{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T23:17:57Z","timestamp":1717802277496},"reference-count":36,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2008,7,1]],"date-time":"2008-07-01T00:00:00Z","timestamp":1214870400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2008,7]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>We describe how Lie-theoretical methods can be used to analyze color related problems in machine vision. The basic observation is that the nonnegative nature of spectral color signals restricts these functions to be members of a limited, conical section of the larger Hilbert space of square-integrable functions. From this observation, we conclude that the space of color signals can be equipped with a coordinate system consisting of a half-axis and a unit ball with the Lorentz groups as natural transformation group. We introduce the theory of the Lorentz group SU(1, 1) as a natural tool for analyzing color image processing problems and derive some descriptions and algorithms that are useful in the investigation of dynamical color changes. We illustrate the usage of these results by describing how to compress, interpolate, extrapolate, and compensate image sequences generated by dynamical color changes.<\/jats:p>","DOI":"10.1017\/s0263574707003906","type":"journal-article","created":{"date-parts":[[2007,10,1]],"date-time":"2007-10-01T10:13:33Z","timestamp":1191233613000},"page":"453-464","source":"Crossref","is-referenced-by-count":2,"title":["Lie methods for color robot vision"],"prefix":"10.1017","volume":"26","author":[{"given":"Reiner","family":"Lenz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,7,1]]},"reference":[{"key":"S0263574707003906_ref30","volume-title":"Topics in Complex Function Theory, Automorphic Functions and Abelian Integrals","author":"Siegel","year":"1971"},{"key":"S0263574707003906_ref2","volume-title":"Color Appearance Models","author":"Fairchild","year":"2005"},{"key":"S0263574707003906_ref1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.neuro.26.041002.131116"},{"key":"S0263574707003906_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-71243-2"},{"key":"S0263574707003906_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9928-5"},{"key":"S0263574707003906_ref19","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610798006425"},{"key":"S0263574707003906_ref17","volume-title":"Linear Operators","author":"Dunford","year":"1988"},{"key":"S0263574707003906_ref32","volume-title":"Color Science","author":"Wyszecki","year":"1982"},{"key":"S0263574707003906_ref18","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/53.1.167"},{"key":"S0263574707003906_ref35","doi-asserted-by":"crossref","unstructured":"35. Solli M. , Andersson M. , Lenz R. and Kruse B. , \u201cColor Measurements with a Consumer Digital Camera Using Spectral Estimation Techniques,\u201d Proceedings of the SCIA 2005, Springer Lecture Notes Comp. Science Vol. 3540, Image Analysis June 19\u201322, 2005, Joeusum, Finland pp. 105\u2013114.","DOI":"10.1007\/11499145_12"},{"key":"S0263574707003906_ref14","doi-asserted-by":"publisher","DOI":"10.1109\/83.931097"},{"key":"S0263574707003906_ref10","first-page":"33","article-title":"Grundlinien einer Theorie der Farbenmetrik im Tagessehen","volume":"63","author":"Schr\u00f6dinger","year":"1920","journal-title":"Ann. 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