Local structure recognition of point cloud using sparse representation

The local structure of point cloud is a key problem in point based geometry processing. In this paper, we propose a dictionary learning based method to extract the local structure. The core idea is: As point cloud can be seen as a linear model in local view, we use the union of multi-subspace to approximate it. An overcomplete dictionary D is used to represent the bases of these subspaces. First, we calculate the neighborhood N of each point by k-NN and build EMST on it, marked as T. Then, each edge in T is used to construct a training set. Most of the samples in training set indicate the trend of the point set. At last, we solve the sparse matrix factorization problem recursively to update D until D stops changing. We present 2D/3D experimental results to show that this method can handle manifold/non-manifold structures.