Three bivariate shape distributions

Recently, motivated by the seemingly accelerating number of 3D models available on the Web, a search engine for 3D models was developed. To query the search engine, a user can specify an example 3D model; the search engine then returns models with similar shapes. To facilitate these searches, 3D models are represented as shape descriptors that can be compared to measure the dissimilarity between shapes. A challenging problem is finding a shape descriptor that can discriminate between many classes of shape. For example, a comparison of the descriptors for a horse and cow should yield a lower dissimilarity than a comparison of the descriptors for the horse and a mug. One approach to this problem is to represent a 3D model's shape as a probability distribution, called a shape distribution, and treat the distance between two 3D models ' pdfs as the dissimilarity between the models ' shapes, for some chosen pdf distance function. For example, a 3D model's D2 shape distribution models the Euclidean distance between two area-weighted random points from the 3D model's surface, and the pdf distance function chosen could, for example, measure the area between two given pdfs. In the initial experiments involving shape distribution based descriptors, the D2-based descriptor was the most discriminating shape distribution based descriptor, however , in recent experiments comparing many different types of descriptor, the D2-based descriptor was outperformed by several other descriptors. To investigate whether the discriminating power of shape distribution based descriptors can be improved , we experimented with descriptors based on three bivariate shape distributions we call DNl, DN2, and DA3. In a precision-recall experiment involving a database of 150 3D models, the {DNl, DN2, DA3}-based descriptor had, on average, {9%, 38%, 14%} greater discriminating power than the D2-based descriptor.