Betti Number for Point Sets

Topology is the foundation for many industrial applications ranging from CAD to simulation analysis. Computational topology mostly focuses on structured data such as mesh, however unstructured dataset such as point set remains a virgin land for topology scientists. The significance of point-based topology can never be overemphasized, especially in the area of reverse engineering, geometric modeling and algorithmic analysis. In this paper, we propose a novel approach to compute the Betti number for point set data and illustrate its usefulness in real world examples. To the best of our knowledge, our work is pioneering and first of its kind in the fields of computational topology.