Morphological residue approach to shape representation

A novel method for shape representation based on the multiresolution representation and morphological residues of the binary image is presented in this paper. A shape description method must have three properties: translation, rotation, and size invariance. The binary image which contains the object to be described is represented by multiresolution pyramid. A set of structuring elements is selected and used to compute morphological residues. The structuring elements are rotated versions of the one initial structuring element. This enables us to achieve rotational invariance of the shape description method. The morphological residue is the difference between the original image area and the eroded image area. It is a basic descriptor used in this method. The morphological residues for each of the structuring elements and each of the multiresolution pyramid levels are computed. The obtained set of morphological residues (numbers) is then sorted by order. The sort will enable comparison of rotated versions of objects. The residues for each pyramid level are normalized to enable more accurate comparison (distance measure) between object descriptors. Real vectors obtained in such a way are used as the shape descriptors. Experiments have been performed to investigate noise robustness of the proposed method, and have shown that method is not sensitive to noise. A set of twenty test images has been created and corrupted by noise. The Euclidean distance between the original and the corrupted images has been computed, and has shown that the proposed method has good shape matching properties.