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On the local behavior of spaces of range image patches

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Abstract

We focus on the quantitative and local topological properties of range images. We consider the spaces Mm of m × m high-contrast patches of range images for m= 3, 5, 7, 9, 11. Using computational topological tools to analyze range image patches, we detect that M3 (M9, M11) has core subsets with the topology of a circle, M3, M5, M7, M9 and that M11 have some subspaces with the topology of a Klein bottle. We also discover that the largest subspace with the Klein bottle’s topology decreases as the measurements of patches increase, which generalizes the results in the paper of H. Adams and G. Carlsson, and demonstrates properties among optical images and range image patches, which are more similar than those established by Lee et al.

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Acknowledgements

The authors are very grateful to the reviewers for valuable comments and corrections.

This work was supported by the National Natural Science Foundation of China (No. 61471409).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qilu University of Technology, Jinan, 250353, People’s Republic of China

    Jinhong Li

  2. School of Science, Shandong Jianzhu University, Jinan, 250101, People’s Republic of China

    Shengxiang Xia

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  1. Jinhong Li
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Correspondence to Shengxiang Xia.

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Li, J., Xia, S. On the local behavior of spaces of range image patches. Multimed Tools Appl 80, 16441–16472 (2021). https://doi.org/10.1007/s11042-020-09913-3

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