Hurlbert A
J Opt Soc Am A. 1986 Oct;3(10):1684-93. doi: 10.1364/josaa.3.001684.
The computational problem underlying color vision is to recover the invariant surface-spectral-reflectance properties of an object. Lightness algorithms, which recover an approximation to surface reflectance in independent wavelength channels, have been proposed as one method to compute color. This paper clarifies and formalizes the lightness problem by proposing a new formulation of the intensity equation on which lightness algorithms are based and by identifying and discussing two basic subproblems of lightness and color computation: spatial decomposition and spectral normalization of the intensity signal. Several lightness algorithms are reviewed, and a new extension (the multiple-scales algorithm) of one of them is proposed. The main computational result is that each of the lightness algorithms may be derived from a single mathematical formula, under different conditions, which, in turn, imply limitations for the implementation of lightness algorithms by man or machine. In particular, the algorithms share certain limitations on their implementation that follow from the physical constraints imposed on the statement of the problem and the boundary conditions applied in its solution.
颜色视觉背后的计算问题是恢复物体不变的表面光谱反射特性。已提出明度算法，即在独立波长通道中恢复表面反射率的近似值，作为计算颜色的一种方法。本文通过提出明度算法所基于的强度方程的新公式，并识别和讨论明度与颜色计算的两个基本子问题：强度信号的空间分解和光谱归一化，来阐明和形式化明度问题。回顾了几种明度算法，并提出了其中一种算法的新扩展（多尺度算法）。主要计算结果是，在不同条件下，每种明度算法都可以从一个单一的数学公式推导出来，这反过来又意味着人类或机器实现明度算法存在局限性。特别是，这些算法在实现上存在某些局限性，这些局限性源于对问题陈述施加的物理约束以及在求解中应用的边界条件。
