Curvature Measures in Visual Information Processing

Erhardt Barth, Christoph Zetzsche, and Gerhard Krieger

ABSTRACT The geometric concept of curvature can help to deal with some
important aspects of information processing in natural and artificial
vision systems. The paper briefly reviews earlier results regarding the
relationship between the notions of curvature, the processing of
information, and the modelling of end-stopped neurons in the visual
cortex. It then focuses on the difference between Gaussian curvature and
the Riemann tensor and reveals the corresponding logical structures.
Furthermore, it is shown how multidimensional deviations from flatness can
be measured by two-dimensional curvature operators. In the context of
image-sequence analysis, a new relationship between the Riemann tensor
components and the computation of the optical flow is found.

E. Barth, C. Zetzsche, and G. Krieger: Curvature measures in visual information processing In: Open Systems and Information Dynamics 5:25-39, 1998.

(pdf  0.09 MB) (PostScript 0.6 MB)