On the Nonlinear Statistics of Range Image Patches

In [7], A. Lee, K. Pedersen, and D. Mumford study the distributions of 3× 3 patches from digital photographs and range scans. G. Carlsson, T. Ishkanov, V. de Silva, and A. Zomorodian in [3] apply computational topological tools to the dataset of optical images studied in [7] 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 [3] to range image patches. By enlarging to 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 in [7].