Principal noiseless color component extraction by linear color composition with optimal coefficients

In this paper, we propose a principal color component extraction method that is simply performed by linear color composition (transformation) of R, G, B colors, but its composite coefficients are calculated so as to obtain a noisy-texture-less principal component of RGB color images. Our method is related to principal component analysis (PCA) and edge preserving smoothing by total variation (TV) minimization. The resultant image becomes a principal color component image with the minimum total variation. We show this problem can be formulated as TV minimization on a spherical manifold for a whitened data matrix. Although this spherical constraint is non-convex, it can be solved by using alternating direction method of multipliers (ADMM). As its application, we show the results of text character extraction from ancient wooden tablets, and how our method extracts faint ink characters while reducing wood grain textures. Our method is unsupervised but has performance equivalent to a linear discriminant analysis (LDA) method with user-assisted information.