Isometric Embeddings in Imaging and Vision: Facts and Fiction.

link: http://arxiv.org/abs/1004.5351
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.