Differential and Numerically Invariant Signature Curves Applied to Object Recognition
- Cite this article as:
- Calabi, E., Olver, P.J., Shakiban, C. et al. International Journal of Computer Vision (1998) 26: 107. doi:10.1023/A:1007992709392
We introduce a new paradigm, the differential invariant signature curve or manifold, for the invariant recognition of visual objects. A general theorem of É. 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.