{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:09:58Z","timestamp":1747195798798,"version":"3.40.5"},"reference-count":36,"publisher":"Optica Publishing Group","issue":"10","license":[{"start":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T00:00:00Z","timestamp":1727308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T00:00:00Z","timestamp":1727308800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["J. Opt. Soc. Am. A"],"published-print":{"date-parts":[[2024,10,1]]},"abstract":"<jats:p>In image processing and color science, colors are often specified by their luminance and chromaticity (such as <jats:italic>Y<\/jats:italic><jats:italic>x<\/jats:italic><jats:italic>y<\/jats:italic>). Chromaticities are color ratios, which can be difficult to compute reliably due to noise, when the tristimulus values are small, e.g.,\u00a0for dark colors. A detailed statistical analysis of ratio distributions shows that below a certain signal\/noise ratio, the computed color ratios are very noisy and often wrong. This contrasts with human vision, where a given chromaticity viewed at high luminance will appear to the viewer as having a distinct color, but when that same chromaticity is viewed at low luminance, it will be seen as dark and almost hue-less. Therefore, dark color processing can take advantage of the perceptual characteristics to avoid producing excessive color noise and unnatural colors. In this study, we perform a detailed analysis of ratio distributions and propose a method to handle dark colors in image processing, using a logarithmic-like transformation (called <jats:italic toggle=\"yes\">plog<\/jats:italic>) that maps dark colors to reduced excitation purity. A color ratio 0\/0 is mapped to 1 (as the neutral). The plog transformation removes the singularity of the logarithmic transformation and allows us to estimate and process the ratios of dark colors in a manner consistent with human color perception without increasing color noise. It also offers the additional benefit of reducing the dynamic range of dark colors for tone reproduction.<\/jats:p>","DOI":"10.1364\/josaa.532767","type":"journal-article","created":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T15:00:40Z","timestamp":1725894040000},"page":"1959","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the ratios and the logarithms of dark colors in image processing"],"prefix":"10.1364","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-0273-4362","authenticated-orcid":true,"given":"Hsien-Che","family":"Lee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4152-1307","authenticated-orcid":true,"given":"Joyce F.","family":"Lee","sequence":"additional","affiliation":[{"name":"University of California"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"285","published-online":{"date-parts":[[2024,9,26]]},"reference":[{"key":"josaa-41-10-1959-R1","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1364\/JOSA.33.000385","volume":"33","author":"Newhall","year":"1943","journal-title":"J. Opt. Soc. Am."},{"key":"josaa-41-10-1959-R2","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1364\/JOSA.46.000281","volume":"46","author":"Judd","year":"1956","journal-title":"J. Opt. Soc. Am."},{"key":"josaa-41-10-1959-R3","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1113\/jphysiol.1965.sp007551","volume":"176","author":"Cornsweet","year":"1965","journal-title":"J. Physiol.-London"},{"key":"josaa-41-10-1959-R4","article-title":"Weber\u2019s law","volume-title":"Inside Psychology: A Science Over 50 Years","author":"LamingRabbitt","year":"2008"},{"key":"josaa-41-10-1959-R5","doi-asserted-by":"publisher","first-page":"207","DOI":"10.3758\/BF03206303","volume":"4","author":"Leshowitz","year":"1968","journal-title":"Percept. Psychophys."},{"volume-title":"Visual Perception","year":"1970","author":"Cornsweet","key":"josaa-41-10-1959-R6"},{"key":"josaa-41-10-1959-R7","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1111\/j.1365-2818.1988.tb04559.x","volume":"149","author":"Jourlin","year":"1988","journal-title":"J. Microsc."},{"key":"josaa-41-10-1959-R8","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1109\/TAU.1968.1161990","volume":"16","author":"Oppenheim","year":"1968","journal-title":"IEEE Trans. Audio Electroacoust."},{"key":"josaa-41-10-1959-R9","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1023\/A:1008259212169","volume":"7","author":"Pinoli","year":"1997","journal-title":"J. Math. Imaging Vis."},{"volume-title":"Theory and Application of Digital Signal Processing","year":"1975","author":"Rabiner","key":"josaa-41-10-1959-R10"},{"key":"josaa-41-10-1959-R11","doi-asserted-by":"publisher","first-page":"828","DOI":"10.1109\/PROC.1972.8782","volume":"60","author":"Stockham","year":"1972","journal-title":"Proc. IEEE"},{"key":"josaa-41-10-1959-R12","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1080\/01621459.1965.10480783","volume":"60","author":"Marsalia","year":"1965","journal-title":"J. Am. Stat. Assoc."},{"key":"josaa-41-10-1959-R13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v016.i04","volume":"10","author":"Marsalia","year":"2006","journal-title":"J. Stat. Softw."