Shape Recognition using the Least Squares Approximation

This paper represents a novel algorithm to represent and recognize two dimensional curve based on its convex hull and the Least-Squared modeling. It combines the advantages of the property of the convex hulls that are particularly suitable for affine matching as they are affine invariant and the geometric properties of a contour that make it more or less identifiable. The description scheme and the similarity measure developed take into consideration technique for shape similarity. According to this method, the contours are extracted and decomposed into portions of curves. Each portion curve is approximated by some explicit curve using the Least Squares approximation. The obtained cubic curves are normalized in order to make the method invariant to scale change. Finally the resulting curves are used to compare and to compute similarity between shapes in images database using the Hausdorff distance. The proposed algorithm has been tested and its performance is found favourable as compared to other matching techniques.