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ANSAC: Adaptive Non-minimal Sample and Consensus

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 Added by Victor Fragoso
 Publication date 2017
and research's language is English




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While RANSAC-based methods are robust to incorrect image correspondences (outliers), their hypothesis generators are not robust to correct image correspondences (inliers) with positional error (noise). This slows down their convergence because hypotheses drawn from a minimal set of noisy inliers can deviate significantly from the optimal model. This work addresses this problem by introducing ANSAC, a RANSAC-based estimator that accounts for noise by adaptively using more than the minimal number of correspondences required to generate a hypothesis. ANSAC estimates the inlier ratio (the fraction of correct correspondences) of several ranked subsets of candidate correspondences and generates hypotheses from them. Its hypothesis-generation mechanism prioritizes the use of subsets with high inlier ratio to generate high-quality hypotheses. ANSAC uses an early termination criterion that keeps track of the inlier ratio history and terminates when it has not changed significantly for a period of time. The experiments show that ANSAC finds good homography and fundamental matrix estimates in a few iterations, consistently outperforming state-of-the-art methods.

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Random sample consensus (RANSAC) is a robust model-fitting algorithm. It is widely used in many fields including image-stitching and point cloud registration. In RANSAC, data is uniformly sampled for hypothesis generation. However, this uniform sampling strategy does not fully utilize all the information on many problems. In this paper, we propose a method that samples data with a L{e}vy distribution together with a data sorting algorithm. In the hypothesis sampling step of the proposed method, data is sorted with a sorting algorithm we proposed, which sorts data based on the likelihood of a data point being in the inlier set. Then, hypotheses are sampled from the sorted data with L{e}vy distribution. The proposed method is evaluated on both simulation and real-world public datasets. Our method shows better results compared with the uniform baseline method.
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Maximum consensus (MC) robust fitting is a fundamental problem in low-level vision to process raw-data. Typically, it firstly finds a consensus set of inliers and then fits a model on the consensus set. This work proposes a new formulation to achieve simultaneous maximum consensus and model estimation (MCME), which has two significant features compared with traditional MC robust fitting. First, it takes fitting residual into account in finding inliers, hence its lowest achievable residual in model fitting is lower than that of MC robust fitting. Second, it has an unconstrained formulation involving binary variables, which facilitates the use of the effective semidefinite relaxation (SDR) method to handle the underlying challenging combinatorial optimization problem. Though still nonconvex after SDR, it becomes biconvex in some applications, for which we use an alternating minimization algorithm to solve. Further, the sparsity of the problem is exploited in combination with low-rank factorization to develop an efficient algorithm. Experiments show that MCME significantly outperforms RANSAC and deterministic approximate MC methods at high outlier ratios. Besides, in rotation and Euclidean registration, it also compares favorably with state-of-the-art registration methods, especially in high noise and outliers. Code is available at textit{https://github.com/FWen/mcme.git}.
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