Shape matching using set of curve geometric invariant point

Abstract

We introduce a non-iterative geometric-based method for shape matching using a novel set of geometric landmarks residing on a 2D contours. These landmarks are intrinsic and are computed from the differential geometry of the curve. We exploit the invariant properties of geometric landmarks that are local and preserved under the affine and some perspective transformation. Geometric invariant exploits coplanar five-point invariant and ration of area constructed from a sequence of consecutive landmarks. These invariants are preserved not only in affine map but weak perspective map as well. To reduce the sensitivity of the landmarks to noise, we use a B-Spline surface representation that smoothes out the curve prior to the computation of the landmarks. The matching is achieved by establishing correspondences between the landmarks after a conformal sorting based on derived absolute invariant and registering the contours. The experiments have shown that the purposed methods are robust and promising even in the presence of noise.