摘要： 为描述颜色光谱所需的基本因子数量，从颜色光谱中提取颜色空间的结构，提出不同于传统线性降维的研究方法。从流形学习的视角出发，假设高维的颜色光谱数据位于一个低维的流形中，将颜色光谱分析中的基本因子数量问题和提取颜色空间结构问题，转化为光谱颜色空间内嵌流形的本征维数估计和流形结构分析问题。采用5种不同的流形本征维度估计算法和6种经典的流形学习算法，对蒙赛尔标准颜色样片光谱进行分析。实验结果表明，在光谱蒙赛尔颜色空间中存在三维的嵌入流形，这一流形的几何结构近似圆锥体，与蒙赛尔颜色系统的原始理论一致。
关键词:
颜色光谱,
蒙赛尔颜色空间,
光谱反射曲线,
流形学习,
本征维数,
非线性降维
Abstract: Aiming at the problem of the number of basic factors needed to describe the color spectral and the structure of color space exacted from the color spectral, this paper provides a new analysis method different from traditional linear techniques of dimension reduction, which is based on manifold learning, supposing high dimensional data of color spectral lies in a low dimensional manifold, transforming the problems of number of basic factors and the extracted structure of color space to the problems of the intrinsic dimension and structure of the embedded manifold of the spectral color space. Five different techniques of intrinsic dimension estimation and six classic manifold learning algorithms are employed to study the spectral dataset of Munsell colors. Experimental results reveal that there exists a 3-dimensional manifold embedded in the spectral Munsell color space and the geometric structure of this manifold looks like a cone, consistent with the original development of the Munsell color system.
Key words:
color spectral,
Munsell color space,
spectral reflectance curve,
manifold learning,
intrinsic dimension,
non-linear dimension reduction
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