Curvature measures in visual information processing
by , ,
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.
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PDF URL: http://dx.doi.org/10.1023/A:1009675801435
Reference:
Curvature measures in visual information processing (Erhardt Barth, Christoph Zetzsche, Gerhard Krieger), In Open Systems & Information Dynamics, Springer Science + Business Media, volume 5, 1998.
Bibtex Entry:
@Article{Barth1998a,
  author    = {Erhardt Barth and Christoph Zetzsche and Gerhard Krieger},
  title     = {Curvature measures in visual information processing},
  journal   = {Open Systems {\&} Information Dynamics},
  year      = {1998},
  volume    = {5},
  number    = {1},
  pages     = {25--39},
  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.},
  doi       = {10.1023/a:1009675801435},
  publisher = {Springer Science + Business Media},
  url       = {http://dx.doi.org/10.1023/A:1009675801435},
}