this paper we describe an algorithm for estimating the surface reflectance functions of objects in a scene with incomplete knowledge of the spectral power distribution of the ambient light. We assume that lights and surfaces present in the environment are constrained in a way that we make explicit below. ' An image-processing system using this algorithm can assign colors that are constant despite changes in the lighting on the scene. This capability is essential to correct color rendering in photography, in television, and in the construction of artificial visual systems for robotics. We describe how constraints on lights and surfaces in the environment make color constancy possible for a visual system and discuss the implications of the algorithm and these constraints for human color vision

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We describe procedures for creating efficient spectral representations for color. The representations generalize conventional tristimulus representations, which are based on the peripheral encoding by the human eye. We use low-dimensional linear models to approximate the spectral properties of surfaces and illuminants with respect to a collection of sensing devices. We choose the linear model basis functions by minimizing the error in approximating sensor responses for collections of surfaces and illuminants. These linear models offer some conceptual simplifications for applications such as printer calibration; they also perform substantially better than principal components approximations for computer graphics applications.

This study's main result is to show that under the conditions imposed by the Maloney-Wandell color constancy algorithm, whereby illuminants are three dimensional and reflectances two dimensional (the 3-2 world), color constancy can be expressed in terms of a simple independent adjustment of the sensor responses (in other words, as a von Kries adaptation type of coefficient rule algorithm) as long as the sensor space is first transformed to a new basis. A consequence of this result is that any color constancy algorithm that makes 3-2 assumptions, such as the Maloney-Wandell subspace algorithm, Forsyth's MWEXT, and the Funt-Drew lightness algorithm, must effectively calculate a simple von Kries-type scaling of sensor responses, i.e., a diagonal matrix. Our results are strong in the sense that no constraint is placed on the initial spectral sensitivities of the sensors. In addition to purely theoretical arguments, we present results from simulations of von Kriestype color constancy in which the spectra of real illuminants and reflectances along with the human-conesensitivity functions are used. The simulations demonstrate that when the cone sensor space is transformed to its new basis in the appropriate manner a diagonal matrix supports nearly optimal color constancy. Key words: color constancy, von Kries, chromatic adaptation, color balancing. 1.

This paper’s main result is to show that under the conditions imposed by the Maloney- Wandell color con-stancy algorithm, color constancy can in fact he ex-pressed in terms of a simple independent adjustment of the sensor responses-in other words as a uon Kries adaptation type of coeficient rule algorithm-so long as the sensor space is first transformed to a new ha-sis. Our overall goal is to present a theoretical analy-sis connecting many established theories of color con-stancy. For the case where surface refiectances are 2-dimensional and illuminants are $dimensional, we prove that perfect color constancy can always be solved for by an independent adjustment of sensor responses, which means that the color constancy transform can he expressed as a diagonal matrix. This result re-quires a prior transformation of the sensor basis and to support it we show in particular that there exists n transformation of the original sensor basis under which the non-diagonal meth,ods of Maloney- Wandell, Forsyth’s MWEXT and Funt and Drew’s lightness al-gorithm all reduce to simpler, diagonal-matrix theones of color constancy. Our results are strong in the sense that no constraint is placed on the initial sensor spec-tral sensitzuities. In addition to purely theoretical ar-guments, the paper contains results from simulations of diagonal-matrix-based color constancy in which the spectra of real illuminants and refiectances along with the human cone sensitivity functions are used. The simulations demonstrate that when the cone sensor space is transformed to its new basis in the appropriate manner, a diagonal matrix supports close to optimal color constancy. 1

Psychophysical findings accumulated over the past several decades indicate that perceptual tasks such as similarity judgment tend to be performed on a low-dimensional representation of the sensory data. Low dimensionality is especially important for learning, as the number of examples required for attaining a given level of performance grows exponentially with the dimensionality of the underlying representation space. In this chapter, we argue that, whereas many perceptual problems are tractable precisely because their intrinsic dimensionality is low, the raw dimensionality of the sensory data is normally high, and must be reduced by a nontrivial computational process, which, in itself, may involve learning. Following a survey of computational techniques for dimensionality reduction, we show that it is possible to learn a low-dimensional representation that captures the intrinsic low-dimensional nature of certain classes of visual objects, thereby facilitating further learning of tasks...

Vision algorithms are often developed in a Bayesian framework. Two estimators are commonly used: maximum a posteriori (MAP), and minimum mean squared error (MMSE). We argue that neither is appropriate for perception problems. The MAP estimator makes insufficient use of structure in the posterior probability. The squared error penalty of the MMSE estimator does not reflect typical penalties. We describe a new

this paper. Finally, to improve the quality of the measured images, each image was acquired along with a dark frame of the same exposure duration. The dark-frame values were measured and subtracted from every measured image to reduce the effects of read noise in the sensors

Outdoor scene classification is challenging due to irregular geometry, uncontrolled illumination, and noisy reflectance distributions. This paper discusses a Bayesian approach to classifying a color image of an outdoor scene. A likelihood model factors in the physics of the image formation process, the sensor noise distribution, and prior distributions over geometry, material types, and illuminant spectrum parameters. These prior distributions are learned through a training process that uses color observations of planar scene patches over time. An iterative linear algorithm estimates the maximum likelihood reflectance, spectrum, geometry, and object class labels for a new image. Experiments on images taken by outdoor surveillance cameras classify known material types and shadow regions correctly, and flag as outliers material types that were not seen previously. 1.

The chromaticities of natural daylights cluster around the blackbody locus. We investigated whether the mechanisms that mediate human color constancy embody this statistical regularity of the natural environment, so that constancy is best when the illuminant change is one likely to occur. Observers viewed scenes displayed on a CRT-based stereoscope and adjusted a test patch embedded in the scene until it appeared achromatic. Scenes were rendered using physics-based graphics software (RADIANCE) coupled with custom extensions that ensured colorimetric accuracy. Across conditions, both the simulated illuminant and the simulated reflectance of scene objects were varied. Achromatic settings from paired conditions were used to compute a constancy index (CI) that characterizes the stability of object appearance across the two illuminants of the pair. Constancy indices were measured for four illuminant changes from a Neutral illuminant (CIE D65). Two of these changes (Blue and Yellow) were consistent with the statistics of daylight, whereas two (Green and Red) were not. The results indicate that constancy was least across the Red change, as one would expect for the statistics of natural daylight. Constancy for the Green direction, however, exceeded that for the Yellow illuminant change and was comparable to that for the Blue. This result is difficult to reconcile with the hypothesis that mechanisms of human constancy incorporate the statistics of daylights. Some possible reasons for the discrepancy are discussed.