L. T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Am. A, 3(10):1673--1683, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... In many earlier studies, spectral power distribution (SPD) of illuminants and reflectance of objects are separately subjected to the principal component analysis (PCA) to obtain the basis functions from which only the few first ones are used in order to reduce complexity and to compress data [5, 6, 11]. It has been showed that these basis functions can be applied for color constancy purposes either in direct way as in the Maloney Wandell algorithm (3 basis functions for illuminations and 2 for object reflectances) 6] or indirectly as in spectral sharpening [2] It may also be used in color ....

L.T. Maloney, Evaluation of Linear Models of Surface Spectral Reflectance with Small Number of Parameters, Journal of Optical Society of America A, Vol. 3, No. 10, October 1986, pp. 1673-1683.

....basis functions. In addition, let S j ( be a basis set for reflectance; for these Brainard et al. 3] see also [18] use either Cohen s [6] Munsell chip reflectance basis or their own basis set developed using a principal component analysis of a large set of Munsell chips (cf. Maloney s analysis [17] of the large sample of natural reflectances obtained by Krinov [15] Judd et al. modeled most daylights using just three to five illumination basis vectors; Cohen concluded that between three and six basis vectors were sufficient for modeling reflectance. The full set of product functions ....

....purposes we must choose just three product basis functions P ( for modeling color signals. We select pairs: P 1 ( E 1 ( S 1 ( P 2 ( E 1 ( S 2 ( P 3 ( E 2 ( S 1 ( 17) Our tests employ Judd s illumination basis functions E i ( For the reflectance basis set, we follow Maloney [17] and carry out a principal component analysis on the Krinov catalogue of 370 natural reflectances [15] 4 Since these reflectances are available in a limited range in the visible 400nm through 650nm in steps of 10nm we keep the analysis to only 26 samples over wavelength. In fact, since we ....

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L.T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Am. A, 3:1673--1683, 1986.

....from the changes due to reflectance. Past works have shown that the illumination change can be modeled as linear transformations in the RGB space (see for instance [20] The argument is supported by early research that the surface reflectance can be represented by low dimensional linear systems [10]. Representing the measured color vector at a pixel x as a row vector E(x) # R 13 , and the radiance of the same pixel under a different illumination as E # (x) the authors of [20] claimed E # (x) E(x)M,M # R 33 . If a population of K pixels are coplanar in the 3D world, and they are ....

L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters", J. Opt. Soc. Am. A/Vol. 3, No. 10, October 1986.

....function f c into N samples, and denoting each discretized function as a column vector, we obtain an equivalent vector representation # c = gl T D(f c )s (1) where D(f c ) is the N N diagonal matrix with f c as diagonal elements. We adopt finite dimensional linear models for both reflectance [13, 16, 3] and illuminant spectrum[11, 18] Assume the reflectance and spectrum are spanned by the column spaces of the matrices B s and B l respectively. The reflectance and spectrum can be rewritten as # s = B s # l = B l # (2) Here # # R n# and # # R n l are coefficient vectors with much lower ....

....matrices B s and B l respectively. The reflectance and spectrum can be rewritten as # s = B s # l = B l # (2) Here # # R n# and # # R n l are coefficient vectors with much lower dimensionality than N . Previous research shows that both the natural light spectrum [11, 18] and reflectance [13, 16, 3] can be approximated accurately with such low dimensional linear systems. Substituting (2) into (1) we get # c = g# T B l T D(f c )B s # Denoting the n l element vector B l T D(f c )B s # as # c , and assuming that g is known, we have a simple bilinear model for color image formation # ....

L.T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Amer.-A, 3(10):1673--1683, October 1986.

....surface reflectance can be well represented by a finite dimensional model of dimension n, where n is the same as the number of camera sensors [4, 5, 2] Here, n is taken to be 3. However, although low dimensional surface reflectance can be justified in the context of the Maloney Wandell model [7], this assumption can sometimes be inaccurate [8] Instead, we would like to argue that in fact the idea of a linear mapping can be fairly well justified, but on entirely different grounds the grounds that, outside of a laboratory setting, lighting is necessarily complex, with many lights of ....

