Development and evaluation of perceptually adapted colour gradients

See discussions, s a s, and au ho p o iles o his publica ion a : h ps://www. esea chga e.ne /publica ion/236131515 De elopmen and E alua ion o Pe cep ually Adap ed Colo G adien s A icleinImage P ocessing, IET · June 2013 DOI: 10.1049/ie -ip .2012.0085 CITATIONS 15 READS 95 4 au ho s, including: Some o he au ho s o his publica ion a e also wo king on hese ela ed p ojec s: Compu e assis ed su ge y View p ojec Au o a Sáez Uni e sidad de Se illa 32 PUBLICATIONS245 CITATIONS SEE PROFILE Begoña Acha Uni e sidad de Se illa 90 PUBLICATIONS1,170 CITATIONS SEE PROFILE Ca men Se ano Uni e sidad de Se illa 105 PUBLICATIONS1,357 CITATIONS SEE PROFILE All con en ollowing his page was uploaded by Begoña Acha on 31 May 2014. The use has eques ed enhancemen o he downloaded ile. De elopmen and e alua ion o pe cep ually adap ed colo g adien s o colo edge de ec ion Au o a S´aez, Ca los S. Mendoza, Bego˜na Acha, Ca men Se ano Abs ac Al hough se e al colo edge de ec o s ha e been p oposed, mos o hem u ilized Euclidean colo dis ances in di e en colo spaces o measu e colo di e ences. In his pape a se o colo g adien s based on colo isual pe - cep ion is p oposed. These colo g adien s a e designed in uni o m colo spaces and use pe cep ual colo di e ence equa ions. In o de o be able o s udy he g adien s pe o mance, hey ha e been applied in a a ia ional le el se o mula ion. A compa a i e s udy has been pe o med. A se o syn he ic images, gene a ed o his pu pose, has allowed ca ying ou an ex- ensi e e alua ion. Bo h quan i a i e and quali a i e measu es a e used. I can be conclude ha de ec o s based on CIE94 colo di e ence equa ion a e he bes ega ding o he co ela ion wi h colo isual pe cep ion. Ou main con ibu ions a e: he de i a ion o pe cep ual colo g adien s, he design o a pe cep ual e alua ion wi h a speci ic syn he ic da ase and he compa ison be ween de ec o s based on di e en colo di e ences. Keywo ds: pe cep ual colo g adien s, pe cep ual e alua ion, colo di e ence equa ions 1. In oduc ion Edge de ec ion is one o he undamen al ope a ions in compu e ision. Edges co espond o ab up discon inui ies in physical quan i ies such as g ay-le el, colo , ex u e o mo ion. In o de o analyze an image, he hu- man isual sys em de ec s changes in i , ha is, discon inui ies. Nowadays, he majo i y o he image p ocessing asks a e de eloped o colo images. The ad an age o colo edge de ec ion schemes o e g ayscale app oaches is easily demons a ed by conside ing he ac ha hose edges ha exis a he bounda y be ween egions o di e en colo s canno be de ec ed in g ayscale P ep in submi ed o Else ie July 1, 2011 images i he e is no change in in ensi y [1]. The colo edge de ec o s can be classi ied in o wo g oups: hose echniques ex ended om g ayscale edge de ec o s which apply he de ec ion me hod in each colo plane and combin- ing he esul s, and hose echniques ha ake in o accoun he ec o na u e o he colo images [2]. Se e al colo edge de ec o s p ese ing his ec o na u e ha e been p oposed [2] bu none o hem ake in o accoun ecen ad ances in measu ing pe cep ual colo di e ences. Di e en algo i hms ha ex end he concep o de i a i e ope a o o h ee-colo -componen pixels ha e been de eloped in he li e a u e. One o simples app oxima ions consis s in gene alizing he ope a o s based on he i s de i a i e, e.g. Sobel, commonly applied in he g ayscale images in o he mul idimensional case. Wesolkowski compa ed se e al edge de ec o s in mul iple colo spaces, and he d ew he conclusion ha he pe o mance o Sobel ope a o is supe io o o he s [3]. This is he eason why Sobel op- e a o is chosen in his pape . As esul s co ela ed wi h pe cep ual colo di e ences a e in ended, RGB space is a oided because i is no a pe cep- ually uni o m colo space. Ins ead, we make use o a pe cep ual uni o m colo space (CIE L∗a∗b∗) and he CIELAB, CIE94 and CIEDE2000 colo di e ence equa ions [4],[5]. A compa a i e s udy be ween hese g adien s is ca ied ou . To e alua e he pe o mance o hem, a a ia ional Le el Se echnique whe e hese colo g adien s con ol ex e nal ene gies is de eloped. As he aim is o measu e how he de ec o s a e co ela ed wi h he human isual pe cep ion, an ex ensi e e alua ion is pe o med. A da abase o med by 96 images has been gene a ed and bo h quan i a i e and quali a i e mea- su es a e used o es he co ela ion be ween he de ec o ou pu and he isually pe cei ed colo di e ence. O he au ho s ha e app oached o he ield o pe cep ual colo edge de ec o s. Howe e , in hei wo k, he e is lack o a hou ogh e alua ion[6], [7], [8]. The es o he pape is o ganized as ollows: Sec ion 2 summa izes he colo g adien s p oposed. The a ia ional Le el Se echnique implemen ed o e alua e he colo g adien s is in oduced b ie ly in Sec ion 3. In Sec ion 4 he comple e de eloped me hod is exposed. The expe imen al esul s a e explained in Sec ion 5. Some conclusions a e p esen ed in Sec ion 6. 2 2. Colo g adien s In his pape se e al pe cep ual colo g adien s a e p oposed and com- pa ed. These colo g adien s a e de eloped in a uni o m colo space and p ese e he ec o na u e o he colo images in ha space. 2.1. Pe cep ual Uni o m Colo Space and Colo Di e ence Equa ions In 1976, In e na ional Commission on Illumina ion (CIE) s anda dized L∗a∗b∗space as pe cep ually uni o m [9]. A colo space is pe cep ually uni- o m i pe cep ual colo di e ences can be measu ed wi h Euclidean dis ances in his space. The h ee coo dina es o L∗a∗b∗ ep esen he ligh ness o he colo (L∗), i s posi ion be ween ed/magen a and g een (a∗) and i s posi ion be ween yellow and blue (b∗). I can also be exp essed in e ms o cylind ical coo dina es wi h he pe cei ed ligh ness L∗, he ch oma C∗ ab and he hue h∗ ab, de ined in (1) and (2) espec i ely. Cab ∗=pa∗2+b∗2(1) hab =a c an b∗2 a∗2(2) CIELAB colo di e ence, also known as ∆E∗ ab, is calcula ed using (3). ∆E∗ ab =p∆L∗2+ ∆a∗2+ ∆b∗2(3) whe e ∆L∗=L∗ 1−L∗ 2(∆a∗and ∆b∗a e de ined in he same manne o coo dina es a∗and b∗). Howe e , subsequen expe imen s demons a ed ha Euclidean dis ance ∆E∗ ab is no an accu a e measu e o pe cei ed colo di e ence be ween wo s imuli. To co ec he p oblem a new di e ence o mula was ecommended by CIE [4] in 1994. ∆E94 ∗=s∆L∗ kLSL2 +∆C∗ ab kCSC2 +∆H∗ ab kHSH2 (4) SL= 1,(5) SC= 1 + 0.045 C∗ ab ,(6) 3 SH= 1 + 0.015 C∗ ab .(7) The ac o s kL,kCand kH, a e included o ma ch he pe cep ion o he backg ound condi ions. La e , CIEDE2000 was de eloped o co ec de iciencies o p e ious colo di e ence equa ions [10]. I s accu acy o p edic small pe cei ed colo di e - ences ha e been demons a ed [11] ∆E00 =s∆L0 KLSL2 +∆C0 KCSC2 +∆H0 KHSH2 +RT∆C0 KCRC ∆H0 KHSH (8) whe e ∆C0and ∆H0a e de ined in [5]. 2.2. P oposed colo g adien s In colo g adien s, he ec o na u e o colo is p ese ed h oughou he compu a ion. Colo images a e iewed as a wo-dimensional h ee channel ec o ield. Each channel in his ec o is cha ac e ized by a disc e e in ege unc ion (x, y). The alue o his unc ion a each poin is de ined by a h ee dimensional ec o in a gi en colo space [2]. The e o e, a pixel is de ined as in (9). (x, y) =   C1(x, y) C2(x, y) C3(x, y) (9) whe e Ci(x, y) ep esen s he alue o he pixel in he i- h colo plane (i= 1,2,3), and (x, y) e e s o he spa ial dimensions in he 2-D plane. The ope a o based on he i s de i a i e, commonly applied in he g ayscale imaging, is gene alized in o mul idimensional case in [2]. Pla anio is ex- ends he Sobel ope a o , wi h he ho izon al and e ical masks shown in (10), by cons uc ing he ec o s: H+= 7+ 2 3+ 8,H−= 9+ 2 2+ 6, V+= 6+ 2 4+ 8,V−= 9+ 2 5+ 7, acco ding o he no a ion used in Figu e 1. They calcula e he colo ec o g adien as H+−H−and V+−V−, espec i ely. In o de o es ima e he colo a ia ion in he e i- cal and ho izon al di ec ions, he ollowing scala s a e calcula ed: kH+−H−k ,kV+−V−k. The magni ude Bo he maximun a ia ion is es ima ed as: 4 B=pkH+−H−k2+kV+−V−k2. 