Reconstruction of Convex Polytope Compositions from 3D Point-clouds

TL;DR

This paper presents a novel pipeline for reconstructing convex polytope compositions from 3D point-clouds, utilizing plane extraction, clustering, and evolutionary optimization to improve reverse engineering and simulation tasks.

Contribution

It introduces a new method combining plane extraction, clustering, and evolutionary algorithms for accurate convex polytope reconstruction from point-cloud data.

Findings

Effective plane extraction and clustering improve reconstruction accuracy

Evolutionary Algorithm efficiently optimizes polytope fitting

Thorough evaluation demonstrates method's robustness across datasets

Abstract

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.