},{"key":"josaa-41-10-1959-R14","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s00362-012-0429-2","volume":"54","author":"D\u00edaz-Franc\u00e9s","year":"2013","journal-title":"Stat. Pap."},{"key":"josaa-41-10-1959-R15","doi-asserted-by":"publisher","first-page":"840005","DOI":"10.1063\/1.4913045","volume":"1648","author":"Oliveira","year":"2015","journal-title":"AIP Conf. Proc."},{"key":"josaa-41-10-1959-R16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-68774-2","volume-title":"Ultra Low Noise CMOS Image Sensors","author":"Boukhayma","year":"2018"},{"key":"josaa-41-10-1959-R17","doi-asserted-by":"publisher","first-page":"1737","DOI":"10.1109\/TIP.2008.2001399","volume":"17","author":"Foi","year":"2008","journal-title":"IEEE Trans. Image Process."},{"key":"josaa-41-10-1959-R18","doi-asserted-by":"crossref","DOI":"10.1117\/3.725073","volume-title":"Photon Transfer","author":"Janesick","year":"2007"},{"key":"josaa-41-10-1959-R19","first-page":"168","article-title":"What is the space of spectral sensitivity functions for digital color cameras?","volume-title":"IEEE Workshop on the Applications of Computer Vision","author":"Jiang","year":"2013"},{"volume-title":"The Algebra of Random Variables","year":"1979","author":"Springer","key":"josaa-41-10-1959-R20"},{"key":"josaa-41-10-1959-R21","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1093\/biomet\/24.3-4.428","volume":"24","author":"Fieller","year":"1932","journal-title":"Biometrika"},{"key":"josaa-41-10-1959-R22","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1093\/biomet\/56.3.635","volume":"56","author":"Hinkley","year":"1969","journal-title":"Biometrika"},{"key":"josaa-41-10-1959-R23","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1080\/03610919408813166","volume":"23","author":"\u00d6ksoy","year":"1994","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"josaa-41-10-1959-R25","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1016\/S0031-8914(43)90575-0","volume":"10","author":"de Vries","year":"1943","journal-title":"Physica"},{"key":"josaa-41-10-1959-R26","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1364\/JOSA.38.000196","volume":"38","author":"Rose","year":"1948","journal-title":"J. Opt. Soc. Am."},{"key":"josaa-41-10-1959-R27","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1080\/713818657","volume":"1","author":"Aguilar","year":"1954","journal-title":"Opt. Acta"},{"key":"josaa-41-10-1959-R28","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1167\/11.1.21","volume":"11","author":"Koenig","year":"2011","journal-title":"J. Vis."},{"key":"josaa-41-10-1959-R29","first-page":"iv","volume":"40","author":"Hill","year":"1910","journal-title":"J. Physiol.-London"},{"key":"josaa-41-10-1959-R30","doi-asserted-by":"publisher","first-page":"1539","DOI":"10.1016\/0042-6989(83)90167-0","volume":"23","author":"Valeton","year":"1983","journal-title":"Vis. Res."},{"key":"josaa-41-10-1959-R31","doi-asserted-by":"publisher","first-page":"624","DOI":"10.1364\/JOSA.36.000624","volume":"36","author":"Blackwell","year":"1946","journal-title":"J. Opt. Soc. Am."},{"key":"josaa-41-10-1959-R32","doi-asserted-by":"publisher","first-page":"2600","DOI":"10.1093\/mnras\/stu992","volume":"442","author":"Crumey","year":"2014","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"josaa-41-10-1959-R33","doi-asserted-by":"publisher","first-page":"127","DOI":"10.5406\/amerjpsyc.124.2.0127","volume":"124","author":"Dzhafarov","year":"2011","journal-title":"Am. J. Psychol."},{"key":"josaa-41-10-1959-R34","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1117\/12.271284","volume":"3036","author":"Lee","year":"1997","journal-title":"Proc. SPIE"},{"key":"josaa-41-10-1959-R36","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1364\/JOSAA.510989","volume":"41","author":"Kawamorita","year":"2024","journal-title":"J. Opt. Soc. Am. A"},{"key":"josaa-41-10-1959-R37","doi-asserted-by":"publisher","first-page":"52","DOI":"10.5594\/j18290","volume":"122","author":"Miller","year":"2013","journal-title":"SMPTE Motion Imaging J."},{"key":"josaa-41-10-1959-R39","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511614392","volume-title":"Introduction to Color Imaging Science","author":"Lee","year":"2005"}],"container-title":["Journal of the Optical Society of America A"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=josaa-41-10-1959&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T21:12:19Z","timestamp":1727385139000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=josaa-41-10-1959"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,26]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024]]},"published-print":{"date-parts":[[2024]]}},"URL":"https:\/\/doi.org\/10.1364\/josaa.532767","relation":{},"ISSN":["1084-7529","1520-8532"],"issn-type":[{"type":"print","value":"1084-7529"},{"type":"electronic","value":"1520-8532"}],"subject":[],"published":{"date-parts":[[2024,9,26]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/JOSAA.532767","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"14 June 2024","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"9 September 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"26 September 2024","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2024 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}