9 5 7 2 1 3 6 4 8 Figu e 1: Sliding window X1=  −1 0 1 −2 0 2 −1 0 1  , X2=  −1−2−1 000 121 (10) In his pape , we p opose calcula ing he g adien along xand ydi ec ion as shown (11) and (12). Gx= ∆EH+,H−(11) Gy= ∆EV+,V−(12) whe e ∆Edeno es he colo di e ence be ween wo ec o s. Then, he g a- dien magni ude can be compu ed as shown in (13). G=qG2 x+G2 y(13) In his pape h ee colo g adien s a e s udied, each one o hem is ob- ained by applying: • (x, y) = [L∗(x, y), a∗(x, y), b∗(x, y)] and ∆Ede e mined by Euclidean dis ance (CIELAB). • (x, y) = [L∗(x, y), a∗(x, y), b∗(x, y)] and ∆Ede e mined by CIE94 colo di e ence equa ion. • (x, y) = [L∗(x, y), a∗(x, y), b∗(x, y)] and ∆Ede e mined by CIEDE2000 colo di e ence equa ion. 5 3. Va ia ional le el se Once a colo g adien is es ima ed, he simples edge de ec o is ob ained by h esholding his g adien . In he h ee p oposed colo g adien es ima- o s, he dynamic ange o he colo g adien di e s be ween he h ee colo di e ence measu es. This implies ha a di e en h eshold should be chosen o de ec edges wi h he di e en g adien es ima o s and he quali y o edges de ec ed om each g adien es ima o depends s ongly on he choice o his h eshold. The e o e, in o de o make he compa ison be ween he h ee g adien es ima o s independen om his choice, a le el se o mula ion has been applied. Le el se me hods [12] ha e been widely used as global app oaches owa ds he op imiza ion o ac i e con ou s o he segmen a ion o objec s o in e es om he backg ound. In hese me hods, in each ime edges a e conside ed o be in he ze o-le el o a scala unc ion φ( ), called le el-se unc ion. The challenge o a le el-se algo i hm is o make φe ol e along so ha i s ze o le el con e ge a he eal bounda ies in he image. The gene al le el se equa ion is p esen ed in (14), ∂φ ∂ +F|∇φ|= 0 (14) whe e F ep esen s he speed unc ion. One o he main challenges in he employmen o le el se echniques is o o e come he gene a ion o shocks in φ, e y sha p o la shape du ing he e olu ion, which can esul in less han accu a e con ou s. Many au ho s a oid his p oblem by e-ini ializing he unc ion φ o a signed unc ion pe iodically. In his pape , his p oblem is o e come wi h he me hod de eloped by Li e al [13]. In he epo ed wo k, a new e m is in oduced in o (14) o main ain he le el se unc ion nea he signed dis ance unc ion, hus a oiding he need o e-ini ializa ion o he le el se unc ion. I has been shown ha he esul ing exp ession is he ollowing g adien low: ∂φ ∂ =µ∆φ−di ∇φ |∇φ|+λδ(φ)di g∇φ |∇φ|+νgδ(φ) (15) whe e µde e mines he de ia ion o φ om a signed dis ance unc ion, λand νa e he coe icien s o he weigh ed leng h o he ze o le el cu e and o he 6 weigh ed a ea inside he ze o le el cu e espec i ely, and is he ime s ep o he expe imen . The second and he hi d e m in he igh hand side o (15) a e espon- sible o d i ing he ze o le el cu e owa ds he objec bounda ies. gis he edge indica o unc ion, usually de ined as: g=1 1 + |∇Gσ∗I|2(16) whe e Gσis he Gaussian ke nel wi h s anda d de ia ion σand Iis he es image. In he p oposed me hod, he edge indica ion unc ion ghas been modi ied o: g=1 1 + |V D(di {I})|2(17) whe e di is an aniso opic di usion il e and V D a e he p oposed colo g adien s ha a e applied o he di used image. The e o e, modi ying he edge indica o unc ion includes wo aspec s: •The Gaussian il e smo hing is subs i u ed by an colo aniso opic di - usion il e [15]. Bo h smoo hing we e es ed bu he colo aniso opic di usion il e ob ained be e esul s acco ding expe imen s. •G adien s he di used image a e compu ed wi h he h ee p oposed colo g adien s app oaches explained in Sec ion 2. 