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.

翻译：现有的大多数鲁棒拟合方法主要针对经典模型（如直线、圆、平面）设计。相比之下，能够鲁棒处理非经典模型（如螺旋曲线、程序化角色模型、自由曲面）的方法则相对较少。此外，现有方法主要侧重于重建非经典模型的单个实例。本文旨在从含噪声数据中重建非经典模型的多个实例。我们将这一多实例拟合任务构建为一个优化问题，该问题包含一个估计器和一个优化器。具体而言，我们提出了一种基于模型到数据误差的新型估计器，它能够在无需预定义误差阈值的情况下处理异常值。由于所提出的估计器关于模型参数不可微，我们采用一种元启发式算法作为优化器来寻求全局最优解。通过在多种非经典模型上的实验结果验证了我们方法的有效性。代码可在 https://github.com/zhangzongliang/fitting 获取。