On qualitative analysis of high-contrast patches in range images

Abstract

In “On the Nonlinear Statistics of Range Image Patches,” H. Adams and G. Carlsson use computational topology to the data set of 5×5 and 7×7 range image patches and show that some density subsets have the topology of a circle. In this chapter, we study the space of range images locally by expending them to 8×8 and 9×9 patches and experimentally prove that the subspaces of the space of all high-contrast patches exist in both cases, topologically equivalent to a circle and the Klein bottle, respectively, which have improved Adams and Carlsson’s results.