Approximate shape matching and symmetry detection for 3D shapes with guaranteed error bounds

In this paper, we describe a system for approximate shape matching and symmetry (rotation and reflection) detection of geometric shapes represented as point clouds. Rather than using the least-squares distance as a measure of similarity between shapes, we use the Hausdorff distance between point sets as the underlying shape metric. This allows us to exploit methods from geometric pattern matching to return symmetries and rigid transformation matches with guaranteed error bounds on the quality of our solution. The approximation is determined by intuitive user-specified input precision and distance threshold parameters. Another important feature of our method is that it leverages FFT-based techniques for string matching to compute all approximate symmetries simultaneously. Our algorithm is simple to implement and is efficient; we present a detailed experimental study.