Feature Matching and Heat Flow in Centro-Affine Geometry

Abstract

In this paper, we study the differential invariants and the invariant heat flow in centro-affine geometry, proving that the latter is equivalent to the inviscid Burgers' equation. Furthermore, we apply the centro-affine invariants to develop an invariant algorithm to match features of objects appearing in images. We show that the resulting algorithm compares favorably with the widely applied Scale-Invariant Feature Transform (SIFT), Speeded Up Robust Features (SURF), and Affine-SIFT (ASIFT) methods.