Design of a Trichromatic Cone Array

Cones with peak sensitivity to light at long (L), medium (M) and short (S) wavelengths are unequal in number on the human retina: S cones are rare (<10%) while increasing in fraction from center to periphery, and the L/M cone proportions are highly variable between individuals. What optical properties of the eye, and statistical properties of natural scenes, might drive this organization? We found that the spatial-chromatic structure of natural scenes was largely symmetric between the L, M and S sensitivity bands. Given this symmetry, short wavelength attenuation by ocular media gave L/M cones a modest signal-to-noise advantage, which was amplified, especially in the denser central retina, by long-wavelength accommodation of the lens. Meanwhile, total information represented by the cone mosaic remained relatively insensitive to L/M proportions. Thus, the observed cone array design along with a long-wavelength accommodated lens provides a selective advantage: it is maximally informative

Matching Color Images: The Impact of Axial Chromatic Aberration

We show how to compute and to use the wavelength-dependent optical transfer function (OTF) to create color matches between spatially patterned images. We model the human OTF as a defocused optical system with a circular aperture. In our model, the defocus arises from axial chromatic aberration and wavelength-independent aberrations. From the computed OTF, it is apparent that high spatial-frequency components of the image can play little role in contrast and color appearance, and that in the spatial-frequency range from 5-20 cpd, the visual system is dichromatic because there is no contrast in the short-wavelength receptor signal. We show how to use the wavelength-dependent OTF to match color images across displays by setting matches in corresponding spatial-frequency bands. Because chromatic aberration so affects the OTF, this new procedure is a significant improvement over the conventional procedure of setting matches point by point. 1 Introduction The color-matching exper..

Linear models of surface and illuminant spectra

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. 1

A probabilistic framework for edge detection and scale selection

We devise a statistical framework for edge detection by performing a statistical analysis of zero crossings of the second derivative of an image. This analysis enables us to estimate at each pixel of an image the probability that an edge passes through the pixel. We present a statistical analysis of the Lindeberg operators that we use to compute image derivatives. We also introduce a confidence probability that tells us how reliable the edge probability is, given the image’s noise level and the operator’s scale. Combining the edge and confidence probabilities leads to a probabilistic scale selection algorithm. We present the results of experiments on natural images.

Rounding Arrangements Dynamically

We describe a robust, dynamic algorithm to compute the arrangement of a set of line segments in the plane, and its implementation. The algorithm is robust because, following Greene 1 and Hobby, 2 it rounds the endpoints and intersections of all line segments to representable points, but in a way that is globally topologically consistent. The algorithm is dynamic because, following Mulmuley, 3 it uses a randomized hierarchy of vertical cell decompositions to make locating points, and inserting and deleting line segments, efficient. Our algorithm is novel because it marries the robustness of the Greene and Hobby algorithms with Mulmuley&apos;s dynamic algorithm in a way that preserves the desirable properties of each. Keywords: arrangement, vertical trapezoidal decomposition, dynamic data structure, randomized algorithm, robustness, rounding 1

Device-Directed Rendering

Rendering systems can produce images that include the entire range of visible colors. Imaging hardware, however, can reproduce only a subset of these colors: the device gamut. An image can only be correctly displayed if all of its colors lie inside the gamut of the target device. Current solutions to this problem are to either correct the scene colors by hand, or to apply gamut mapping techniques to the final image. We propose a methodology called device-directed rendering that performs scene color adjustments automatically. Device-directed rendering applies classic minimization techniques to a symbolic representation of the image that describes the relationship of the scene lights and surfaces to the pixel colors. This representation can then be evaluated to produce an image that is guaranteed to be in gamut. While our primary application has been correcting out-of-gamut colors, this methodology can be generally applied to the problem of adjusting a scene description to accommodate co..