Invariant property of contour: VPIUD with arbitrary neighbourhood

A new invariant of contour VPIUD-virtual perimeter increment under dilation-has been proposed. Based on the contour propagation model, VPIUD is defined as the sum of secondary waves of a contour which represents the virtual perimeter under dilation minus the perimeter of the contour. It has been proved that VPIUD is invariant and binary for any component. In this paper, the invariant property of contour VPIUD has been discussed with arbitrary neighbourhood. We demonstrate that VPIUD has a clear physical meaning: a contour dilates around convex vertices and reduces around concave vertices. In 6 and 8-neighborhood, the contribution of contour pixels to VPIUD is directly linked with local curvature, therefore VPIUD is equivalent to total curvature, another invariant. VPIUD can be used to distinguish between hole and outer contours, without affecting images. The proposed algorithm has been implemented at ease and results of contour classification are presented