Generalized Differentiable RANSAC (2212.13185v3)

Abstract: We propose $\nabla$-RANSAC, a generalized differentiable RANSAC that allows learning the entire randomized robust estimation pipeline. The proposed approach enables the use of relaxation techniques for estimating the gradients in the sampling distribution, which are then propagated through a differentiable solver. The trainable quality function marginalizes over the scores from all the models estimated within $\nabla$-RANSAC to guide the network learning accurate and useful inlier probabilities or to train feature detection and matching networks. Our method directly maximizes the probability of drawing a good hypothesis, allowing us to learn better sampling distributions. We test $\nabla$-RANSAC on various real-world scenarios on fundamental and essential matrix estimation, and 3D point cloud registration, outdoors and indoors, with handcrafted and learning-based features. It is superior to the state-of-the-art in terms of accuracy while running at a similar speed to its less accurate alternatives. The code and trained models are available at https://github.com/weitong8591/differentiable_ransac.

• The paper presents a differentiable RANSAC using Gumbel-Softmax to optimize hypothesis sampling across the estimation pipeline.
• It integrates a learnable quality function that refines model scoring by optimizing for average model performance rather than selecting the best model.
• It enables end-to-end training with neural networks like LoFTR, achieving state-of-the-art accuracy in vision tasks such as pose estimation and 3D registration.

Understanding Generalized Differentiable RANSAC

The paper presents a new approach dubbed $\nabla$-RANSAC, a generalized differentiable variant of the RANSAC algorithm, which is pivotal in numerous computer vision applications such as pose estimation and 3D point cloud registration. Traditional RANSAC implements a randomized hypothesize-and-verify paradigm which, despite its robustness and efficiency, lacks differentiability, thereby limiting its integration with machine learning models aimed at learning data-driven hypotheses. This work tackles these limitations through relaxation and differentiable solver techniques, where gradients can be propagated, thus making the entire estimation pipeline adaptable for learning.

Key Contributions

1. Differentiable RANSAC Components: The paper proposes differentiable counterparts for the different components of RANSAC. The gradient propagation through the pipeline is enabled by relaxation techniques utilizing Gumbel-Softmax (GS) sampling which provides a learned sampling distribution. This is instrumental in scenarios where the sampling probabilities need optimization for determining good hypotheses.
2. Learnable Quality Function: The paper introduces a method by which the model utilizes a trainable quality function. This function marginalizes over all model scores to guide learning, aiming for accurate inlier probabilities. In contrast to maximizing the best model directly, the framework optimizes for the average model, delivering improved sampling distributions.
3. End-to-End Training Enablement: Through integration with neural networks, $\nabla$-RANSAC becomes capable of being trained fully end-to-end with configurable metrics like pose error. This feature is showcased by its incorporation with LoFTR, enabling enhanced feature matching predictions and confidences.

Evaluation and Implications

The paper provides extensive evaluations of $\nabla$-RANSAC across several datasets and fundamental computer vision tasks. The results indicate that it surpasses state-of-the-art methods in terms of accuracy while maintaining comparable runtime efficiency. Specifically, for fundamental and essential matrix estimation and 3D point cloud registration, $\nabla$-RANSAC not only improves model accuracy but also reveals the advantages of integrating this methodology with advanced ML models like LoFTR.

Future Prospects

With the introduction of differentiable solvers and optimizable sampling strategies, this research paves the way for significant improvements in the domain of robust geometric estimation. Future research avenues could explore integrating $\nabla$-RANSAC in more sophisticated computer vision systems requiring learned robust models, or expanding this methodology further in optimizing other machine learning tasks involving similar randomized and robust estimation processes.

In sum, $\nabla$-RANSAC equips researchers with a potent tool for optimizing robust estimation tasks using machine learning techniques, potentially democratizing the usage of rich, data-driven geometric estimation solutions across a broad spectrum of real-world applications.