Provenzi Edoardo
CNRS, Bordeaux INP, IMB, UMR 5251, Université de Bordeaux, Talence, France.
J Math Neurosci. 2020 May 12;10(1):7. doi: 10.1186/s13408-020-00084-x.
This is the first half of a two-part paper dealing with the geometry of color perception. Here we analyze in detail the seminal 1974 work by H.L. Resnikoff, who showed that there are only two possible geometric structures and Riemannian metrics on the perceived color space [Formula: see text] compatible with the set of Schrödinger's axioms completed with the hypothesis of homogeneity. We recast Resnikoff's model into a more modern colorimetric setting, provide a much simpler proof of the main result of the original paper, and motivate the need of psychophysical experiments to confute or confirm the linearity of background transformations, which act transitively on [Formula: see text]. Finally, we show that the Riemannian metrics singled out by Resnikoff through an axiom on invariance under background transformations are not compatible with the crispening effect, thus motivating the need of further research about perceptual color metrics.
这是一篇关于颜色感知几何的两部分论文的上半部分。在此，我们详细分析了H.L.雷斯尼科夫1974年的开创性工作，他证明了在与通过均匀性假设完善后的薛定谔公理集兼容的感知颜色空间[公式：见正文]上，仅存在两种可能的几何结构和黎曼度量。我们将雷斯尼科夫的模型重塑为更现代的色度学框架，为原论文的主要结果提供了一个简单得多的证明，并激发了进行心理物理学实验以反驳或确认背景变换线性的必要性，背景变换在[公式：见正文]上可迁作用。最后，我们表明雷斯尼科夫通过关于背景变换下不变性的一个公理挑选出的黎曼度量与锐化效应不兼容，从而激发了对感知颜色度量进行进一步研究的必要性。
