Determination of Significant Color Map

This paper propose an approach to extract the most significant color information that takes into account 1) the inherent sensitivity of the Human Visual System (HVS) to color variations and 2) the sensitivity of the HVS to specific colors of a given image. By giving higher importance to the significant colors in the stabilization control formulation, it is possible to retain the consistency of only the most significant colors to a human viewer. Such restriction is critical due to the limited actuation authorities of typical xerographic color printing process. To account for color-specific sensitivity, we make use of the CIE L*a*b* color formulation. To account for the image-specific sensitivity, we make use of the fact that the HVS have lower sensitivity to high frequency components (detail) of high chrominance image. Moreover, typically “smooth” images are visually more irrelevant compared to textured and detailed images. These effects in the color and spatial domain are taken into account to reduce the redundancy in the image representation by following similar procedure to that used in wavelet transform coding decomposition. Introduction The color reproduction characteristics(CRC) function describes how a printer maps the desired colors into actual printed colors. These printed colors vary with time due to printer dynamics as well as environmental and material variations, resulting in inconsistent color prints. In our current and previous works [1, 2, 3, 4], we have looked into control and sensing issues of maintaining tone and color consistency. The key control challenge is the high dimensional print-map (in that a color printer can reproduced high numbers of colors) with limited actuation authorities. This means that it is not possible to maintain the consistency of all the printed colors. In this paper, we developed a technique to stabilize only colors that are significant to a human viewer. Specifically there are two main redundancies of a printed image. The first is the inherent sensitivity of the Human Visual System (HVS) to color variations. In fact it is well known that human does not differentiate two colors with a ∆E∗ 94 < 1 [5]. The second redundancy can be found on the printed color image itself. For a color image, the redundancies can be found in the color and spatial representation of the image. Human visual system (HVS) has lower sensitivity to high frequency components (details) of high chrominance image. Moreover, typically “smooth” images are visually more irrelevant compared to textured and detailed images. These effects in the color and spatial domain are taken into account to reduce the redundancy in the image representation by following similar procedure to that used in wavelet transform coding [6]. The multi-resolution properties of wavelet decomposition is particularly well suited to the characteristics of the HVS because psycho-visual studies show that the human visual system can be modeled using multiple perceptual channels, which are octavewise spread over the spatial frequency range. From one octave to the next, the summation area (area of the retina contributing to the perceived signal) also changes by a factor of four. This behavior match that of the dyadic structure of the discrete wavelet transform. Problem Formulation In both sensing and control for maintaining color consistency, it is convenient to take the input colorspace as the CMY colorspace and the output colorspace as the CIE L∗a∗b∗ colorspace [1]. Uniformly discretizing the CMY colorspace domain, by M1, M2 and M3 points in each of the C, M, Y coordinates respectively, the CRC can be adequately approximated by its response at a finite number of Mt = M1M2M3 color combinations. Let L∗ i a ∗ i b ∗ i (k) denotes the i-th values of the Mt discretized points time-varying output color gamut of the printer. In this context, the time dependent error vector, ē(k) ∈R3Mt of discretized output of the spatial signal is given by: ē(k)= [ ∆L∗ 1(k), . . . ,∆L ∗ Mt (k),∆a ∗ 1(k), . . . ,∆a ∗ Mt (k),∆b ∗ 1(k), . . . ,∆b ∗ Mt (k) ] (1) where ∆L∗ i (k) := L ∗ i (k)−L∗∗ i , ∆ai (k) := ai (k)− a∗∗ i , ∆bi (k) := bi (k)− b∗∗ i . L∗∗ i a∗∗ i b∗∗ i gives the i-th value of the nominal color gamut. In the color stabilization control formulation [1], we can then specify the relative importance of the CRC errors at different colors for their stabilization given by the performance index term: J(k) = ēT (k)Weē(k) ∈R (2) where the error weighting is given by We ∈ R3Mt×3Mt . The error weighting matrix is made up of the color and image specific weightings i.e.: