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Proceedings Paper
Volume: 31 | Article ID: 37
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Analyzing Perceptual Uniformity using Jacobian Determinants
  DOI :  10.2352/CIC.2023.31.1.39  Published OnlineNovember 2023
Abstract
Abstract

The CIE LAB color space was established by color scientists to be approximately perceptually uniform. The Y′CBCR color space is widely assumed by video engineers to be approximately perceptu¬ally uniform. However, these two color spaces have quite different transforms from tristimuli (radiometric) coordinates; they clearly cannot have the same perceptual performance. It is instructive to ask: Where in color space is Y′CBCR quantization the worst, when evaluated in terms of LAB? And, conversely, where in color space does LAB quantize most coarsely, when evaluated in Euclidean Y′CBCR difference? The Jacobian corresponding to a color coordinate in 3 space is a 3 × 3 matrix of partial derivatives. The determinant of that matrix is analogous to volume. We compute numerical Jacobian determinants to explore how unit LAB volumes at sample points spanning a target color space map to volumes in Y′CBCR. Where that volume is quite large, we expect poor perceptual performance of Y′CBCR. Where that volume is quite small, Y′CBCR is over-¬quantizing, and may have poor codeword utilization – but in such regions it’s reasonable to suspect the performance of LAB. We present “heat maps” that visualize where Y′CBCR per¬forms poorly compared to LAB (and vice versa).

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David A. LeHoty, Charles Poynton, "Analyzing Perceptual Uniformity using Jacobian Determinantsin Color and Imaging Conference,  2023,  pp 211 - 214,  https://doi.org/10.2352/CIC.2023.31.1.39

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