# Direct Fitting of Gaussian Mixture Models

arXiv: https://arxiv.org/abs/1904.05537 · HTML: https://mlsanity.com/paper/1904.05537/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2019.

## Built on by (most cited first, 3 of 3)

- [Approximate Differentiable Rendering with Algebraic Surfaces](https://mlsanity.com/paper/2207.10606/) (2022)
- [Online Learning of a Probabilistic and Adaptive Scene Representation](https://mlsanity.com/paper/2103.16832/) (2021)
- [A Geometric Gaussian Mixture Representation of Plane Curves](https://mlsanity.com/paper/2606.06505/) (2026)

## Abstract (arXiv)

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.