the degree of dpttion. The sme pproximtion is lso pplied to obtin G c nd B c. Then, ccording to the originl model, we trnsform the dpted color from the CAT02 spce to the Hunt Pointer Estévez spce by the M H trnsformtion mtrix, R Rc G M H M CAT 02 G. (7) c B B c Substituting (5) nd (6) into (7) yields R' X G ' D M H Y. B' Z (8) A non-liner response compression bsed on the generlized Michelis Menten eqution [29] is then pplied to the dpted color. For the R' chnnel, the compression cn be pproximted s follows: FR L / R FLR/00, 27.3 FR/ L where F L is luminnce dpttion fctor, L 0.2 (5 A) 0.( ) (5 A) 5LA 5LA F L L (9), (20) nd L A is the luminnce of the dpting field in cd/m 2 [6]. The sme pproximtion is lso pplied to G nd. Then the chromtic response A cn be pproximted s follows: A 2R G B Nbb 2 R G B Nbb, where N bb is temporry quntity [6] determined by N bb Y b Yw 0.2 B (2), (22)

8 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 8 nd Y b is the luminnce of the bckground. Finlly, the lightness ttribute is pproximted by (32) cz A 2 R G B / 20 J Aw 2 R w G w B w / 20 where A w is the chromtic response of the reference white, B w, nd G w cz (23) R w re the dpted color vlues of the reference white, c is viewing condition prmeter tht cn be set to for drk surround, 0.59 for dim surround, nd 0.69 for norml surround, nd z is computed by z =.48 + Y b Y W. (24) 2) Bckwrd trnsformtion: Let be the Y component of the new reference white nd denote the rtio of to Y w by k. Then, we hve (25) Here, ll symbols with tilde on top denote vlues derived in the bckwrd process, i.e., from the new reference white. The chromtic response of the new white point only needs to be clculted once for the entire imge nd is exctly clculted. Let the rtio of be β. From (23), we hve, Similrly, the correlte for red-green is (33) Thus the responses in Hunt Pointer Estévez spce nd its compression re R 2 / 20 p2 G 2 / / B / 9 / 9 2 / 9 b 2 / 20 p2 R k 2 / / k G, / 9 / 9 2 / 9 b B R R 00 R R 400. FL 400. F L R R R k R. Finlly, the new tristimulus vlues cn be pproximted by (34) (35) æ J ö A = A w ç è00 ø /cz (26) (36) Then, J J J J A Aw Aw A where J 00 / cz / cz / cz / cz / cz/ cz cn be clculted by, (27) AA,. The correlte for yellow-blue cp2 cp2 cp2 p2 p b, b b, (28) p csc h d cot h f p csc h p csc h p p 2 where (29) (30) nd (3) Thus, V. EXPERIMENTS (37) Four experiments were conducted to evlute the performnce of the proposed method. In the first experiment, we evluted the ccurcy nd time complexity of the simplified CIECAM02. In the second experiment, we evluted the effect of hue djustment on imge brightness. In the third experiment, we evluted the brightness gin of the proposed method. Finlly, we performed subjective experiment to compre our method with four other methods. A. Accurcy nd Time Complexity of the Simplified CIECAM02 We compred the efficiency of CIECAM02 with tht of the simplified model by testing them on 000 normlized luminnce vlues which rnge from [0., 0., 0.] to [,, ] with step size equls 0.. For ech luminnce vlue, the computtion time of ech model for performing forwrd nd bckwrd color trnsform ws mesured. Both models were implemented using MATLAB R202 on ThinkPd T430 notebook computer with Intel i5 processor (2.6GHz) nd 4GB memory. The verge computtion time for CIECAM02 is seconds, while the verge computtion time for the simplified model is seconds. The results show tht the simplified model reduces bout 50% of the computtion

9 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 9 (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Fig. 2. A set of 2 smples of the 44 test imges used in this work. TABLE I TIME COMPLEXITY EVALUATION (IN SECONDS) Imge nme Originl Simplified Imge nme Originl Simplified method method method method vin house bboon isbe brbr len bech lighthouse bikes lighthouse bots monrch building ocen building prrots cps pepper cemetry plne church rpids clown siling coins siling dncers siling dolls siling door sculpture fishing sttue flower strem fruit wll girl windows house womn house womnht * Originl method: 9.22 ± 2.83 (verge nd stndrd devition) * Simplified method: 3.92 ± 0.46 (verge nd stndrd devition) time for color trnsformtion. To investigte the ccurcy of the simplified model, we tested it on the sme normlized luminnce vlues