Multi-instance robust fitting for non-classical geometric models

2026-02-05

AI Summary

Existing robust fitting methods are largely confined to classical geometric models and struggle to reconstruct multi-instance non-classical geometric structures—such as helical curves, procedural characters, or free-form surfaces—in the presence of noise and outliers. This work formulates the problem as a global optimization task and introduces a model-to-data, non-differentiable error estimator that operates without requiring a pre-specified inlier threshold. Coupled with a metaheuristic optimization algorithm, the proposed approach enables robust fitting by jointly reconstructing multiple instances of non-classical geometric models. To the best of our knowledge, this is the first method capable of such joint reconstruction, achieving high accuracy and strong robustness across a variety of complex scenarios.

Technology Category

• Search and Optimization: Non-convex Optimization
• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

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.

Problem

• multi-instance
• robust fitting
• non-classical models
• geometric reconstruction
• outlier handling

Innovation

• multi-instance fitting
• non-classical geometric models
• robust estimation
• model-to-data error
• meta-heuristic optimization