<title>Linear model of surface and scanner characterization method</title>

Abstract

In color reproduction research, a linear model designed to minimize the error between original surface reflectance spectra and reproduced spectra is useful in the process of producing an accurate color match between the original image and reproduction under a variety of illuminants, but it is inappropriate in efficiency. We propose an efficient linear model based on surface reflectance spectra and a unified wavelength function of Cifi 193 1 stanthrd observer representing human perceptual property. The surface spectra weighted with the unified wavelength function were introduced to minimize the human perceptual error between original reflectance spectra and reproduced spectra and to reduce the number of the spectral basis functions. The performance of reflectance spectra-to-CIELAB transformation on our proposed linear model is tested and compared with a conventional model based on reflectance spectra under a variety of illuminants. The results of our linear model is superior to that of the conventional model. With Munsell 400 color patches, D65 illuminant and 4-dimensional linear model, the mean color difference of our model is 1.28 CIELAB unit. And an algorithm for color scanner characterization using our model is made and tested, and the results are shown.

On Spectral Models And Colour Constancy Clues

“…In a LSM, the space of spectral functions is confined to a 3D linear subspace of the function space. Interesting particular cases of LSM are models in which the bases are step-wise functions (socalled "banded spectral model" (Stiles and Wyszecki 1962;Land and McCann 1971;Nyuberg et al 1971) or the functions of spectral sensitivity of the sensor (Lee et al 1995). However, all these models have the same drawback: they cannot adequately describe stimuli of a high saturation (Maloney, 1986).…”

Color linear model

“…The color differences of the LAB unit of the 690 spectrum reconstructed by each linear model for five standard illuminants are given in table 4 in the case of three dimensional basis vectors. The CMF(D65) is the CMF estimated by equation (10) under the illuminant D65 and LAB(D6s) is the case of the LAB estimated in D6s. CIE D65 standard illuminant is assumed as a representative of illuminant.…”

“…First, relationship between the error of reconstructed reflectance and the dimension of basis functions has been observed in the linear model [2,3,7]. Second is to analyze not only the error of reconstructed reflectance but also color difference on color space for real applications [6,10,11 ] A linear model designed to minimize the error between original SR and reproduced one is inappropriate in efficient color representation because it is not designed to minimize color differences. Moreover, it is important to remember that basis functions should be derived independent of illuminants because color constancy is get "an invariant" under the varying illuminants.…”

“…Figure 2represent the furst four basis vectors for SR weighted by LABp=2. The feature of the LAB basis vector is different from tl~ conventional and CMF cases[10]. The relation between a matrix of original SR S and a reconstructed one S' becomes as:S' = B h W h = B h (Bh +S) = (B h Bh +)S = Ph S.(24) Let a matrix for mapping the original spectra S onto the reconstructed spectra S' be the projection matrix Ph, via the basis vectors.…”

On the properties of some low-parameter models for color reproduction in terms of spectrum transformations and coverage of a color triangle

“…In the paper we discuss linear models [2,9,20,21,22,23,24,25,26,27,28,29]. They are of interest because, on the one hand, they are computationally efficient, and, on the other hand, they are closed under addition.…”