A topological analysis of high-contrast patches in natural images

Abstract

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.