Development of Fundamental Techniques for Color Image Processing to be Applied for Computational Analysis of Color in Painting Arts

这项研究是将科学方法引入美学领域的一次尝试。对绘画艺术中色彩的数学分析的各种例子进行了综述。实例包括颜色组合和颜色组成的分析、色差图像的计算、Haar小波变换的空间波长分析以及分段线性逼近在灰度提取中的应用。对彩色图像计算处理所需的基本概念和技术进行了思考。定义了图像的数学模型。介绍了色彩数学分析的逆映射、量化和分割等前提条件，并在此基础上开发了一个软件系统。该软件系统用于绘画艺术中色彩的各种数学分析。分析包括色彩空间分布的色彩组合分析、色彩组成分析和色差图像的计算。介绍了利用分维和信息熵来衡量绘画中色彩组合的复杂性的尝试。对法国化学家、色彩科学家M-E·切弗鲁尔的色彩和谐理论进行了重新思考。NHK制作的ART程序中介绍了一些研究结果。

This research is an attempt to introduce scientific approach to the field of aesthetics.A general survey is made to review various examples of mathematical analyses of color in painting arts. The examples include, analyses of color combination and color composition, computation of color difference images, analysis on spatial wave-length by Haar wavelet transformation, and application of piecewise linear approximation for the extraction of gradation.Consideration is made on basic concepts and techniques required for processing color images computationally. A mathematical model of an image is defined. Prerequisites for mathematical analysis of color, such as inverse mapping, quantization and segmentation are introduced.A software system is developed based on the consideration. The software system is applied for various mathematical analyses of color in painting arts.The analyses include, analyses of color combination through distribution in a color space, analyses of color composition and computation of color difference image.An attempt to measure the complexity of color combination in paintings applying fractal dimension and information entropy is introduced.Reconsideration of the theory of harmony of colors by M.-E. Chevreul, a French chemist and color scientist, is made.Some of the results of the research are presented in the art program produced by NHK.