# CONSAC: Robust Multi-Model Fitting by Conditional Sample Consensus

arXiv: https://arxiv.org/abs/2001.02643 · HTML: https://mlsanity.com/paper/2001.02643/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2020.

## Built on by (most cited first, 30 of 30)

- [Pow3R: Empowering Unconstrained 3D Reconstruction with Camera and Scene Priors](https://mlsanity.com/paper/2503.17316/) (2025)
- [DeepLSD: Line Segment Detection and Refinement with Deep Image Gradients](https://mlsanity.com/paper/2212.07766/) (2022)
- [GeoCalib: Learning Single-image Calibration with Geometric Optimization](https://mlsanity.com/paper/2409.06704/) (2024)
- [MultiBodySync: Multi-Body Segmentation and Motion Estimation via 3D Scan Synchronization](https://mlsanity.com/paper/2101.06605/) (2021)
- [Deep vanishing point detection: Geometric priors make dataset variations vanish](https://mlsanity.com/paper/2203.08586/) (2022)
- [AnyCalib: On-Manifold Learning for Model-Agnostic Single-View Camera Calibration](https://mlsanity.com/paper/2503.12701/) (2025)
- [Cuboids Revisited: Learning Robust 3D Shape Fitting to Single RGB Images](https://mlsanity.com/paper/2105.02047/) (2021)
- [Convex Relaxation for Robust Vanishing Point Estimation in Manhattan World](https://mlsanity.com/paper/2505.04788/) (2025)
- [Vanishing Point Estimation in Uncalibrated Images with Prior Gravity Direction](https://mlsanity.com/paper/2308.10694/) (2023)
- [Finding Geometric Models by Clustering in the Consensus Space](https://mlsanity.com/paper/2103.13875/) (2021)
- [Multi-instance Point Cloud Registration by Efficient Correspondence Clustering](https://mlsanity.com/paper/2111.14582/) (2021)
- [Multi-body SE(3) Equivariance for Unsupervised Rigid Segmentation and Motion Estimation](https://mlsanity.com/paper/2306.05584/) (2023)
- [Learning Instance-Aware Correspondences for Robust Multi-Instance Point Cloud Registration in Cluttered Scenes](https://mlsanity.com/paper/2404.04557/) (2024)
- [PointCLM: A Contrastive Learning-based Framework for Multi-instance Point Cloud Registration](https://mlsanity.com/paper/2209.00219/) (2022)
- [Revisiting Sampson Approximations for Geometric Estimation Problems](https://mlsanity.com/paper/2401.07114/) (2024)
- [PARSAC: Accelerating Robust Multi-Model Fitting with Parallel Sample Consensus](https://mlsanity.com/paper/2401.14919/) (2024)
- [ScaleLSD: Scalable Deep Line Segment Detection Streamlined](https://mlsanity.com/paper/2506.09369/) (2025)
- [Deep Single Image Camera Calibration by Heatmap Regression to Recover Fisheye Images Under Manhattan World Assumption](https://mlsanity.com/paper/2303.17166/) (2023)
- [Robust Shape Fitting for 3D Scene Abstraction](https://mlsanity.com/paper/2403.10452/) (2024)
- [SIDAR: Synthetic Image Dataset for Alignment & Restoration](https://mlsanity.com/paper/2305.12036/) (2023)
- [Instance by Instance: An Iterative Framework for Multi-instance 3D Registration](https://mlsanity.com/paper/2402.04195/) (2024)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [CalibAnyView: Beyond Single-View Camera Calibration in the Wild](https://mlsanity.com/paper/2605.14615/) (2026)
- [Improved Convex Decomposition with Ensembling and Negative Primitives](https://mlsanity.com/paper/2405.19569/) (2024)
- [MRG: A Multi-Robot Manufacturing Digital Scene Generation Method Using Multi-Instance Point Cloud Registration](https://mlsanity.com/paper/2501.02041/) (2025)
- [Accelerating Outlier-robust Rotation Estimation by Stereographic Projection](https://mlsanity.com/paper/2502.06337/) (2025)
- [Neural Guided Sampling for Quantum Circuit Optimization](https://mlsanity.com/paper/2510.12430/) (2025)
- [MID: A Self-supervised Multimodal Iterative Denoising Framework](https://mlsanity.com/paper/2511.00997/) (2025)
- [SweepLSD: A One-Pass, O(width)-Memory Line Segment Detector with an Integer-Only Streaming Core and a Real-Time FPGA Realization](https://mlsanity.com/paper/2608.22086/) (2026)
- [Robust Multi-Model Fitting through Learning Neighbor Regions](https://mlsanity.com/paper/2609.15348/) (2026)

## Abstract (arXiv)

We present a robust estimator for fitting multiple parametric models of the same form to noisy measurements. Applications include finding multiple vanishing points in man-made scenes, fitting planes to architectural imagery, or estimating multiple rigid motions within the same sequence. In contrast to previous works, which resorted to hand-crafted search strategies for multiple model detection, we learn the search strategy from data. A neural network conditioned on previously detected models guides a RANSAC estimator to different subsets of all measurements, thereby finding model instances one after another. We train our method supervised as well as self-supervised. For supervised training of the search strategy, we contribute a new dataset for vanishing point estimation. Leveraging this dataset, the proposed algorithm is superior with respect to other robust estimators as well as to designated vanishing point estimation algorithms. For self-supervised learning of the search, we evaluate the proposed algorithm on multi-homography estimation and demonstrate an accuracy that is superior to state-of-the-art methods.