We propose a combinatorial solution for the problem of non-rigidly matching a3D shape to 3D image data. To this end, we model the shape as a triangular meshand allow each triangle of this mesh to be rigidly transformed to achieve asuitable matching to the image. By penalising the distance and the relativerotation between neighbouring triangles our matching compromises between imageand shape information. In this paper, we resolve two major challenges: Firstly,we address the resulting large and NP-hard combinatorial problem with asuitable graph-theoretic approach. Secondly, we propose an efficientdiscretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledgethis is the first combinatorial formulation for non-rigid 3D shape-to-imagematching. In contrast to existing local (gradient descent) optimisationmethods, we obtain solutions that do not require a good initialisation and thatare within a bound of the optimal solution. We evaluate the proposed method onthe two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-imageregistration and demonstrate that it provides promising results.
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