A Similarity Retrieval Method for Three-Dimensional Shapes by Using Mathematical Morphology

Abstract

Similarity retrieval for three-dimensional models has been in the spotlight because of the increase in digital archives. We propose a similarity estimation method that uses mathematical morphology. It consists of a feature extraction and a similarity estimation process. First, position of a shape is determined by eigenvectors of the covariance matrix, and an amount of feature corresponding to the projections and hollows of the shape is extracted by repeating mathematical morphology. As the direction of the shape is occasionally reversed in the case that the eigenvectors of the covariance matrix are used, we apply the standard deviation to an amount of feature. Second, the degree of similarity between the amount of feature and those which are preserved in advance is calculated. Experimental results showed that our method is more effective than conventional ones.