correspondences by matching quality and generates hypotheses from the most promising correspondences. USAC extends the standard hypothesize-and-verify structure in RANSAC and presents a universal framework that integrates advantages of previous parametric methods. In addition, some other approaches relying on local parametric structures have also been developed, such as agglomerative correspondence clustering (ACC) [@cho2009feature], multi-structures robust fitting (Multi-GS) [@chin2010accelerated], Hough voting and inverted Hough voting (HVIV) [@Chen2013Robust]. ACC uses Hessian-affine detector [@Mikolajczyk2004Hessian], which is invariant to affine transformations, to estimate the local homography matrix as constraints. The initial correspondences are then clustered based on the constraints, and the clusters with inliers are supposed to be larger than the ones constituted by outliers. Multi-GS generates a series of tentative hypotheses by random sampling and considers that two correspondences from the same local structure are inliers if they share a common list of hypotheses. HVIV employs the BPLR detector [@Kim2011Boundary] to cluster correspondences and estimates the homographic transformation for each correspondence as well. The most plausible correspondence in each cluster is then selected using normalized kernel density estimation.

For non-parametric methods, their theoretical foundations are not always the same. A widely-used strategy is exploiting the consistency information of local geometric structures or appearance 