Heat Kernel applied on a manifold encodes intrinsic information about the geometry and topology of the manifold in a multi-scale manner. We present algorithms for discovery of this encoded information and convert it to knowledge of the structure of the shape . Heat Mapping produces perceptually consistent mesh segmentation through automatically discovering the number of segments and applying a clustering algorithm on the points in embedded heat space to segment a 3d shape. Heat Walk, converts the implicit information in the heat kernel to explicit knowledge about the pathways for maximum heat flow capacity and uses this knowledge for 3d shape segmentation. Extensive experimental evidence shows these methods are robust to a variety of noise factors including topological short circuits, surface holes, pose variations, variations in tessellation, missing features, scaling, as well as normal and shot noise. The Temperature Distribution shape descriptor understands the shape by evaluating the surface temperature distribution evolution with time after applying unit heat at each vertex. Experimental results demonstrate the effectiveness of TD descriptor within applications of 3D shape matching and searching for the models at different poses and various noise levels.
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