described bove. For ech luminnce vlue, corresponding luminnce vlue ws computed using α = 0. nd D = Compring to the exct solutions computed using CIECAM02, the errors for different luminnce combintions re ll within ±2.3%, which indictes tht the simplified model is ccurte enough for color trnsformtion. We compred the computtion time of the originl method with tht of the simplified method. Both methods were pplied to 44 test imges (Fig. 2) selected from the imge sets of Wterloo [8], Kodk [9], nd SIPI [20] but different from the imges used in the off-line subjective experiment (Section III.F). TABLE II AVERAGE COMPUTATION TIME FOR EACH STEP OF THE PROPOSED METHOD Min steps Sub steps MATLAB codes C codes Procm model 0.02s s Qulity optimiztion 3.052s 0.44s * Itertions to convergence Cost function of Eqution (3) 0.025s 0.002s Eqution (4) 0.025s 0.002s Brightness scling + Hue djustment Inverse procm model 0.843s 0.04s Overll computtion time 3.92s 0.86s * Suppose the sme solver s our MATLAB implementtion is used, the verge computtion time for the qulity optimiztion would be 0.44s (0.002s 20 itertions) The resulting computtion time of ech test imge is listed in Tble I. The verge computtion time of the originl method nd the simplified method, respectively, re 9.22 nd 3.92 seconds. Approximtely 80% of the computtion time is sved. In ddition, the stndrd devition of the computtion time is reduced from 2.83 to The verge computtion time of ech step of our MATLAB implementtion is shown in Tble II. The overll computtion time is 3.92s in verge, nd the qulity optimiztion step, which tkes 3.052s, is the min bottleneck. The overll computtion time reduces to 0.86s for the C implementtion of the simplified method, s shown in Tble II. The computtion time is proportionl to the number of itertions required for the solver to converge. We tke close look t the bottleneck nd find tht, in verge, 20 itertions re required to obtin the optiml solution. B. Effect of Hue Adjustment on Imge Brightness The effect of hue djustment on imge brightness ws quntittively evluted. We forced D, the mount of hue djustment, to be constnt in the optimiztion process described by (3) nd compred the resulting α vlues cross four different levels of hue djustments: D is set to 0, 0.02, 0.05, nd A lrger α vlue indictes brighter imge. A totl of 44 uniform color imges were used in this evlution. The hue vlue rnges from 0 to 360 with step size of 0, nd the chrom vlue rnges from 25 to 00 with step size of 25. The test projection surfces were mgent (hue vlue is 320), yellow (hue vlue is 60), nd cyn (hue vlue is 70). The results for the mgent projection surfce re shown in Fig. 3. It cn be seen tht α vries with respect to the hue nd chrom of the test imge. It becomes lrger when the hue of the test imge is closer to the hue of the projection surfce, nd the pek-to-vlley difference increses s the chrom of the test imge increses. This revels how our method djusts the brightness of test imge bsed on the color of the projection surfce. Fig. 3 lso shows tht α increses s D increses. This indictes tht the lrger the hue djustment, the brighter the resulting imge is. Similr observtion cn be found from the results for the yellow nd cyn projection surfces. To exmine the brightness gin of the hue djustment, we computed the rtio between α vlues for trils with hue

10 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 0 Fig. 5. The α gins (brightness gins) of different test imges for mgent projection surfce. Uniform color imges nd 44 test imges. (c) (d) Fig. 3. The α vlues (color scling rtio) of uniform color imges on mgent screen (hue vlue is 320). Fig. 6. The EMMens of the winning times of different lgorithms. Fig. 4. The α gins (brightness gins) of different test imges for mgent projection surfce. Uniform color imges with D=0.02, Uniform color imges with D=0.05, nd (c) Uniform color imges with D=0.08. TABLE III AVERAGE COLOR SHIFT DUE TO PERCEPTUAL COMPENSATION (c) D = 0.02 D = 0.05 D = % 7.6% 7.42% djustment (D = 0.02, 0.05, nd 0.08) nd without hue djustment (D = 0). The results for the mgent projection surfce re shown in Figs. 4 (c). It cn be seen tht the α gin increses when the hue of the imge is wy from mgent, nd it reches the pek vlue when the hue of the test imge is bout 60, which is the