Affine Invariance Contour Descriptor Based on the Equal Area Normalization

In this study, we present a one dimensional descriptor for the two dimensional object silhouettes which in theory remains absolutely invariant under affine transforms. The proposed descriptor operates on the affine enclosed area. We design a normalizing contour method. After this normalization, the number of points on a contour between two appointed positions doesn’t change with affine transforms. We prove that for the filtered contour, the area of a triangle whose vertices are the centroid of the contour and a pair of successive points on the normalized contour is linear under affine transforms. Experimental results indicate that the proposed method is invariant to: boundary starting point variation, affine transforms even in the case of high deformations and noise on shapes in a given. We also propose a method to simulate the noise contaminating the test shapes and define the signal-to-noise ratio for a shape. In addition, the proposed normalization method can be associated to other algorithms for increasing their robustness to affine transforms and decreasing their complexity in similarity measurements.