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On large color differences in non‐euclidean color spaces
Author(s) -
Völz Hans G.
Publication year - 2002
Publication title -
macromolecular symposia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.257
H-Index - 76
eISSN - 1521-3900
pISSN - 1022-1360
DOI - 10.1002/1521-3900(200209)187:1<953::aid-masy953>3.0.co;2-u
Subject(s) - riemann hypothesis , geodesic , sample space , mathematics , euclidean space , calculus (dental) , pure mathematics , limit (mathematics) , space (punctuation) , basis (linear algebra) , computer science , mathematical analysis , statistics , geometry , medicine , dentistry , operating system
The color difference formulas CIE94 and CMC are only applicable to small color differences. For this reason, three papers have been written in which a basis for Euclideanization of these systems and, thus, for the calculation of large color differences was established. The original articles gave the equations for the Riemann spaces that were used to determine by calculus of variation the geodesics for acceptability. Several examples were shown. Subsequently, a direct method of transforming the Riemann space into a Euclidean space was published. With additional calculations, this method could also be applied successfully to the CMC system. This was also proven by examples. Several flaws that surfaced in both systems were listed and corrected (missing upper application limit, missing warning regarding non‐Euclideanicity, lack of standardization, missing invariance for the event that reference and sample were transposed).