Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach
Abstract
Computer vision deals with image understanding at various levels. At the low level, it addresses issues such us planar shape recognition and analysis. Some classical results on differential invariants associated to planar curves are relevant to planar object recognition under different views and partial occlusion, and recent results concerning the evolution of planar shapes under curvature controlled diffusion have found applications in geometric shape decomposition, smoothing, and analysis, as well as in other image processing applications. In this work we first give a modern approach to the theory of differential invariants, describing concepts like Lie theory, jets, and prolongations. Based on this and the theory of symmetry groups, we present a high level way of defining invariant geometric flows for a given Lie group. We then analyze in detail different subgroups of the projective group, which are of special interest for computer vision. We classify the corresponding invariant flows and show that the geometric heat flow is the simplest possible one. This uniqueness result, together with previously reported results which we review in this paper, confirms the importance of this class of flows.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 10, 1993
- Accession Number
- ADA459617
Entities
People
- Allen Tannenbaum
- Guillermo Sapiro
- Peter Olver
Organizations
- University of Minnesota