A combined distance measure for 2D shape matching

We present a method for 2D shape matching using a combination of distance functions and discrete curvature. The eccentricity transform computes the longest geodesic distance across the object. This transform is invariant to translation and rotation. The maximal eccentricity points yield diameters across the image. We compute the Euclidean distances from the boundary to the diameter to characterize the curvature of the shape. Our shape descriptor is comprised of the best matches retrieved from the normalized histogram of the eccentricities, the Hausdorff distance between the set of distances to the diameter and a measure of the number of points lying on either side of the diameter along with the peak values. We evaluate this descriptor on 2D image databases consisting of rigid and articulated shapes by ranking the number of matches. In almost all cases, the shapes are matched with at least one shape from the same class.