Lee, Ann B. and Pedersen, Kim S. and Mumford, David (2009) On the nonlinear statistics of range image patches. SIAM Journal on Imaging Sciences, 2 (1). pp. 110-117. ISSN 1936-4954 http://resolver.caltech.edu/CaltechAUTHORS:20090810-153124267
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In [A. B. Lee, K. S. Pedersen, and D. Mumford, Int. J. Comput. Vis., 54 (2003), pp. 83–103], the authors study the distributions of 3 × 3 patches from optical images and from range images. In [G. Carlsson, T. Ishkanov, V. de Silva, and A. Zomorodian, Int. J. Comput. Vis., 76 (2008), pp. 1–12], the authors apply computational topological tools to the data set of optical patches studied by Lee, Pedersen, and Mumford and find 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. In this paper, we apply the techniques of Carlsson et al. to range patches. By enlarging to 5×5 and 7×7 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.
|Additional Information:||© 2009 SIAM. Received December 26, 2007; accepted October 7, 2008; published January 30, 2009. This research was supported in part by DARPA HR 0011-05-1-0007 and NSF DMS 0354543. AMS Subject Classifications: 62H35, 65D18|
|Subject Keywords:||range images; topology; persistent homology|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Jason Perez|
|Deposited On:||11 Aug 2009 04:21|
|Last Modified:||26 Dec 2012 11:10|
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