# Finding Geometric Models by Clustering in the Consensus Space

arXiv: https://arxiv.org/abs/2103.13875 · HTML: https://mlsanity.com/paper/2103.13875/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 81 references that are in the map.
- First posted on arXiv 25 Mar 2021.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fine-tuning CNN Image Retrieval with No Human Annotation](https://mlsanity.com/paper/1711.02512/) (2017)
- [Large-Scale Image Retrieval with Attentive Deep Local Features](https://mlsanity.com/paper/1612.06321/) (2016)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [MAGSAC++, a fast, reliable and accurate robust estimator](https://mlsanity.com/paper/1912.05909/) (2019)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm](https://mlsanity.com/paper/1906.02290/) (2019)
- [CONSAC: Robust Multi-Model Fitting by Conditional Sample Consensus](https://mlsanity.com/paper/2001.02643/) (2020)
- [Multi-Class Model Fitting by Energy Minimization and Mode-Seeking](https://mlsanity.com/paper/1706.00827/) (2017)
- [Progressive NAPSAC: sampling from gradually growing neighborhoods](https://mlsanity.com/paper/1906.02295/) (2019)
- [DeFMO: Deblurring and Shape Recovery of Fast Moving Objects](https://mlsanity.com/paper/2012.00595/) (2020)
- [Efficient Initial Pose-graph Generation for Global SfM](https://mlsanity.com/paper/2011.11986/) (2020)
- [Calibrated and Partially Calibrated Semi-Generalized Homographies](https://mlsanity.com/paper/2103.06535/) (2021)
- [The World of Fast Moving Objects](https://mlsanity.com/paper/1611.07889/) (2016)
- [Intra-frame Object Tracking by Deblatting](https://mlsanity.com/paper/1905.03633/) (2019)
- [Sub-frame Appearance and 6D Pose Estimation of Fast Moving Objects](https://mlsanity.com/paper/1911.10927/) (2019)
- [Searching for Representative Modes on Hypergraphs for Robust Geometric Model Fitting](https://mlsanity.com/paper/1802.01129/) (2018)
- [FMODetect: Robust Detection of Fast Moving Objects](https://mlsanity.com/paper/2012.08216/) (2020)
- [Geometric Multi-Model Fitting with a Convex Relaxation Algorithm](https://mlsanity.com/paper/1706.01553/) (2017)
- [Non-Causal Tracking by Deblatting](https://mlsanity.com/paper/1909.06894/) (2019)
- [Mode-Seeking on Hypergraphs for Robust Geometric Model Fitting](https://mlsanity.com/paper/1603.07807/) (2016)

## Built on by (most cited first, 8 of 8)

- [SupeRANSAC: One RANSAC to Rule Them All](https://mlsanity.com/paper/2506.04803/) (2025)
- [PARSAC: Accelerating Robust Multi-Model Fitting with Parallel Sample Consensus](https://mlsanity.com/paper/2401.14919/) (2024)
- [Image Matching by Bare Homography](https://mlsanity.com/paper/2305.08946/) (2023)
- [Image Matching Filtering and Refinement by Planes and Beyond](https://mlsanity.com/paper/2411.09484/) (2024)
- [Robust Shape Fitting for 3D Scene Abstraction](https://mlsanity.com/paper/2403.10452/) (2024)
- [3D Focusing-and-Matching Network for Multi-Instance Point Cloud Registration](https://mlsanity.com/paper/2411.07740/) (2024)
- [Outlier-Robust Multi-Model Fitting on Quantum Annealers](https://mlsanity.com/paper/2504.13836/) (2025)
- [Robust Multi-Model Fitting through Learning Neighbor Regions](https://mlsanity.com/paper/2609.15348/) (2026)

## Abstract (arXiv)

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.