We propose a novel method, called Multi-X, for general multi-class multi-instance model fitting - the problem of interpreting input data as a mixture of noisy observations originating from multiple instances of multiple types. The proposed approach combines global energy optimization and mode-seeking in the parameter domain. Robustness is achieved by using an outlier class. Key optimization parameters like the outlier threshold are set automatically within the algorithm. Considering that a group of outliers may form spatially coherent structures in the data, we propose a cross-validation-based technique removing statistically insignificant instances. Multi-X outperforms significantly the state-of-the-art on the standard AdelaideRMF (multiple plane segmentation, multiple rigid motion detection) and Hopkins datasets (motion segmentation) and in experiments on 3D LIDAR data (simultaneous plane and cylinder fitting) and on 2D edge interpretation (circle and line fitting). Multi-X runs in time approximately linear in the number of data points at around 0.1 second per 100 points, an order of magnitude faster than available implementations of commonly used methods.

本文提出一种名为Multi-X的多分类多实例模型拟合通用公式，通过一种新的标签空间移动技术，在模型参数的密度分布区域内自动设定关键的优化参数以实现快速且鲁棒的优化。并且结合基于交叉验证的技术去除数据中的离群点。该公式在公开数据集中的多种问题的表现均优于现有技术。

通过能量最小化和模式寻求进行多类模型拟合