On the Local Behavior of Spaces of Natural Images

In this study we concentrate on qualitative topological analysis of the local behavior of the space of natural images. To this end, we use a space of 3 by 3 high-contrast patches M. We develop a theoretical model for the high-density 2-dimensional submanifold of M showing that it has the topology of the Klein bottle. Using our topological software package PLEX we experimentally verify our theoretical conclusions. We use polynomial representation to give coordinatization to various subspaces of M. We find the bestfitting embedding of the Klein bottle into the ambient space of M. Our results are currently being used in developing a compression algorithm based on a Klein bottle dictionary. Keywords : topology; natural images; manifold; filtration; Klein bottle; persistent homology

• Type: Journal
• Year: 2008
• Where: IJCV
• Authors: Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, Afra Zomorodian
• Keywords: IJCV 2008, Klein Bottle, Natural Images, Qualitative Topological Analysis