4. Me hodology The da a low diag am in Figu e 2 gi es an o e iew o he main s eps o he pe cep ual colo de ec o s based on p oposed colo g adien s. a. Uni o m colo space ans o m. The RGB image is ans o m in o he uni o m colo space CIE L∗a∗b∗, p e iously desc ibed. b. Aniso opic di usion il e ing. In he aniso opic di usion [14] a wi hin- egion smoo hing is la gely pe o med wi hou blu ing be ween- egion bounda ies. In his pape an ex ension o he me hod o colo image is implemen ed [15], whe e a sepa a e aniso opic di usion o ch oma ic 7 Figu e 2: P oposed sys em and ach oma ic channels is pe o med. This way inds i s a ionale in he models o colo ision: he human isual sys em senses colo in o - ma ion h ough pho o ecep o s which can be ega ded as h ee se s o il e s uned o he wa eleng hs o ed, g een and blue; his in o ma ion is hen spli in o ch oma ic (2-D) and ach oma ic (1 -D) channels be- o e being u he and independen ly p ocessed. Neu ophysiological e - idence shows ha he e exis s a pe ec ag eemen be ween he second Human Visual Sys em p ocessing s age and he opponen -colo s heo y based on he h ee an agonis ic mechanisms ed-g een, blue-yellow and black-whi e. These s imuli can also be con enien ly exp essed in e ms o hue, sa u a ion and ligh ness. Hue and sa u a ion a e p ocessed o- ge he using he o malism o phaso s: hue is he phase and sa u a ion is he magni ude o a complex unc ion de ined as he complex ch o- ma ici y. The scala ach oma ic in o ma ion ep esen ed by ligh ness is sepa a ely di used. c. Pe cep ual colo g adien s compu a ion. The p oposed colo g adien s explained in Sec ion 2 a e compu ed om di used image. d. Le el se echnique. The le el se o mula ion explained in Sec ion 3 is applied wi h he edge indica o unc ion as: g=1 1 + |V D(di {I})|2(18) 8 (a) (b) (c) (d) Figu e 7: a) Tes image. b) Ou pu o de ec o based on CIELAB. c) Ou pu o de ec o based on CIE94. d) Ou pu o de ec o based on CIEDE2000. 6. Conclusions In his pape h ee di e en pe cep ually adap ed colo g adien s ha e been p oposed. These g adien s ha e been in eg a ed in a le el-se ame- wo k o colo edge de ec ion. This colo edge de ec ion algo i hm is used o e alua e he h ee colo g adien s wi h wo e alua ion es s: a subjec i e es and a quan i a i e e alua ion measu e. To his pu pose, a syn he ic image da abase ollowing CIE guidelines o coo dina ed esea ch on colo di e ence e alua ion [17] has been de eloped. The edge de ec o using he colo g adi- en based on CIE94 esul ed he bes bo h acco ding o he subjec i e es and he pe cei ed quan i a i e measu e (pe cei ed FP a ). An addi ional ad an age o CIE94 colo di e ence equa ion is i s low compu a ional cos when compa ed o CIEDE2000 di e ence equa ion. 15 Re e ences [1] A.N. E ans, X.U. Liu, A mo phological g adien app oach, IEEE T ans- ac ion on Image P ocessing, 15(6) (2006) 1454-1563. [2] K.N. Pla anio is, A.N. Vene sanopoulos, Colo Image P ocessing and Applica ions, Sp inge -Ve lag, Be lin, 2000. [3] S. Wesolkowski, M.E. Je nigan, R.D. Dony, Compa ison o colo image edge de ec o s in mul iple colo space, ICIP, (2009) 796-799. 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Mi a, Colo segmen a ion based on sepa a e aniso opic di usion o ch oma ic and ach oma ic channels, IEEE P o- ceedings Vision, Image and Signal P ocessing, 148(3) (2001) 141-150. [16] S.Y. Zhu, K.N. Pla anio is,A.N. Vene sanopoulos, Comp ehensi e anal- ysis o edge de ec ion in colo image p ocessing, Op ical Enginee ing, 38(4) (1999) 612-625. [17] A.R. Robe son, CIE guidelines o coo dina ed esea ch on colou - di e ence e alua ion, Colo Res. Appl. 3(3) (1987) 149-151. [18] G. Sha ma, W. Wu, E.N. Dalal, The CIEDE2000 colo -di e ence o - mula: Implemen a ion no es, supplemen a y es da a, and ma hema i- cal obse a ions, Colo Resea ch and Applica ion, 30(1) (2005) 21-30. [19] W.K. P a , Digi al Image P ocessing, Wiley-In e science, New Yo k, 1978. 17 View publica ion s a sView publica ion s a s