Curvature from a non-differential viewpoint:

perspectives from visual information processing

Erhardt Barth, Christoph Zetzsche, and Gerhard Krieger

ABSTRACT : We show that the formidable geometric machinery for dealing with curvature can help to understand some important aspects of information processing in natural and artificial vision systems. The paper briefly reviews some previous results regarding the relationship between the notions of curvature, the processing of information, and the modeling of non-linear neurons in the visual cortex. It then focuses on the difference between Gaussian curvature and the Riemann tensor, and reveals the corresponding logical structures. In the context of image-sequence analysis a new relationship between the Riemann tensor and the computation of the optical flow is found. It is hoped that our less-differential curvature operators can create some attractors of interest in the physical sciences.

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 "Curvature measures in  visual information processing"  as a more recent and  extended version of this paper.