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

Source: [Multi-Class Model Fitting by Energy Minimization and Mode-Seeking](<https://www.sota2.com/research/paper/68fa63d41e209131cea010d1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T20:50:10.530Z

Authors: Daniel Barath, Jiri Matas

Published: 2017-06-02T19:32:07.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Object Motion Segmentation on Hopkins Traffic2 45](<https://www.sota2.com/research/sota/object-motion-segmentation-on-hopkins-traffic2-45.md>): Object motion segmentation; Hopkins Traffic2 45; Mean Misclassification Error: 9.

- [Object Motion Segmentation on Hopkins Traffic3 45](<https://www.sota2.com/research/sota/object-motion-segmentation-on-hopkins-traffic3-45.md>): Object motion segmentation; Hopkins Traffic3 45; Mean Misclassification Error: 32.

- [Motion Segmentation on Hopkins Motions 155 scenes](<https://www.sota2.com/research/sota/motion-segmentation-on-hopkins-motions-155-scenes.md>): Motion Segmentation; Hopkins Motions 155 scenes; Runtime (s): 0.95.

- [Two-view motion fitting on AdelaideRMF Two-view motions 19 scenes](<https://www.sota2.com/research/sota/two-view-motion-fitting-on-adelaidermf-two-view-motions-19-scenes.md>): Two-view motion fitting; AdelaideRMF Two-view motions 19 scenes; Avg. Misclassification Error: 17.1.

- [Homography fitting on AdelaideRMF Homographies 19 scenes](<https://www.sota2.com/research/sota/homography-fitting-on-adelaidermf-homographies-19-scenes.md>): Homography fitting; AdelaideRMF Homographies 19 scenes; Avg Misclassification Error: 8.7.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1706.00827>)

[PDF](<https://arxiv.org/pdf/1706.00827.pdf>)