PIECEWISE-PLANAR APPROXIMATION OF LARGE 3D DATA AS GRAPH-STRUCTURED OPTIMIZATION

We introduce a new method for the piecewise-planar approximation of 3D data, including point clouds and meshes. Our method is designed to operate on large datasets (e.g. millions of vertices) containing planar structures, which are very frequent in anthropic scenes. Our approach is also adaptive to the local geometric complexity of the input data. Our main contribution is the formulation of the piecewise-planar approximation problem as a non-convex optimization problem. In turn, this problem can be efficiently solved with a graph-structured working set approach. We compare our results with a state-of-the-art region-growing-based segmentation method and show a significant improvement both in terms of approximation error and computation efficiency.