  When fitting Gaussian Mixture Models to 3D geometry, the model is 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. This modification enables fitting higher-quality GMMs under a wider
range of initialization conditions. Additionally, models obtained from this
fitting method are shown to produce an improvement in 3D registration for both
meshes and RGB-D frames. This result is general and applicable to arbitrary
geometric objects, including representing uncertainty from sensor measurements.
