提出新方法，从噪声数据中精准拟合多个非经典几何模型。
Multi-instance robust fitting for non-classical geometric models
- 基于模型到数据误差设计新估计算法，无需预设误差阈值。
- 在多种非经典模型上实现多实例拟合，抗噪性能强。
- 适合处理螺旋曲线等复杂形状的重建任务。
现有鲁棒拟合方法主要针对直线、圆、平面等经典模型，而对螺旋曲线、程序化字符模型和自由曲面等非经典模型的研究较少，且多数方法仅能重建单个实例。本文旨在从噪声数据中重建多个非经典模型实例，将多实例拟合问题建模为包含估计算法与优化器的联合优化问题。提出一种基于模型到数据误差的新估计算法，可在无预设误差阈值条件下有效处理异常值。由于该估计算法对模型参数不可微，采用元启发式算法作为优化器以搜索全局最优解。实验在多种非经典模型上验证了方法的有效性，代码已开源。
原文摘要 · Abstract (English)
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.
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