Abstract
Based on modern invariant theory and symmetry groups, a high level way of defining invariant geometricflows for a given Lie group is described in this work. We then analyze in more detail different subgroups ofthe projective group, which are of special interest for computer vision. We classify the corresponding invariantflows and show that the geometric heat flow is the simplest possible one. Results on invariant geometric flows ofsurfaces are presented in this paper as well. We then show how the planar curve flow obtained for the affine groupcan be used for geometric smoothing of planar shapes and edge preserving enhancement of MRI. We concludethe paper with the presentation of an affine invariant geometric edge detector obtained from the classification ofaffine differential invariants.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 275-287 |
| Number of pages | 13 |
| Journal | Proceedings of SPIE - The International Society for Optical Engineering |
| Volume | 2277 |
| DOIs | |
| State | Published - Oct 25 1994 |
| Externally published | Yes |
| Event | Automatic Systems for the Identification and Inspection of Humans 1994 - San Diego, United States Duration: Jul 24 1994 → Jul 29 1994 |
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering
Keywords
- Affine edge detector
- Invariant flows
- Invariant theory
- MRI enhancement
- Symmetry groups