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 $\mathcal{P} $ 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 $\mathcal{P} $. 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.

中文翻译：

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颜色感知的几何形状。第1部分：均匀色彩空间的结构和度量。

这是关于颜色感知几何的两部分论文的前半部分。在这里，我们详细分析HL Resnikoff在1974年所做的开创性工作，该工作表明，在感知色彩空间$ \ mathcal {P} $上，与薛定ding公理集兼容的两个可能的几何结构和黎曼度量符合以下假设：同质性。我们将Resnikoff的模型改写为更现代的色度设置，提供了对原始论文主要结果的简单得多的证明，并激发了心理物理学实验来迷惑或确认背景变换的线性，这些变换对$ \ mathcal { P} $。最后，