Computing Covering Polyhedra of Non-Convex Objects

We present an algorithm to build covering polyhedra for digital 3D objects, by iteratively filling local concavities. The resulting covering polyhedron is convex and is a good approximation of the convex hull of the object. The algorithm uses 3x3x3 operators and requires a few minutes for a 128 x 128 x 128 image, when implemented on a sequential computer. Once the covering polyhedron has been obtained, the object concavities can be identified by subtracting the object from the polyhedron and suitably post-processing the set difference. Features characterising the concavities can then be extracted and used as a tool for quantitative shape analysis.