Conformal Alpha Shape-based Multi-scale Curvature Estimation from Point Clouds

Multi-scale geometrical and topological analyses of point clouds can reveal their rich structures. Because conformal alpha shapes of point clouds are hierarchical shapes under different mesh resolution or internal alpha values, their surface curvature estimations are one of the multi-scale geometrical analyses. We present a robust method for computing surface curvature of conformal alpha shapes on point cloud data, and provide theoretical guarantees on the robustness of our method. An approach is proposed to estimate the internal alpha scale parameters. The methods can be used to extract local curvatures of hierarchical shapes and as a multi-scale geometrical analysis method of point clouds. It is useful in many applications ranging from bio-geometric modeling to surface reconstruction. We describe an implementation of the algorithm and show example outputs.