Reconstruction of Convex Polytope Compositions from 3D Point-clouds
This addresses a hard optimization problem for applications in reverse engineering and rigid body dynamics simulations, presenting an incremental approach.
The paper tackles the problem of reconstructing compositions of convex polytopes from 3D point-clouds, proposing a pipeline that uses plane extraction, convex clustering, and an evolutionary algorithm to achieve perfect fits, with evaluation on multiple datasets detailing method strengths and weaknesses.
Reconstructing a composition (union) of convex polytopes that perfectly fits the corresponding input point-cloud is a hard optimization problem with interesting applications in reverse engineering and rigid body dynamics simulations. We propose a pipeline that first extracts a set of planes, then partitions the input point-cloud into weakly convex clusters and finally generates a set of convex polytopes as the intersection of fitted planes for each partition. Finding the best-fitting convex polytopes is formulated as a combinatorial optimization problem over the set of fitted planes and is solved using an Evolutionary Algorithm. For convex clustering, we employ two different methods and detail their strengths and weaknesses in a thorough evaluation based on multiple input data-sets.