Direct Fitting of Gaussian Mixture Models
This addresses a specific bottleneck in 3D geometry processing for computer vision and graphics applications, though it appears incremental as it modifies an existing approach rather than introducing a new paradigm.
The paper tackles the problem of fitting Gaussian Mixture Models to 3D geometry by proposing a formulation that fits directly to triangular meshes instead of point clouds, resulting in higher-quality models and improved 3D registration for meshes and RGB-D frames.
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.