Finding the largest volume parallelepipedon of arbitrary orientation in a solid

Abstract

3D Computer Vision algorithms are a subject of research and application for several industrial processes. The Volume of Interest (VOI) usually refer to sub-objects with basic shapes for computing these algorithms. However, in many cases the objects are available as irregular shapes with many vertices, and in order to apply algorithms effectively, it is essential to compute the largest volume parallelepipedon contained in 3D objects. There are no other approximation algorithms for nding the largest volume parallelepipedon of arbitrary orientation inscribed in a closed 3D contour with a computational cost better than the algorithm proposed in this paper, been O(n3).