Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R3 in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.
All Science Journal Classification (ASJC) codes
- Signal Processing
- Human-Computer Interaction
- Computer Vision and Pattern Recognition
- Computer Graphics and Computer-Aided Design