Emil Saucan (Mathematics, Technion)
The celebrated Nash Embedding Theorem is extensively employed in recent years in various theoretical, as well as practical, aspects of Computer Graphics and Image Processing. However, in practice, this kind of application encounters certain obstructions, rendering the use of the Embedding Theorem as somewhat problematic. We explore therefore its practicability in Vision, Graphics and other Imaging sciences.
As a solution for some of the problems mentioned above, the use of a PL version of the Theorem, due to Burago and Zalgaller, regarding the existence of isometric embeddings of polyhedral surfaces in R3, has been suggested. We briefly examine the proof of this last result and we show that their proof does not extended directly to higher dimensions.
In addition, a number of possible adaptations, relaxations and somewhat different approaches to the Embedding Theorem, rendering it more practical for imaging, are also considered.