Method for Detecting Position and Orientation of Convex Objects in 3D Scans

We have developed an algorithm for detecting the center positions and orientations of mono-disperse objects which pack a container from the data collected in a 3 dimensional scan such as obtained by MRI. The algorithm is applied to a variety of geometrical convex shapes including, ellipsoids, cubes and tetrahedrons. From the positions and orientations we are able to reconstruct the number and type of interparticle contacts and constraints and thus to test Maxwell's Isostatic conjecture in the case of ``random close packing.'' We also obtain translational and orientational correlation functions.