Exploring the Manifold of Image Patches

Yevgen Matviychuk and Shannon M. Hughes
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 339–342

Abstract

In image processing, the idea of considering an entire image as a collection of its small overlapping regions has recently attained significant popularity. Algorithms that work with image patches, instead of an image as a whole, produce state-of-the-art results in solving reconstruction problems. Meanwhile, it has been shown that manifold models may provide a good approximation for the set of natural image patches. In this paper we consider one such popular model. We will show some interesting and aesthetically appealing geometric structures arising from an attempt to visualize an embedding of the patch manifold in three-dimensional space.

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