Fixing the RANSAC Stopping Criterion

2025-03-10

AI Summary

The classical RANSAC stopping criterion—used for over four decades—exhibits systematic theoretical bias, leading to severe undersampling and model recall failure in low-inlier-ratio or high-model-complexity scenarios. Method: We rigorously derive and empirically validate the source of error in the original stopping probability formula, and propose a concise, exact, analytically tractable closed-form stopping criterion that requires no approximation and is compatible with all RANSAC variants. Contribution/Results: Our criterion fundamentally enhances the reliability and stability of robust estimation while preserving the original algorithmic framework—enabling plug-and-play integration. Experiments demonstrate significant improvements in model recall rate and convergence consistency under challenging conditions, providing a more rigorous theoretical foundation and practical guarantee for geometric vision estimation.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Other Foundations of Computer Vision
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

For several decades, RANSAC has been one of the most commonly used robust estimation algorithms for many problems in computer vision and related fields. The main contribution of this paper lies in addressing a long-standing error baked into virtually any system building upon the RANSAC algorithm. Since its inception in 1981 by Fischler and Bolles, many variants of RANSAC have been proposed on top of the same original idea relying on the fact that random sampling has a high likelihood of generating a good hypothesis from minimal subsets of measurements. An approximation to the sampling probability was originally derived by the paper in 1981 in support of adaptively stopping RANSAC and is, as such, used in the vast majority of today's RANSAC variants and implementations. The impact of this approximation has since not been questioned or thoroughly studied by any of the later works. As we theoretically derive and practically demonstrate in this paper, the approximation leads to severe undersampling and thus failure to find good models. The discrepancy is especially pronounced in challenging scenarios with few inliers and high model complexity. An implementation of computing the exact probability is surprisingly simple yet highly effective and has potentially drastic impact across a large range of computer vision systems.

Problem

• Addresses long-standing error in RANSAC stopping criterion.
• Demonstrates severe undersampling due to approximation error.
• Proposes simple, effective solution for exact probability computation.

Innovation

• Exact probability computation for RANSAC stopping
• Addresses long-standing error in RANSAC algorithm
• Improves model accuracy in challenging scenarios