Partial similarity of shapes using a statistical significance measure

Partial matching of geometric structures is important in computer vision, pattern recognition and shape analysis applications. The problem consists of matching similar parts of shapes that may be dissimilar as a whole. Recently, it was proposed to consider partial similarity as a multi-criterion optimization problem trying to simultaneously maximize the similarity and the significance of the matching parts. A major challenge in that framework is providing a quantitative measure of the significance of a part of an object. Here, we define the significance of a part of a shape by its discriminative power with respect do a given shape database - that is, the uniqueness of the part. We define a point-wise significance density using a statistical weighting approach similar to the term frequency-inverse document frequency (tf-idf) weighting employed in search engines. The significance measure of a given part is obtained by integrating over this density. Numerical experiments show that the proposed approach produces intuitive significant parts, and demonstrate an improvement in the performance of partial matching between shapes.