David H. Marimont

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.

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 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 images noise level and the operators scale. Combining the edge and confidence probabilities leads to a probabilistic scale selection algorithm. We present the results of experiments on natural images.

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 of the gamut of the target device. Current solutions to this problem are either to 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. Although 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 constraints on the output image pixel values.

Analytical methods for uncalibrated stereo and motion reconstruction

We present a new approach to relative stereo and motion reconstruction from a discrete set of point correspondences in completely uncalibrated pairs of images. This approach also yields new projective invariants, and we present some applications to object recognition. Finally, we introduce a new approach to camera self-calibration from two images which allows full metric reconstruction up to some unknown scale factor. We have implemented the proposed methods and present examples using real images.

Robust Anisotropic Diffusion: Connections Between Robust Statistics, Line Processing, and Anisotropic Diffusion

Relations between anisotropic diffusion and robust statistics are described in this paper. We show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image. The “edge-stopping” function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework. This connection leads to a new “edge-stopping” function based on Tukeys biweight robust estimator, that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion. The robust statistical interpretation also provides a means for detecting the boundaries (edges) between the piecewise smooth regions in the image. Finally, connections between robust estimation and line processing provide a framework to introduce spatial coherence in anisotropic diffusion flows.