Electrical Engineering-Systems Dept.

*** SEMINAR ***

Or Litany

(M.Sc. student under the supervision of Dr. Alexander Bronstein)

On the subject:

Regularized multi-part shape matching

Multi-part shape matching is an important class of problems, arising in many fields such as computational archaeology, biology, geometry processing, computer graphics and vision, e.g. when one tries to put back together a fractured bone. The problem is especially hard when handling real parts as these contain various scanning artifacts. In this work, we address the problem of simultaneous matching and segmentation of multiple shapes. We assume to be given a reference (Model) shape and multiple parts partially matching the reference (Data). Each of these parts can have additional clutter, have overlap with other parts, or there might be missing parts. Extending the regularized partial shape matching method introduced by Bronstein et. al., we formulate the problem in hand as a union of such individual problems, linking them together through a segmentation constraint. This results in a non-convex problem, yet it can be viewed as iteratively reweighed ICP and is solved by means of alternating minimization. We show numerous algorithm outlines for a complete solution for both the segmentation variables and the rigid transformations to align the parts to the Model. The different algorithms differ mainly in the choice of constraint, be it the distance between the parts and the model, or the area of each part. The choice depends on the desired application and the a priori knowledge. We show an efficient discretization, and present experimental results of efficient and accurate assembly of fractured synthetic and real objects.