Edge-crease detection and surface reconstruction from point clouds using a second-order variational model

The automatic detection of geometric features, such as edges and creases, from objects represented by 3D point clouds (e.g., LiDAR measurements, Tomographic SAR) is a very important issue in different application domains including urban monitoring and building reconstruction. A limitation of many methods in the literature is that they rely on rasterization or interpolation of the original grid, with consequent potential loss of detail. Recently, a second-order variational model for edge and crease detection and surface regularization has been presented in literature and succesfully applied to DSMs. In this paper we address the generalization of this model to unstructured grids. The model is based on the Blake-Zisserman energy and allows to obtain a regularization of the original data (noise reduction) which does not affect crucial regions containing jumps and creases. Specifically, we focus on the detection of these features by means of two auxiliary functions that are computable by solving specific differential equations. Results obtained on LiDAR data by solving the equations via Finite Element Method are presented.