# Geometric Multi-Model Fitting with a Convex Relaxation Algorithm

arXiv: https://arxiv.org/abs/1706.01553 · HTML: https://mlsanity.com/paper/1706.01553/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2017.

## Built on by (most cited first, 6 of 6)

- [Cuboids Revisited: Learning Robust 3D Shape Fitting to Single RGB Images](https://mlsanity.com/paper/2105.02047/) (2021)
- [Finding Geometric Models by Clustering in the Consensus Space](https://mlsanity.com/paper/2103.13875/) (2021)
- [Robust Shape Fitting for 3D Scene Abstraction](https://mlsanity.com/paper/2403.10452/) (2024)
- [MultiLink: Multi-class Structure Recovery via Agglomerative Clustering and Model Selection](https://mlsanity.com/paper/2505.10874/) (2025)
- [Graph-theoretical approach to robust 3D normal extraction of LiDAR data](https://mlsanity.com/paper/2205.11460/) (2022)
- [Robust Multi-Model Fitting through Learning Neighbor Regions](https://mlsanity.com/paper/2609.15348/) (2026)

## Abstract (arXiv)

We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by minimising the energy of the overall classification. Our approach is similar to state-of-the-art energy minimisation techniques which use a global energy. However, we deal with the scaling factor (as the number of models increases) of the original combinatorial problem by relaxing the solution. This relaxation brings two advantages: first, by operating in the continuous domain we can parallelize the calculations. Second, it allows for the use of different metrics which results in a more general formulation. We demonstrate the versatility of our technique on two different problems of estimating structure from images: plane extraction from RGB-D data and homography estimation from pairs of images. In both cases, we report accurate results on publicly available datasets, in most of the cases outperforming the state-of-the-art.