Learning in graphical models
Shape matching using edit-distance: an implementation
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Squigraphs for fine and compact modeling of 3-D shapes
IEEE Transactions on Image Processing
Fast approximate convex decomposition using relative concavity
Computer-Aided Design
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To simplify the matching and recognition of 3D objects, we propose to decompose a complex 3D shape into simpler primitive parts. Our partitioning of objects relies on their topological Reeb graphs. Taking advantage of the properties of Morse theory, we detect the critical points of the global geodesic function. These points define the levels at which the segmentation happens. To preserve the geometry of objects, we choose to use level curves instead of intervals. To proceed with object matching, we propose a kernel-based technique to register Reeb graphs. This optimal positioning of two Reeb graphs prepares for a pairwise comparison of the geometry of their primitives.