A topological analysis of high-contrast patches in natural images
- College of Science, Shandong Jianzhu University, Jinan 250101, P. R. China.
In this paper, we study qualitative topological analysis of spaces of natural images locally. We apply the
techniques of computational topology to the space of 3×3, 4×4, 5×5, 6×6 and 7×7 high-contrast patches.
We show that in each case there is a subspace of the space of all high-contrast patches that is topologically
equivalent to the Klein bottle and we found that the size of the largest subspace having the Klein bottle’s
homology decreases with increasing of the size of patches. The data sets used in this paper are different
from that discussed in the paper ”on the local behavior of spaces of natural images”, we conformed our
findings by applying the same methods to the different sizes patches.
Share and Cite
Shengxiang Xia, A topological analysis of high-contrast patches in natural images, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 1, 126--138
Xia Shengxiang, A topological analysis of high-contrast patches in natural images. J. Nonlinear Sci. Appl. (2016); 9(1):126--138
Xia, Shengxiang. "A topological analysis of high-contrast patches in natural images." Journal of Nonlinear Sciences and Applications, 9, no. 1 (2016): 126--138
- persistent homology
- natural images
- high-contrast patches
- Klein bottle
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