Adaptive Trees and Pose Identification from External Contours of Polyhedra

We first describe two stochastic algorithms which build trees in high dimensional Euclidean spaces with some adaptation to the geometry of a chosen target subset. The second one produces search trees and is used to approximately identify in real time the pose of a polyhedron from its external contour. A search tree is first grown in a space of shapes of plane curves which are a set of precomputed polygonal outlines of the polyhedron. The tree is then used to find in real time a best match to the outline of the polyhedron in the current pose. Analyzing the deformation of the curves along the tree thus built, shows progressive differentiation from a simple convex root shape to the various possible external contours, and the tree organizes the complex set of shapes into a more comprehensible object.