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On the nonlinear statistics of range image patches. (English) Zbl 1175.62066

Summary: A. B. Lee, K. S. Pedersen and D. Mumford [Int. J. Comput. Vis. 54, No.  1–3, 83–103 (2003; Zbl 1070.68661)] studied the distributions of \(3\times3\) patches from optical images and from range images. G. Carlsson, T. Ishkanov, V. de Silva and A. Zomorodian [ibid. 76, 1–12 (2008)] applied computational topological tools to the data set of optical patches studied by Lee, Pedersen and Mumford and found geometric structures for high density subsets. One high density subset is called the primary circle and essentially consists of patches with a line separating a light and a dark region.
We apply the techniques of Carlsson et al. to range patches. By enlarging to \(5\times5\) and \(7\times7\) patches, we find core subsets that have the topology of the primary circle, suggesting a stronger connection between optical patches and range patches than was found by Lee, Pedersen and Mumford.

MSC:

62H35 Image analysis in multivariate analysis
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65C60 Computational problems in statistics (MSC2010)

Citations:

Zbl 1070.68661
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