Isometric Embeddings in Imaging and Vision: Facts and Fiction

Abstract

We explore the practicability of Nash's Embedding Theorem in vision and imaging sciences. In particular, we investigate the relevance of a result of Burago and Zalgaller regarding the existence of isometric embeddings of polyhedral surfaces in ${\mathbb{R}}^3$ and we show that their proof does not extended directly to higher dimensions.

23 pages, 1 figure Second version: Corrections made, subsection added

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