[OPTICAL REVIEW Vol. 16, No. 6 (2009) 601-612]
© 2009 The Optical Society of Japan

Derivation of the Analytical Solution of Color2Gray Algorithm and Its Application to Fast Color Removal Based on Color Quantization

Go TANAKA, Noriaki SUETAKE*, and Eiji UCHINO

Graduate School of Science and Engineering, Yamaguchi University, Yamaguchi 753-8512, Japan

(Received June 11, 2009; Accepted September 25, 2009)

In order to convert a color image into a monochrome one, the lightness components of pixels have to date been used as gray-levels for the representation of the monochrome image. However, saliencies of an image embedded only in the chrominance components are eliminated in such conversion. To cope with this problem, “Color2Gray” algorithm, which excels in the color removal of digital images, has been proposed by Gooch et al. [ACM Trans. Graphics 24 (2005) 634]. In this paper, the algorithm is first analyzed and its mathematical property is revealed. Then a fast Color2Gray algorithm is proposed by using the mathematical property. Finally, the validity and the effectiveness of the proposed algorithm are proven by some experiments.

Key words: color-to-monochrome conversion, color removal, Color2Gray algorithm, color image, monochrome image, optimization problem, conjugate gradient method, computational cost reduction

*E-mail address: suetake@sci.yamaguchi-u.ac.jp