Munsell reflectance spectra represented in three‐dimensional Euclidean space

Romney, A. Kimball; Indow, Tarow

doi:10.1002/col.10144

Cited by 31 publications

(26 citation statements)

References 25 publications

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“…They did not take into account the cone sensitivity curves, nor did they apply the cube root transformation. The calculations of the neural network, which are equivalent to SVD, resulted in a 3D coordinate structure virtually identical to that obtained on the same spectra by using SVD (21).…”

Section: Discussionsupporting

confidence: 62%

Functional computational model for optimal color coding

Romney

Chiao

2009

Proc. Natl. Acad. Sci. U.S.A.

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This paper presents a computational model for color coding that provides a functional explanation of how humans perceive colors in a homogeneous color space. Beginning with known properties of human cone photoreceptors, the model estimates the locations of the reflectance spectra of Munsell color chips in perceptual color space as represented in the CIE L*a*b* color system. The fit between the two structures is within the limits of expected measurement error. Estimates of the structure of perceptual color space for color anomalous dichromats missing one of the normal cone photoreceptors correspond closely to results from the Farnsworth-Munsell color test. An unanticipated outcome of the model provides a functional explanation of why additive lights are always red, green, and blue and provide maximum gamut for color monitors and color television even though they do not correspond to human cone absorption spectra.perceptual color ͉ retina ͉ neuroscience ͉ dichromats T he aim of this article is to formulate a model for color coding that estimates how humans perceive color as a function of their cone sensitivity curves. The model is functional in the sense that it answers some of the how and why questions about color processing raised below. The model is computational in the sense that it provides formulas to predict, among other things, how normal human color perception with three cone photoreceptors differs from human color perception where one cone is missing. We will use the term optimal in the sense that the code carries the maximum amount of information using minimal channel capacity or bandwidth.All visual information used by the brain in processing visual images, including the information about the color of objects, originates in the photoreceptors in the retina. The function of human color vision is to assign the colors of objects in the visual environment to locations in a coherent perceptual color space. The information about the color of an object resides in its reflectance spectra. Color is inferred from light reflected from the surfaces of objects. That light is the product of the reflectance spectrum of the object and the wavelength composition of the illumination. Basically, the retina has to consolidate the information received by many millions of highly redundant wavelength-sensitive photoreceptor cells into an informationefficient and compressed code for transmission through the approximately one million fibers of the optic nerve. The code carrying the visual information down the optic nerve must contain information about the color of objects. We emphasize the fact that the physiological implementation of color coding is beyond the scope of this article. Even though the abstract mathematical calculations of our model implemented by a computer clearly have no physiological analogs, we do think that computations that result in outcomes similar to those of our model are carried out by the human visual system in some fashion. The bandwidth limitations of the optic nerve suggest that much of the color ...

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Section: Discussionsupporting

confidence: 62%

Functional computational model for optimal color coding

Romney

Chiao

2009

Proc. Natl. Acad. Sci. U.S.A.

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“…Some representations of its spectra have been shown to include natural spectra, such as those from flowers, flower clusters, leaves, and berries (Jaaskelainen et al 1990). Previous studies of the Munsell set have found that the number of basis functions needed to approximate its spectra ranges from 3 to 8, depending on the criterion of fit and whether part or all of the set was used (Cohen 1964;Maloney 1986;Parkkinen et al 1989;Jaaskelainen et al 1990;Usui et al 1992;Vrhel et al 1994;Lenz et al 1996;Owens et al 2000;Westland et al 2000;Romney and Indow 2003). In all these studies, however, the adequacy of the approximation was based on theoretical criteria, rather than on psychophysical measurement.…”

Section: Introductionmentioning

confidence: 99%

Perceptual Limits on Low-Dimensional Models of Munsell Reflectance Spectra

Oxtoby

Foster

2005

Perception

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Abstract. Some experimental and theoretical approaches to surface-colour perception depend on approximating surface reflectance spectra by low-dimensional models. In the psychophysical experiment reported here, observers had to discriminate between patterns of Munsell surfaces and their spectral approximations under either the same or different illuminants. The approximations were produced by principal component analysis, by independent component analysis, and by artificial neural networks trained with a supervised-learning rule. In all experimental conditions, observers required, on average, at least 5 basis functions for discrimination performance to be at chance, thus placing a lower limit on the dimensionality of models of Munsell reflectance spectra.

