Abstract
We introduce a new paradigm, the differential invariant signature curve or manifold, for the invariant recognition of visual objects. A general theorem of E. Cartan implies that two curves are related by a group transformation if and only if their signature curves are identical. The important examples of the Euclidean and equi-affine groups are discussed in detail. Secondly, we show how a new approach to the numerical approximation of differential invariants, based on suitable combination of joint invariants of the underlying group action, allows one to numerically compute differential invariant signatures in a fully group-invariant manner. Applications to a variety of fundamental issues in vision, including detection of symmetries, visual tracking, and reconstruction of occlusions, are discussed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 107-135 |
| Number of pages | 29 |
| Journal | International Journal of Computer Vision |
| Volume | 26 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1998 |
Bibliographical note
Funding Information:⁄Supported in part by NSF Grant DMS 92-03398. †Supported in part by NSF Grant DMS 95-00931. ‡Supported in part by NSF Grant ECS-9122106, by the Air Force Office of Scientific Research F49620-94-1-00S8DEF, by the Army Research Office DAAH04-93-G-0332, DAAH04-94-G-0054, and AFOSR-MURI.
Keywords
- Curve shortening flow
- Differential invariant
- Equi-affine group
- Euclidean group
- Joint invariant
- Numerical approximation
- Object recognition
- Signature curve
- Snake
- Symmetry group