Geometric methods in perceptual image processing

Perceptual image processing refers to the algorithmic transformation of information in which input images are turned into inferred descriptions (e.g., three-dimensional shape and material properties) of the objects being viewed. The ability of humans to derive such information--even when such problems are ill-posed--demonstrates the utility of modeling aspects of human visual perception for use in graphics and vision applications. In this thesis, we first study the problem of color constancy and characterize the applicability of the generalized von Kries models in terms of rank constraints on the measured world. We show that our world, as measured by some spectral databases, approximately meets these rank constraints and we provide an algorithm for computing an optimal color basis for generalized von Kries modeling. These color constancy notions are then used to derive a new color space for illumination-invariant image processing (in which algorithms manipulate the intrinsic image instead of working directly on RGB values). The derived color space also possesses other useful perceptual features: Euclidean distances approximate perceptual distances, and the coordinate directions have an intuitive interpretation in terms of color opponent channels. Finally, we draw some connections between curves in an image and shape understanding. We single out suggestive contours and illumination valleys as particularly interesting because although one is defined in terms of three-dimensional geometry and the other in terms of image features, the two produce strikingly similar results (and effectively convey a sense of shape). This suggests that the two types of curves capture similar pieces of geometric information. To explore this connection, we develop some general techniques for recasting questions about the image as questions about the surface.