On the Local Behavior of Spaces of Natural Images

@article{Carlsson2007OnTL,
  title={On the Local Behavior of Spaces of Natural Images},
  author={Gunnar E. Carlsson and Tigran Ishkhanov and Vin de Silva and Afra Zomorodian},
  journal={International Journal of Computer Vision},
  year={2007},
  volume={76},
  pages={1-12}
}
Abstract 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… 
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