Curvature Estimation on Point Cloud Using an Indicator Function

Curvature estimation is essential for many computational techniques on point cloud, which can be obtained, for example, by scanning real-world objects by a 3D scanner. We propose a novel technique to directly estimate mean curvature and Gaussian curvature on point cloud. We view the object surface as the indicator function of the scanned object and then smooth the function. Curvatures can be computed from the gradient and Hessian of the smoothed indicator function explicitly. We use an integral formula to approximate the gradient and Hessian on point cloud. The surface approximation and smoothing filter are implicit inside the integral formulas. And the experiments show our method is the fastest method that outputs mean curvature and Gaussian curvature with accuracy comparable to other established methods.