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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PostScript files are available on the server in Munich but we recommend
"Curvature
measures in visual information processing" as a more recent
and extended version of this paper.