complementry color of mgent. This indictes tht the brightness gin peks when the hue of the test imge is the complementry color of the projection surfce. Finlly, we evluted the percentge of color shift cused by hue djustment. For ech of the 44 uniform color imges, we compred between the compensted colors with hue djustment (D = 0.02, 0.05, nd 0.08) nd those without hue djustment (D = 0). The verge color shift for ech D vlue is shown in Tble III. The mount of color shift increses s D increses, but not in liner mnner. The increment decreses s D increses. C. Brightness Gin The brightness gin of the proposed method ws evluted. The 44 uniform color imges described in Section V. B nd the 44 imges described in Tble I were used s test imges. For ech test imge, we computed the rtio between the α vlues with hue djustment (D nd α were obtined by (3)) nd those without hue djustment (D = 0 s described in Section III. B). Fig. 5 shows the results of the uniform color imges, where the vlues of α gin remin nerly constnt when the hue of the imge is wy from the hue of the projection surfce. This indictes tht the optimiztion tends to find D vlue tht mximizes the α gin while preserving the brightness of the colors tht re similr to the projection surfce. Fig. 5 shows the results of the 44 test imges. The vlues of α gin rnges from.35 to.45, nd the verge is.4. D. Performnce Comprison To benchmrk our method with previous ones, subjective test ws conducted on 34 test imges tht were not used in the

11 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < (c) (d) (c) (d) (e) (f) Fig. 7. Comprison of different compenstion lgorithms. Originl imge projected on white screen, Originl imge projected on green screen. (c), (d), (e), nd (f), respectively, re the compenstion results generted by GRC, PRC, CMB, nd the proposed methods. off-line subjective experiment (Section III.D). Five mle nd five femle subjects were involved in the experiment. The ge of the subjects rnges from 2 to 26. The proposed method ws compred with three other methods: GRC [], PRC [7], nd CMB [3]. We implemented GRC nd PRC ourselves nd used the originl code of CMB. The procedure ws the sme s tht of the experiment described in Section III.F except tht we compred the results for ech test imge. The results show tht the proposed method outperforms the other methods in 974 out of 020 comprisons (34 test imges 0 subjects 3 competing lgorithms). The wining rte is more thn 95%. An ANOVA [2] ws conducted on the totl number of times ech combintion won. The EMMEANS of the ANOVA re shown in Fig. 6. The difference in EMMEANS between the proposed method nd ech of the other methods psses t-test [38] with confidence level of 99%, suggesting tht the results re sttisticlly relible. Figs. 7 9, respectively, show the results of three test imges projected on green, blue, nd red projection surfce. All the compenstion results re cptured using Cnon 700D cmer with fixed ISO, perture, nd shutter speed. To fithfully present the results, slightly lrger re thn the projected imge is cropped nd shown in the figures so tht the reders cn see the color nd texture of the projection surfce. By exmining the cost in Fig. 7, the white house in Fig. 8, the mgent flowers in Fig. 9, we cn see tht the proposed method preserves imge color better thn the other methods. In (e) Fig. 8. Comprison of different compenstion lgorithms. Originl imge projected on white screen, Originl imge projected on blue screen. (c), (d), (e), nd (f), respectively, re the compenstion results generted by GRC, PRC, CMB, nd the proposed methods. ddition, the proposed method preserves imge brightness better thn PRC nd CMB. This leds to resulting imge with more vivid color (e.g. the yellow color in Fig. 9) nd more imge detils (e.g. the lower prt of the cost in Fig. 7 nd the tree in Fig. 8). Similr findings bout the strength of our lgorithm cn lso be obtined for other test imges not shown here. The results presented bove lso show the robustness of the proposed lgorithm cross different color projection surfces. Since the proposed method hs consistent performnce for the red, green, nd blue projection surfces, it would hve similr performnce for projection surfces whose color is mixture of the primry colors. The proposed method ws compred with three other methods: GRC [], RRC [36], nd PRC [7]. Fig. 20 shows the results of test imge projected on wood-grin projection surfce. Clerly, the results show tht the proposed method is better thn the other methods in deling with texture surfces nd tht the ppliction of the proposed method is not limited to projection surfces with uniform color. VI. LIMITATIONS Theoreticlly, not ll colors re reproducible becuse color (f)

