adaptive threshold, the model will be discarded. When fitting the fundamental matrix by epipolar geometry constraint, USAC utilizes DEGENSAC [@Chum2005Two] for degeneracy. It assumes that the generated model is often incorrect in the context of images containing a dominant scene plane. Accordingly, DEGENSAC employs a homographic transformation to reject the generated fundamental model if there are five or more sampled correspondences lying on the same plane. Eventually, USAC adds a local optimization (LO-RANSAC [@Chum2003Locally]) to refine the minimal-sample model. It re-samples correspondences only from the set of selected inliers and refines the previous model by the sampling subset. This whole process is repeated until achieving confidence in solution or iterations reach the upper bound $n_{usac}$.

**Vector Field Consensus [@Ma2014Robust].** VFC interpolates a vector field where the posteriori probability of a correct correspondence is estimated by the Bayes rule.

For a correspondence $c_i$, the transformation to a motion field is expressed as $(\mathbf{x}_{i},\text{ }\mathbf{x}_{i}^{'})\to(\mathbf{u}_{i},\text{ }\mathbf{v}_{i})$, where $\mathbf{u}_{i}=\mathbf{x}_{i}$ and $\text{ }\mathbf{v}_{i}=\mathbf{x}_{i}^{'}-\mathbf{x}_{i}$. In this motion field, VFC holds the assumption that the noise around inliers indicated by $z_{i}=1$ follows the Gaussian distribution and the noise around outliers indicated by $z_{i}=0$ follows the uniform distribution. Thus, the probability is a mixture model given by 