## 2 Related Works  
Since the RANSAC [11] method was proposed, many methods based on RANSAC have been developed to enhance the effectiveness of the RANSAC method. The RANSAC method is an algorithm to find the best model and inliers conforming to a model from a set of data. It first randomly selects a certain subset of data from the set to construct a model. After obtaining the model, its quality is determined by a predefined threshold. Once the RANSAC model is obtained, it selects which data points in the set are inliers and which are outliers. RANSAC iterates this process continuously until it reaches the set maximum number of iterations. In the process mentioned above, many methods have made improvements to the RANSAC pipeline as shown in Figure 4 and achieved better results than RANSAC [8; 9; 10; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. When sampling correspondence in RANSAC, all point pairs contribute equally to the model evaluation. However, we can roughly assess the correctness of the matches by considering factors such as the confidence of the matches and other relevant information. N adjacent points sample consensus (NAPSAC) [14] considers that inliers should be concentrated around a hyperplane, while outliers are uniformly distributed outside a spherical region. It performs point sampling by adjusting the radius of the hypersphere. Locally optimized random sample consensus (LO-RANSAC) [12] uses local optimization to reweight all inliers to avoid the influence of outliers. During each sampling, points are selected from the inliers. Progressive sample consensus (PROSAC) [22] uses a probabilistic prior to guide the sampling process, where points with higher confidence are more likely to be considered, thus accelerating the computation process. Group sample consensus (GroupSAC) [15] introduces the concept of grouping on top of NAPSAC, grouping points based on their similarity. Points within the same group are more likely to be inliers if they exhibit strong intra-group consistency. Universal sample consensus (USAC) [16]  
Figure 4: Illustration of the robust model estimation process. Both traditional methods and deep learning-based approaches broadly rely on the RANSAC framework. The entire process can be divided into four stages: sampling, model computation, evaluation, and selecting the best model. summarizes the advantages of previous work and forms a standard framework. In [18], graph-cut random sample consensus ((GC-RANSAC) abstracts points into a graph, assuming that neighboring points have the same inlier/outlier classification to optimize the model. MAGSAC [8] and MAGSAC++ [9] avoid manually setting thresholds and evaluate the model by marginalizing thresholds and using point scores as weights. [PERSON] et al. [23] revisited the Sampson approximation in epipolar geometry and explained when the Sampson distance approximation works most effectively. Currently, some methods have also integrated deep learning into the pipeline of RANSAC and achieved promising results by combining traditional model quality evaluation steps. Differentiable random sample consensus (DSAC) [17] designs neural networks to predict sampling distributions and model scores separately. Neural-guided random sample consensus (NG-RANSAC) [19] uses the distance from the points to the ground truth model as supervision signals, which achieves probabilistic sampling for points. However, in the above works, the sampling process remained non-differentiable. The emergence of Gumbel-Softmax [24] bridged the gap in the sampling process, where generalized differentiable random sample consensus (D-RANSAC) firstly applies Gumbel-Softmax [24] to the RANSAC pipeline, making the entire RANSAC process end to end. Recently, there have also been some methods that apply other deep learning paradigms, such as [21, 25]. Reinforcement learning sample consensus (RLSAC) [25] firstly applies reinforcement learning paradigms to robust estimation.