Oriented Bounding Box Computation Using Particle Swarm Optimization

The problem of finding the optimal oriented bounding box (OBB) for a given set of points in R 3 , yet simple to state, is computa-tionally challenging. Existing state-of-the-art methods dealing with this problem are either exact but slow, or fast but very approximative and unreliable. We propose a method based on Particle Swarm Optimization (PSO) to approximate solutions both effectively and accurately. The original PSO algorithm is modified so as to search for optimal solutions over the rotation group SO(3). Particles are defined as 3D rotation matrices and operations are expressed over SO(3) using matrix products, exponentials and logarithms. The symmetry of the problem is also exploited. Numerical experiments show that the proposed algorithm outperforms existing methods, often by far.