12 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 (c) (c) (d) (d) (e) (f) Fig. 20. Comprison of different compenstion lgorithms. Originl imge projected on white screen, Originl imge projected on wood-grin surfce. (c), (d), (e), nd (f) respectively, re the compenstion results generted by GRC, RRC, PRC, nd the proposed methods. the proposed method, but the contrst dpttion is not. It would be topic for future reserch to investigte how contrst dpttion cn be considered in rdiometric compenstion. (e) Fig. 9. Comprison of different compenstion lgorithms. Originl imge projected on white screen, Originl imge projected on red screen. (c), (d), (e), nd (f), respectively, re the compenstion results generted by GRC, PRC, CMB, nd the proposed methods. projection surfce hs smller gmut thn white surfce. This should be esy to understnd by considering the extreme cse where blck surfce bsorbs ll wvelengths of the visible light nd reflects none. Though gmut mpping cn help preserve the color ppernce of n imge, the color of the imge inevitbly degrdes due to the smll gmut of the projection surfce. In prctice, the performnce of the proposed pproch is limited by the resolution of the cmer nd projector. The cmer digitlly smples the imge shown on the projection surfce. The size of ech smpled re depends on the cmer sensor resolution nd the distnce of the cmer to the projection surfce. According to the Nyquist-Shnnon smpling theory, n imge cn be reconstructed from the smpled dt if the highest sptil frequency of the imge is no greter thn one hlf of the smpling rte. The resolution of the cmer utomticlly imposes n upper bound on the sptil frequency of the imge tht cn be compensted, nd so does the projector resolution. The contrst dpttion of HVS is not considered in this work. Specificlly, color ppernce depends on dpttion processes of HVS tht djust color sensitivity both to the verge of color (through chromtic dpttion) nd to the vrition of color (through contrst dpttion) [37]. Under complete chromtic dpttion, the verge color ppers chromtic, nd the contrst dpttion lters the perceived color contrst reltive to the verge color [37]. The chromtic dpttion is modeled in (f) VII. CONCLUSION In this pper, we hve described method to improve the rdiometric compenstion for procm system. This method djusts imge color bsed on the nchoring theory to reduce the clipping rtifct while preserving the color ppernce of the projected imge [39]. The proposed method hs three notble fetures. First, it combts the chromtic illusion due to the projection surfce by considering the chromtic dpttion property of HVS. Second, unlike previous methods tht use liner pproch for brightness scling, it considers the nonliner chrcteristic of humn eyes by dopting the CIECAM02 model for ll imge opertions to preserve the imge ppernce. Finlly, the weighting prmeters used in the method re determined through subjective experiment to strike blnce between color clipping nd imge dimming. As evidenced by user rtings, the proposed method significntly improves the perceptul qulity of the compensted imges. REFERENCES [] M. D. Grossberg, H. Peri, S. K. Nyr, nd P. N. Belhumeur, Mking one object look like nother: controlling ppernce using projector-cmer system, in Proc. IEEE Int. Conf. Computer Vision nd Pttern Recognition, vol., pp , Jn [2] A. Mjumder nd R. Stevens, LAM: Luminnce ttenution mp for photometric uniformity in projection bsed displys, in Proc. ACM Symp. Virtul Relity Softwre nd Technology, pp , [3] A. Mjumder, D. Jones, M. McCrory, M. E. Ppk, nd R. Stevens, Using cmer to cpture nd correct sptil photometric vrition in multi-projector displys, presented t the IEEE Int. Workshop on Projector-Cmer Systems, [4] D. G. Alig, Y. H. Yeung, A. Lw, B. Sjdi, nd A. Mjumder, Fst high-resolution ppernce editing using superimposed projections, ACM Trns. Grphics, vol. 3, no. 2, rticle no. 3, pp. 2, Apr. 202.

