Geometric invariant signatures and flows: Classification and applications in image analysis

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.

Duke Scholars

Author Guillermo Sapiro Electrical and Computer Engineering