L.T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Am. A, 3:1673--1683, 1986.

....spectrum will look red to a human observer. Accurate measures of surface spectral reflectance are useful for object recognition, segmentation and material classification. Current research: A series of studies have demonstrated that the spectral reflectance curves of reflectances are not arbitrary[Mal86, PHJ89, VGI94] Indeed it is now accepted that reflectance curves can be accurately represented with a small (6, 7 or 8) basis functions. However, recovery of reflectances (e.g. the basis coefficients) can be confounded by the choice of viewing illuminants. Investigations have been carried out ....

L.T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Am. A, 3:1673--1683, 1986.

....reflectances are 3 dimensional then every (ffl) is a 3 Theta 3 matrix. It follows that response triples obtained under one light can be mapped to those of another by a 3 Theta 3 matrix. p 1 = ffl 1 )oe ; p 2 = ffl 2 )oe ) p 2 = ffl 2 ) ffl 1 ) Gamma1 p 1 (11) Studies[6, 8] have shown that a 3 dimensional model is quite reasonable. Thus it follows that the color distributions of the same surfaces viewed under two illuminants are linearly related to a good approximation. 2.5 Illuminant Invariant Moments Taubin and Cooper [14] have recently developed efficient ....

L.T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Am. A, 3:1673--1683, 1986.

....X t X. Since U and V are unitary matrices, it can easily be verified that when X = UWV t , cf. Equation (5) then X Gamma = VW Gamma U t , where W Gamma has a general diagonal entry equal to w Gamma1 i , i = 1 : R, and zeros elsewhere. It has been found by several studies [33 36] that the singular values of a matrix of spectral reflectances such as R t are strongly decreasing, and by consequence that reflectance spectra can be described accurately by a quite small number of parameters. It has thus been proposed to only take into account the first r R singular values ....

L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters," Journal of the Optical Society of America A, vol. 3, pp. 1673-- 1683, Oct. 1986.

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L. T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Am. A, 3(10):1673--1683, 1986.

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Laurence T. Maloney, "Evaluation of Linear Models of Surface Spectral Reflectance with Small Numbers of Parameters," J. Opt. Soc. Am., Vol. 3, No. 10, Oct. 1986, pp. 1673-1683.

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MALONEY, L. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. Journal of the Optical Society of America A 3, 10 (1986), 1673--1683.

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L. T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Amer., A1, 1986.

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L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters," Journal of the Optical Society of AmericaA3, pp. 1673--1683, October 1986.

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L.T. Maloney, Evaluation of linear models of surface spectral reflectance with small numbers of parameters, J. Opt. Soc. Am. A, Volume 3, pages 1673-1683, 1986

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L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters," Journal of the Optical Society of America A 3, pp. 1673--1683, October 1986.

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L. T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. J. Opt. Soc. Am. A, 3(10):1673--1683, 1986.

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L. T. Maloney. Evaluation of linear models of surface spectral reflectance with small numbers of parameters. Journal of the Optical Society of America A, 3(10):1673--1683, 1986.

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L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters," J. Opt. Soc. Am. A 3, 1673--1683 (1986).

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L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters," J. Opt. Soc. Am. A 3, 1673--1683 (1986).

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L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters", J. Opt. Soc. Am. A, 10, 1673-1683 (1986).

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L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters", J. Opt. Soc. Am. A 10, pp. 1673-1683, 1986.

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L.T. Maloney, "Evaluation of linear models of surface spectral reflectance with small number of parameters", Physicsbased vision principles and practise: Color, pp. 87-98, 1992.

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L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters", J. Opt. Soc. Am. A 10, pp. 1673-1683, 1986.

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L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters", J. Opt. Soc. Am. A, 10, pp. 1673-1683, 1986.

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L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small number of parameters," J. Opt. Soc. Am. A 3, 1673--1683 (1986).

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