# Multi-instance robust fitting for non-classical geometric models

arXiv: https://arxiv.org/abs/2602.05602 · HTML: https://mlsanity.com/paper/2602.05602/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 3 of 3)

- [ParSeNet: A Parametric Surface Fitting Network for 3D Point Clouds](https://mlsanity.com/paper/2003.12181/) (2020)
- [Latent Semantic Consensus For Deterministic Geometric Model Fitting](https://mlsanity.com/paper/2403.06444/) (2024)
- [Weakly and Self-Supervised Class-Agnostic Motion Prediction for Autonomous Driving](https://mlsanity.com/paper/2509.13116/) (2025)

## Abstract (arXiv)

Most existing robust fitting methods are designed for classical models, such as lines, circles, and planes. In contrast, fewer methods have been developed to robustly handle non-classical models, such as spiral curves, procedural character models, and free-form surfaces. Furthermore, existing methods primarily focus on reconstructing a single instance of a non-classical model. This paper aims to reconstruct multiple instances of non-classical models from noisy data. We formulate this multi-instance fitting task as an optimization problem, which comprises an estimator and an optimizer. Specifically, we propose a novel estimator based on the model-to-data error, capable of handling outliers without a predefined error threshold. Since the proposed estimator is non-differentiable with respect to the model parameters, we employ a meta-heuristic algorithm as the optimizer to seek the global optimum. The effectiveness of our method are demonstrated through experimental results on various non-classical models. The code is available at https://github.com/zhangzongliang/fitting.