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Moroney, M.D. Firchild, nd T. Newmn, The performnce of CIECAM02, in Proc. IS&T/SID 0th Color Imging Conf., pp , Scottsdle, AZ, Nov [32] T.-C. Wng, T.-H. Hung, nd H. H. Chen. Rdiometric compenstion for procm system bsed on nchoring theory. IEEE. Int. Conf. Imge Process., pp , Sept [33] P. Bodrogi nd T. Q. Khn, (202). Illumintion, color nd imging: evlution nd optimiztion of visul displys. John Wiley & Sons, pp [34] A. Grundhofer, Prcticl non-liner photometric projector compenstion. in Proc. the IEEE Conf. Computer Vision nd Pttern Recognition Workshops, 203. [35] PetPixel. (202, Nov. 7). The cmer versus the humn eye [Online]. [36] K. Fujii, M. D. Grossberg, nd S. K. Nyr, A projector-cmer system with rel-time photometric dpttion for dynmic environments. in Proc. IEEE Conf. Computer Vision nd Pttern Recognition, vol., pp , [37] M. A. Webster, J. A. Wilson, Interctions between chromtic dpttion nd contrst dpttion in color ppernce, Vision Reserch, vol. 40, no. 28, pp , [38] Wikimedi Foundtion. (204, Jn. 4). Student's t-test [Online]. [39] T.-H Hung, T.-C Wng, K.-T Shih, nd H. H. Chen, Perceptul rdiometric compenstion system dptble to projector-cmer system, U.S. Ptent , Mr. 26, 205. Ti-Hsing Hung received his M.S. degree in Electricl Engineering from Ntionl Tiwn University in He is currently working towrd the Ph.D. degree in the Grdute Institute of Communiction Engineering, Ntionl Tiwn University. His reserch interests re in the re of perceptul bsed imge nd video processing. Ting-Chun Wng received the B.S. degree in electricl engineering from Ntionl Tiwn University, Tipei, Tiwn, in 202. His reserch interests re in the re of multimedi informtion retrievl nd nlysis nd signl processing. Homer H. Chen (S 83 M 86 SM 0 F 03) received the Ph.D. degree in electricl nd computer engineering from the University of Illinois t Urbn-Chmpign. Since August 2003, he hs been with the College of Electricl Engineering nd Computer Science, Ntionl Tiwn University, Tipei, Tiwn, where he is Irving T. Ho Chir Professor. Prior to tht, he held vrious R&D mngement nd engineering positions with U.S. compnies over period of 7 yers, including AT&T Bell Lbs, Rockwell Science Center, ivst, nd Digitl Islnd (cquired by Cble & Wireless). He ws U.S. delegte for ISO nd ITU stndrds committees nd contributed to the development of mny new interctive multimedi technologies tht re now prt of the MPEG-4 nd JPEG-2000 stndrds. His professionl interests lie in the brod re of multimedi signl processing nd communictions. Dr. Chen ws n Associte Editor of the IEEE Trnsctions on Circuits nd Systems for Video Technology from 2004 to 200, the IEEE Trnsctions on Imge Processing from 992 to 994, nd Pttern Recognition from 989 to 999. He served s Guest Editor for the IEEE Trnsctions on Circuits nd systems for video Technology in 999, the IEEE Trnsctions on Multimedi in 20, IEEE Journl of Selected Topics in Signl Processing in 204, nd the Springer Multimedi Applictions nd Tools in 205. Currently he is on the Fourier Awrd Committee nd the Fellow Reference Committee of the IEEE Signl Processing Society.