Michael H. Brill

Necessary and sufficient conditions for Von Kries chromatic adaptation to give color constancy

Necessary and sufficient spectral conditions are presented for Von Kries chromatic adaptation to give color constancy. Von-Kries-invariant reflectance spectra are computed for illuminant spectral power distributions that are arbitrary linear combinations of the first three daylight phases. Experiments are suggested to test models of color constancy using computed spectra (either exact or approximate) within the illuminant-invariant framework.

Heuristic analysis of von Kries color constancy

The properties of constancy models based on the proportionality rule of von Kries are examined in a series of simplified examples. It is found that the breadth of receptor-sensitivity functions causes metamerism, thwarting color constancy. Overlap of these functions limits the accuracy of von Kries adaptation for a more subtle reason: it causes nonzero off-diagonal elements in the transformation matrix relating object reflectance to receptor stimulations. Such off-diagonal elements make von Kries adaptation an inexact color-constancy scheme, even when the illuminant is restricted to prevent metamerism.

General methods for determining projective invariants in imagery

Abstract This paper presents the results of a study of projective invariants and their applications in image analysis and object recognition. The familiar cross-ratio theorem, relating collinear points in the plane to the projections through a point onto a line, provides a starting point for their investigation. Methods are introduced in two dimensions for extending the cross-ratio theorem to relate noncollinear object points to their projections on multiple image lines. The development is further extended to three dimensions. It is well known that, for a set of points distributed in three dimensions, stereo pairs of images can be made and relative distances of the points from the film plane computed from measurements of the disparity of the image points in the stereo pair. These computations require knowledge of the effective focal length and baseline of the imaging system. It is less obvious, but true, that invariant metric relationships among the object points can be derived from measured relationships among the image points. These relationships are a generalization into three dimensions of the invariant cross-ratio of distances between points on a line. In three dimensions the invariants are cross-ratios of areas and volumes defined by the object points. These invariant relationships, which are independent of the parameters of the imaging system, are derived and demonstrated with examples.

Image segmentation by object color: a unifying framework and connection to color constancy

A unifying framework is presented for algorithms that use the bands of a multispectral image to segment the image at material (i.e., reflectance) boundaries while ignoring spatial inhomogeneities incurred by accidents of lighting and viewing geometry. The framework assumes that the visual stimulus (image field) from a uniformly colored object is the sum of a small number of terms, each term being the product of a spatial and a spectral part. Based on this assumption, several quantities depending on the reflected light can be computed that are spatially invariant within object boundaries. For an image field either from two light sources on a matte surface or from a single light source on a dielectric surface with highlights, the invariants are the components of the unit normal to the plane in color space spanned by the pixels from the object. In some limited cases the normal to the plane can be used to estimate spectral-reflectance parameters of the object. However, in general the connection of color-constancy theories with image segmentation by object color is a difficult problem. The concomitant constraints on segmentation and color-constancy algorithms are discussed in light of this fact.

Remarks on signal-processing explanations of the trichromacy of vision

We present criticism of signal-processing arguments recently used to explain the trichromacy of color vision. In particular, we note that illuminant spectral power distributions (SPDs) can be metameric even when the signal-processing arguments state that trichromatic vision represents such SPDs without ambiguity. Being statistical in nature, these arguments need not apply to each individual SPD; however, further use of the arguments calls for attributing them to some ensemble of SPDs and then testing whether the ensemble satisfies the underlying statistical assumptions.

Contributions to the theory of invariance of color under the condition of varying illumination

Any visual-processing algorithm aimed at attaining color constancy will in fact attain it only for restricted spectral classes of illuminants and reflectances. These classes constitute implicit heuristics for the physical world, in an artificial-intelligence sense. In the present work, physically reasonable spectral classes are presented which insure that von Kriess law of chromatic adaptation will — in its simplest form — restore object colors in human tristimulus space to illuminant-invariant positions in the space. Algebraic functions of the adapted tristimulus values are presented which are illuminant-invariant for some departures from the spectral heuristics. These functions, a hierarchy of invariants, may be useful in developing lighting and pigment standards for partially controlled viewing environments.

Physical and informational constraints on the perception of transparency and translucency

Scale-invariant constraints on reflectances that together comprise a translucent/transparent sheet over a patchwork matte background are shown to be equivalent to the scale-invariant constraints emerging from Metellis [1] model of transparency perception. If the visual system has access only to inseparable products of reflectance and illuminant intensity, these scaleinvariant rules are the only ones assessable by the visual system. Having been thus physically and informationally justified, the rules are recommended for use in pattern recognition of translucent objects on a background. Generalization of these ideas to colored translucency is also discussed.

Doppler-based detection in reverberation-limited channels: effects of surface motion and signal spectrum

This paper describes an algorithm to predict for a monostatic sonar system, the detection advantage (against reverberation) obtained by tuning a replica correlator to the Doppler-frequency offset predicted for a moving target. The effects of the signal spectrum on the replica-correlator output are modeled by the Q-function, which is the lag-time-integrated square envelope of the ambiguity surface. Random motion in the reflecting surface is included by convolving the Q-function with the monostatic frequency-spread function derived from stationary-phase scattering theory. Results are discussed based on gated-CW and Newhall pulsed-HFM waveforms, to illustrate situations in which waveform design can help Doppler detection and those in which it cannot.<<ETX>>

Analysis of human color mechanisms using sinusoidal spectral power distributions

We examined the effects of probing human color mechanisms using sinusoidal spectral power distributions (SPDs) varying in frequency (i.e., from 0.1 to 5.0 cycles/300 nm for a constant starting phase) and phase (i.e., from 0 to 360 deg for a fixed frequency of 1 cycle/300 nm) through computer simulation using several color models. Predicted modulation sensitivity functions (MSFs) in spectral frequency and phase differ among the models and indicate that measurements of the minimum amplitudes necessary to detect sinusoidal SPDs would be useful for distinguishing among theories of color vision. MSFs obtained from similar analyses of dichromats color mechanisms reveal characteristic patterns of modulation sensitivities and suggest that such measures could serve to distinguish type and degree of color-vision defect. Some implications based on sinusoidal approximations to illuminant and reflectance spectra are discussed along with more general considerations regarding sine-wave SPDs as a probe for mechanisms of color vision.

Some invariant linear methods in photogrammetry and model-matching

For several useful tasks in photogrammetry and in model-based vision, noniterative methods that require only the inversion of systems of linear equations are developed. The methods are based on the theory of projective invariants. The tasks addressed are resection, intersection, and transfer, or model matching (with or without ground control points). The following kinds of transfer are examined: (a) coplanar object points (transfer to image 2 done using four reference points in image 1); (b) stereo camera system (transfer to stereo camera pair 2 done using four reference points in stereo pair 1); (c) general multicamera configuration (transfer of a ninth point to image 3 done using eight tie points in images 1 and 2).<<ETX>>