EB-RANSAC: Random Sample Consensus based on Energy-Based Model

Muneki Yasuda; Nao Watanabe; Kaiji Sekimoto

stat.MLMar 12, 2026

EB-RANSAC: Random Sample Consensus based on Energy-Based Model

Authors: Muneki Yasuda, Nao Watanabe, Kaiji Sekimoto

Organizations: Graduate School of Science and Engineering, Yamagata University · TSCSK Corporation

Abstract

Random sample consensus (RANSAC), which is based on a repetitive sampling from a given dataset, is one of the most popular robust estimation methods. In this study, an energy-based model (EBM) for robust estimation that has a similar scheme to RANSAC, energy-based RANSAC (EB-RANSAC), is proposed. EB-RANSAC is applicable to a wide range of estimation problems similar to RANSAC. However, unlike RANSAC, EB-RANSAC does not require a troublesome sampling procedure and has only one hyperparameter. The effectiveness of EB-RANSAC is numerically demonstrated in two applications: a linear regression and maximum likelihood estimation.

Figures & tables

Figure 1: Illustration of the EB-RANSAC estimator in equation ( 14 ). Top panel: the empirical distribution of $D$ that has outliers’ probability in its tail. Bottom panel: the EB-RANSAC estimator obtained by removing low probability region (lower than the cut-off threshold) from the empirical distribution.

Figure 2: (a) Estimators obtained from the EB-RANSAC with $\beta=5$ and standard LMS methods. (b) MSE plot for various $\beta$ s. The blue broken line represents the MSE of the LMS estimator.

Figure 3: (a) Gaussians obtained from the EB-RANSAC with $\beta=5$ and standard MLE methods. The bars represent the histogram of the dataset that is normalized such that the maximum value is equal to two for easier comparison with the Gaussians. (b) KLD between the EB-RANSAC estimator and the inlier Gaussian. The blue broken line represents the KLD of the ML estimator.

Figure 4: EB-RANSAC estimators for $\beta=-2,-1,0,1$ . The bars represent the data histogram that is the same as that shown in figure 3 (a).

Figure 5: (a) Normalized histogram of the dataset. (b) Estimators obtained from the EB-RANSAC (with $\beta=4$ ) and the standard MLE methods. The red broken line represents the inlier distribution $\mathcal{E}(x\mid 2)$ . (c) Values of $\lambda$ obtained from the EB-RANSAC method for $\beta\in[4,8]$ . For comparison, the value of $\lambda$ obtained from the standard MLE method ( $\lambda\approx 0.653$ ) also plotted (the blue broken line). A jump of $\lambda$ is observed at $\beta_{c}\approx 6.65$ .

Figure 6: (a) Landscapes of the modified EB-RANSAC loss in equation ( 16 ) for various values of $\beta$ . (b) Schematic of the jump behavior. At $\beta=\beta_{c}$ , the minimum point is switched, which causes the jump transition.

Robust Estimation

Robust estimation infers reliable parameters and states despite outliers, heavy-tailed noise, data contamination, or model uncertainty.

See all 83 papers

DS-SAC: Density Search for Sample Consensus
Jul 4, 2026Suraj Thapa, Muhammad Aminul IslamMulti-View Geometry Robust Estimation
Tagliatela College of Engineering, University of New Haven, 300 Boston Post Rd, West Haven, 06516, CT, USA.
Non-Minimal Sampling and Consensus for Prohibitively Large Datasets
Apr 24, 2026Seong Hun Lee, Patrick Vandewalle, Javier CiveraCamera Pose Estimation Point Cloud Registration
I3A, University of Zaragoza, 50018 Zaragoza, Spain · EAVISE, KU Leuven, 2860 Sint-Katelijne-Waver, Belgium
RANSAC Scoring Done Right
Jun 12, 2026James Pritts, Felix Seegräber, Kevin KöserMulti-View Geometry Robust Estimation
Marine Data Science, Institut für Informatik Kiel University, Germany

Jul 4, 2026J/K move · Enter open · S save

DS-SAC: Density Search for Sample Consensus

Suraj Thapa, Muhammad Aminul Islam

Tagliatela College of Engineering, University of New Haven, 300 Boston Post Rd, West Haven, 06516, CT, USA.

Multi-View Geometry Robust Estimation

Open paper AskPDF arXiv

Robust geometric model estimation is a fundamental problem in computer vision. RANSAC and its variants remain widely used for this task; however, they rely on stochastic minimal sampling. In this article, we propose Density Search Sample Consensus (DS-SAC), a deterministic robust estimation framework, that avoids repeated random sampling by searching dense regions. Starting from an initial model estimated from the available points, the method performs local exploration via forward and backward search. To facilitate global exploration, DS-SAC recursively partitions the point set using signed residuals and searches each valid partition for high-consensus models. We show that DS-SAC has polynomial complexity with respect to the number of points, making it an efficient alternative to stochastic consensus-based methods. Experiments on large-scale real-world datasets for homography, fundamental matrix, and essential matrix estimation show that DS-SAC achieves higher AUC scores, competitive or lower median pose errors, and faster runtime compared with widely used robust estimators, including RANSAC, MAGSAC, LO-RANSAC, and GC-RANSAC.

Abstract

Robust Estimation

Explore similar work

DS-SAC: Density Search for Sample Consensus

Non-Minimal Sampling and Consensus for Prohibitively Large Datasets

RANSAC Scoring Done Right