Generalized MPU implicits using belief propagation

In this paper, we present a new algorithm to reconstruct 3D surfaces from an unorganized point cloud based on generalizing the MPU implicit algorithm through introducing a powerful orientation inference scheme via Belief Propagation. Instead of using orientation information like surface normals, local data distribution analysis is performed to identify the local surface property so as to guide the selection of local fitting models. We formulate the determination of the globally consistent orientation as a graph optimization problem. Local belief networks are constructed by treating the local shape functions as their nodes. The consistency of adjacent nodes linked by an edge is checked by evaluating the functions and an energy is thus defined. By minimizing the total energy over the graph, we can obtain an optimal assignment of labels indicating the orientation of each local shape function. The local inference result is propagated over the model in a front-propagation fashion to obtain the global solution. We demonstrate the performance of the proposed algorithm by showing experimental results on some real-world 3D data sets.