Multi-Class Model Fitting by Energy Minimization and Mode-Seeking

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.