Directed mean Hausdorff distance of parameterized freeform shapes in 3D: a case study

Abstract

Shape matching in 3D is a process underlying several applications, including engineering, medicine, and animation. Searching, recognition, and matching of shape patterns directly in 3D model-space is far from a mature technique. In this paper we report an investigation of the computation of shape similarity based on Hausdorff-like measures. We have assessed a number of properties of the directed Hausdorff distance between 3D shapes, namely accuracy, robustness, and computational complexity of the algorithms. The driving application here was the reuse of digitized shapes in geometric modeling. The shapes involved in the analysis were from sampled physical object surfaces, or they were synthetic shapes. To support the application it was necessary to extend the search space beyond rigid and affine transformation spaces; a number of deformation parameters (intrinsic shape parameters) needed to be introduced. The sensitivity of the Hausdorff distance to pose parameters and to intrinsic shape parameters was investigated. Shape parameter estimation turned out to be feasible when an appropriate fitting strategy was selected. Besides a short straight ridge, ridges developing along a 3D spine can also be successfully registered. Finally, it is demonstrated how the performance of the algorithms is improved by a 3D binning technique.