# Finding Geometric Models by Clustering in the Consensus Space

Source: [Finding Geometric Models by Clustering in the Consensus Space](<https://www.sota2.com/research/paper/68fa6f131e209131cea43b61>)

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

Data updated: 2026-01-04T05:05:25.363Z

Authors: Daniel Barath, Denys Rozumny, Ivan Eichhardt, Levente Hajder, Jiri Matas

Published: 2021-03-25T14:35:07.000Z

## Abstract

We propose a new algorithm for finding an unknown number of geometric models, e.g., homographies. The problem is formalized as finding dominant model instances progressively without forming crisp point-to-model assignments. Dominant instances are found via a RANSAC-like sampling and a consolidation process driven by a model quality function considering previously proposed instances. New ones are found by clustering in the consensus space. This new formulation leads to a simple iterative algorithm with state-of-the-art accuracy while running in real-time on a number of vision problems - at least two orders of magnitude faster than the competitors on two-view motion estimation. Also, we propose a deterministic sampler reflecting the fact that real-world data tend to form spatially coherent structures. The sampler returns connected components in a progressively densified neighborhood-graph. We present a number of applications where the use of multiple geometric models improves accuracy. These include pose estimation from multiple generalized homographies; trajectory estimation of fast-moving objects; and we also propose a way of using multiple homographies in global SfM algorithms. Source code: https://github.com/danini/clustering-in-consensus-space.

## 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.

- [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: 3.1.

- [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: 5.

- [Trajectory Estimation via Line Segment Detection on TbD Easy 30](<https://www.sota2.com/research/sota/trajectory-estimation-via-line-segment-detection-on-tbd-easy-30.md>): Trajectory Estimation via Line Segment Detection; TbD Easy 30; Average Error (px): 1.39.

- [Trajectory Estimation via Line Segment Detection on TbD-3D Challenging 50](<https://www.sota2.com/research/sota/trajectory-estimation-via-line-segment-detection-on-tbd-3d-challenging-50.md>): Trajectory Estimation via Line Segment Detection; TbD-3D Challenging 50; Avg Error (px): 2.84.

- [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): 0.04.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2103.13875>)

[PDF](<https://arxiv.org/pdf/2103.13875.pdf>)

[Implementation](<https://github.com/danini/clustering-in-consensus-space>)