Adams, Henry; Carlsson, Gunnar On the nonlinear statistics of range image patches. (English) Zbl 1175.62066 SIAM J. Imaging Sci. 2, No. 1, 110-117 (2009). 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. Cited in 4 Documents MSC: 62H35 Image analysis in multivariate analysis 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry 65C60 Computational problems in statistics (MSC2010) Keywords:range images; topology; persistent homology Citations:Zbl 1070.68661 PDFBibTeX XMLCite \textit{H. Adams} and \textit{G. Carlsson}, SIAM J. Imaging Sci. 2, No. 1, 110--117 (2009; Zbl 1175.62066) Full Text: DOI Link