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

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.

We introduce NONSAC (Non-Minimal Sampling and Consensus), a general framework for robust and scalable model estimation from arbitrarily large datasets contaminated with noise and outliers. NONSAC repeatedly samples non-minimal subsets of data and generates model hypotheses using a robust estimator, producing multiple candidate models. The final model is selected based on a predefined scoring rule that evaluates hypothesis quality. Our framework is estimator-agnostic and can be integrated with existing geometric fitting algorithms such as RANSAC to improve both scalability and robustness to outliers. We propose and evaluate various scoring rules for NONSAC on relative camera pose estimation, Perspective-n-Point, and point cloud registration. Furthermore, we showcase the applicability of NONSAC to correspondence-free point cloud registration by hypothesizing all-to-all correspondences.

The most widely used RANSAC variants score candidate models by counting inliers or summing per-point scores that saturate beyond a residual threshold. Every such score requires a user-supplied parameter that is a function of the inlier scale, which must itself be estimated from contaminated data. We remove this dependence by reversing the usual order of inference: rather than estimating the scale and then scoring against it, we marginalize the inlier scale analytically in closed form under a conjugate Inverse-Gamma prior for a fixed inlier partition, then optimize over partitions. A single closed-form expression spans the non-informative Jeffreys limit and informative empirical-Bayes priors, so the same score adapts across data-rich and data-scarce regimes without any change to the algorithm. The proposed RANSAC score is the first in which the inlier scale is genuinely absent from the formula. The score admits O(N log N ) computation via sort-and-sweep. On a benchmark of nearly 70 000 image pairs spanning different two-view estimation problems and both engineered and learned feature pipelines, the proposed score exceeds the state of the art (RANSAC, MSAC, GaU, MAGSAC): it stays nearly flat under threshold miscalibration where baselines degrade, reaches near-optimal accuracy from as few as two validation pairs where baselines need ont he order of 100 times more,. and tightens its prior regularization as validation data grows scarce.