There exist many choices of 3D shape representation. Some recent work has advocated for the use of Gaussian Mixture Models as a compact representation for 3D shapes and scenes. These models are typically fit to point clouds, even when the shapes were obtained as 3D meshes. Here we present a formulation for fitting Gaussian Mixture Models (GMMs) directly to a triangular mesh instead of using points sampled from its surface. Part of this work analyzes a general formulation for evaluating likelihood of geometric objects in the limit of sampled points. These modifications enable fitting higher-quality GMMs under a wider range of initialization conditions. The resulting GMMs are shown to produce an improvement in 3D registration for both meshes and RGB-D frames.
Martial Hebert (Advisor)
Christopher G. Atkeson
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