MAGSAC: marginalizing sample consensus (1803.07469v2)

Abstract: A method called, sigma-consensus, is proposed to eliminate the need for a user-defined inlier-outlier threshold in RANSAC. Instead of estimating the noise sigma, it is marginalized over a range of noise scales. The optimized model is obtained by weighted least-squares fitting where the weights come from the marginalization over sigma of the point likelihoods of being inliers. A new quality function is proposed not requiring sigma and, thus, a set of inliers to determine the model quality. Also, a new termination criterion for RANSAC is built on the proposed marginalization approach. Applying sigma-consensus, MAGSAC is proposed with no need for a user-defined sigma and improving the accuracy of robust estimation significantly. It is superior to the state-of-the-art in terms of geometric accuracy on publicly available real-world datasets for epipolar geometry (F and E) and homography estimation. In addition, applying sigma-consensus only once as a post-processing step to the RANSAC output always improved the model quality on a wide range of vision problems without noticeable deterioration in processing time, adding a few milliseconds. The source code is at https://github.com/danini/magsac.

• The paper introduces a threshold-free RANSAC by marginalizing over noise scales to eliminate static inlier-outlier thresholds.
• The paper employs weighted least-squares fitting with likelihood-based inlier weights to refine models without predetermined thresholds.
• The paper demonstrates superior geometric accuracy and computational efficiency on real-world datasets, proving its practical robustness.

Marginalizing Sample Consensus (MAGSAC) in Robust Model Estimation

The paper presents a novel approach in the field of robust model estimation, specifically applicable to the RANSAC framework, widely used in computer vision for tasks such as fundamental matrix, homography, and essential matrix estimation. The proposed methodology, termed MAGSAC (Marginalizing Sample Consensus), introduces a noteworthy innovation by eliminating the need for a user-defined inlier-outlier threshold within RANSAC algorithms. This is achieved through a process of marginalizing over a range of noise scales, referred to as $\sigma$-consensus.

Key Contributions

1. Elimination of Static Thresholds: Traditional RANSAC algorithms depend heavily on a manually defined noise scale parameter $\sigma$, which is crucial for determining the inlier-outlier threshold. MAGSAC negates this requirement by integrating a novel marginalization strategy that averages model quality over a continuum of noise scales.
2. Weighted Least-Squares Fitting: To refine the models produced, MAGSAC employs a weighted least-squares fitting approach, where weights are derived from the likelihood of points being inliers across various possible noise scales. This bypasses the need for a definitive inlier set, thus making the model refinement process more flexible to variations in data quality.
3. Revised Model Quality and Termination Criteria: The paper introduces a new quality measure for model evaluation that does not rely on fixed thresholds and incorporates a termination criterion adjusted for the lack of a concrete inlier set.
4. Performance and Applicability: The paper evaluates MAGSAC against state-of-the-art methods using real-world datasets across various tasks. Empirical evaluations demonstrate that MAGSAC consistently shows superior geometric accuracy and, in scenarios with high outlier ratios, can outperform competitors in computational efficiency as well. Notably, when MAGSAC is used as a post-processing step to refine RANSAC outputs, it consistently improves model quality with minimal computational overhead.

Numerical Results and Implications

The experimental results are robust, validating the MAGSAC's capability in enhancing the accuracy of model fitting tasks. For instance, MAGSAC displays significant improvements in handling the epipolar geometry challenges in the datasets employed. The numerical outcomes reveal that MAGSAC surpasses the traditional RANSAC, MSAC, and other variants by aligning better with manually annotated inliers, thereby reducing RMS errors significantly in various settings, whether it be fundamental, essential matrix, or homography estimation.

Practical and Theoretical Implications

Practically, MAGSAC's ability to operate without a pre-specified $\sigma$ dramatically increases the method's applicability across diverse datasets, relieving users from the cumbersome process of threshold calibration, which differs scene by scene. Theoretically, this work contributes to the paradigm of robust estimation by demonstrating that marginalization techniques can effectively substitute heuristic-based parameters commonly used in sample consensus approaches.

Future Directions

Given the demonstrated efficacy of MAGSAC, potential future directions include extending the methodology to accommodate other forms of models and environments where noise characteristics are less predictable. Furthermore, exploring GPU-accelerated implementations could enhance its utility in real-time applications. Continued investigation into balancing computational load with model precision will further MAGSAC's adoption in high-stakes image processing tasks.

The introduction of MAGSAC represents a significant step in refining robust estimation methods, minimizing manual intervention, and adapting to the idiosyncrasies of real-world data in a principled manner.