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“…A final test of how well the reflectance spectra can be approximated by just the L and M cones may be made by comparing the location of the sample spectra derived from the empirical basis functions with the location of the sample spectra derived from estimated basis functions based on the L and M cone sensitivity curves. Romney and Indow (5,11) demonstrated that the dot product of the reflectance spectra and basis functions results in coordinates that locate the spectra in a three-dimensional Euclidean space (see, for example, figure 4 in ref. 11, similar except for illumination by D65).…”

Section: A Model Of How Cone Sensitivity Curves Are Aggregated In Thementioning

confidence: 99%

Modeling lateral geniculate nucleus cell response spectra and Munsell reflectance spectra with cone sensitivity curves

Romney

D’Andrade²

2005

Proc. Natl. Acad. Sci. U.S.A.

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We find that the cell response spectra of lateral geniculate nucleus cells, as well as the reflectance spectra of Munsell color chips, may be modeled by using the cone sensitivity functions of the long and medium cones. We propose a simple model for how the neural signals from the photoreceptors might be combined in the retina to closely approximate the reflectance spectra of Munsell color chips without input from the short cone.vision ͉ color perception R ecent research reveals that lateral geniculate nucleus (LGN) cell response spectra are fairly smoothly distributed in Munsell perceptual color space in a manner similar to the reflectance spectra of Munsell color chips (1). The findings were based on data reported by De Valois et al. (2), who measured spectral response data on 147 LGN cells. Neural signals reach the LGN through the optic nerve, which consists of the axons of ganglion cells in the retina. Each axon carries signals aggregated from a number of photoreceptors. The aim of this paper is to examine the LGN response spectra for clues as to how the responses of the long (L), medium (M), and short (S) cones (photoreceptors) are aggregated through the various layers of the retina to produce the LGN response spectra. From these clues, we construct a simple model of how the reflectance spectra of the Munsell chips might be represented by these aggregation processes.We assume that the color appearance of objects originates in their reflectance spectra that, together with the illumination source, determine the light stimuli reaching the photoreceptors or cones in the retina. We seek understanding of how photoreceptors are combined in the retina to produce a distribution of the LGN response spectra that is similar in distribution to the reflectance spectra of objects (1). First, we explore the contribution of the cones to the basis functions of the LGN spectral response curves. We recognize that these representations are statistical constructions and do not necessarily represent how the neural system actually functions. However, we can obtain some insight into the way the system might function from such an examination. We then propose a model of how the cone sensitivity curves might be combined to produce response spectra that closely approximate reflectance spectra of ordinary objects such as flowers, fruits, and Munsell color chips. We denote the data consisting of the response spectra of the 147 LGN cells as R NϫM , where N ϭ 147 cells and M ϭ 12 sampled wavelength locations with responses measured in spikes per second (each cell was measured at three light intensities, and the 147 values are means of the three measures). We used the raw recorded data uncorrected for base firing rates. In general, PCA or singular value decomposition analyzes a matrix such as R in the following way (5) Cone Contributions to the Basis Functions of the LGN Neuronswhere both UU T and VV T are identity matrices, and ⌬ KϫK ϭ ( ͌ k ) is a diagonal matrix. Values of k (Ͼ0) and v jk are obtained, respectively, as eigenvalues and ei...

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Munsell reflectance spectra represented in three‐dimensional Euclidean space

Cited by 31 publications

References 25 publications

Functional computational model for optimal color coding

Functional computational model for optimal color coding

Perceptual Limits on Low-Dimensional Models of Munsell Reflectance Spectra

Modeling lateral geniculate nucleus cell response spectra and Munsell reflectance spectra with cone sensitivity curves

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