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

## TL;DR

The paper introduces Multi-X, a novel multi-class model fitting method that uses energy minimization and mode-seeking, providing robust and automatic optimization for interpreting complex noisy data.

## Contribution

It extends alpha-expansion techniques with a mode-seeking move and introduces automatic parameter setting and outlier removal, advancing multi-class model fitting.

## Key findings

- Multi-X outperforms state-of-the-art methods on various datasets.
- The method effectively handles multiple classes and noisy data.
- Automatic parameter tuning enhances robustness and efficiency.

## Abstract

We propose a general formulation, called Multi-X, for multi-class multi-instance model fitting - the problem of interpreting the input data as a mixture of noisy observations originating from multiple instances of multiple classes. We extend the commonly used alpha-expansion-based technique with a new move in the label space. The move replaces a set of labels with the corresponding density mode in the model parameter domain, thus achieving fast and robust optimization. Key optimization parameters like the bandwidth of the mode seeking 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 publicly available datasets for diverse problems: multiple plane and rigid motion detection; motion segmentation; simultaneous plane and cylinder fitting; circle and line fitting.