Isometric Embeddings in Imaging and Vision: Facts and Fiction

2010/04/29 by Emil Saucan, Saucan, Emil · 2 citations
Computer Science · Mathematics · #30C65 #52B70 #53C42 #57R40 #Complex Variables (math.CV) #Computer Vision and Pattern Recognition (cs.CV) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities #cs.CV #math.CV #math.DG #msc:30C65 #msc:52B70 #msc:53C42 #msc:57R40

paper · pdf · doi:10.48550/arxiv.1004.5351

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

openalex publication_date 2010/04/29 · arxiv created 2010/05/11 · arxiv updated 2010/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℝ³ and we show that their proof does not extended directly to higher dimensions.

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• On the properties of the combinatorial Ricci flow for surfaces
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