# A Real-Time Multi-Model Parametric Representation of Point Clouds

arXiv: https://arxiv.org/abs/2509.14773 · HTML: https://mlsanity.com/paper/2509.14773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 10 of 10)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Gaussian-LIC: Real-Time Photo-Realistic SLAM with Gaussian Splatting and LiDAR-Inertial-Camera Fusion](https://mlsanity.com/paper/2404.06926/) (2024)
- [Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric Fits](https://mlsanity.com/paper/1901.01255/) (2019)
- [Quadric Representations for LiDAR Odometry, Mapping and Localization](https://mlsanity.com/paper/2304.14190/) (2023)
- [GMMap: Memory-Efficient Continuous Occupancy Map Using Gaussian Mixture Model](https://mlsanity.com/paper/2306.03740/) (2023)
- [A Minimalist Approach to Type-Agnostic Detection of Quadrics in Point Clouds](https://mlsanity.com/paper/1803.07191/) (2018)
- [GEVO: Memory-Efficient Monocular Visual Odometry Using Gaussians](https://mlsanity.com/paper/2409.09295/) (2024)
- [SLIM: Scalable and Lightweight LiDAR Mapping in Urban Environments](https://mlsanity.com/paper/2409.08681/) (2024)
- [Obstacle Avoidance of Resilient UAV Swarm Formation with Active Sensing System in the Dense Environment](https://mlsanity.com/paper/2202.13381/) (2022)
- [CURL-SLAM: Continuous and Compact LiDAR Mapping](https://mlsanity.com/paper/2506.21077/) (2025)

## Abstract (arXiv)

In recent years, parametric representations of point clouds have been widely applied in tasks such as memory-efficient mapping and multi-robot collaboration. Highly adaptive models, like spline surfaces or quadrics, are computationally expensive in detection or fitting. In contrast, real-time methods, such as Gaussian mixture models or planes, have low degrees of freedom, making high accuracy with few primitives difficult. To tackle this problem, a multi-model parametric representation with real-time surface detection and fitting is proposed. Specifically, the Gaussian mixture model is first employed to segment the point cloud into multiple clusters. Then, flat clusters are selected and merged into planes or curved surfaces. Planes can be easily fitted and delimited by a 2D voxel-based boundary description method. Surfaces with curvature are fitted by B-spline surfaces and the same boundary description method is employed. Through evaluations on multiple public datasets, the proposed surface detection exhibits greater robustness than the state-of-the-art approach, with 3.78 times improvement in efficiency. Meanwhile, this representation achieves a 2-fold gain in accuracy over Gaussian mixture models, operating at 36.4 fps on a low-power onboard computer.