Model-free Consensus Maximization for Non-Rigid Shapes

Abstract

Many computer vision methods use consensus maximization to relate measurements containing outliers with the correct transformation model. In the context of rigid shapes, this is typically done using Random Sampling and Consensus (RANSAC) by estimating an analytical model that agrees with the largest number of measurements (inliers). However, small parameter models may not be always available. In this paper, we formulate the model-free consensus maximization as an Integer Program in a graph using 'rules' on measurements. We then provide a method to solve it optimally using the Branch and Bound (BnB) paradigm. We focus its application on non-rigid shapes, where we apply the method to remove outlier 3D correspondences and achieve performance superior to the state of the art. Our method works with outlier ratio as high as 80%. We further derive a similar formulation for 3D template to image matching, achieving similar or better performance compared to the state of the art.

Unsupervised Learning of Consensus Maximization for 3D Vision Problems

“…Again, we observe that the unsupervised method adapts to the method-specific outlier statistics, whereas the method pretrained on synthetic outliers fails to generalize. Compared to the isometric consensus maximization method MFCM [33], we loose more inliers, which can be attributed to the fact that piecewise rigidity is not the entirely correct deformation model. In Fig.…”

“…Consensus maximization is a well studied topic [12,17,30,20], and is usually solved with RANSAC [13,35,44,37]. In contrast to heuristic approaches, global methods provide optimality guaranties [10,33,42,2,15,3,23,49]. Recently, supervised machine learning has been leveraged to solve consensus maximization and robust estimation.…”

“…1. Training is conducted in a curriculum learning fashion: starting with one global transformation [25] 4211 / 772 1.0 3756 / 1227 1.0 MFCM [33] 3918 Table 1. Non-rigid 3D shape matching.…”

“…Our results on FAUST [6] intra-and inter-subjects vs. [22] and [33]. We report the number of true positive (inliers) and false positive (remaining outliers) matches, as well as run time on CPU.…”

“…Polynomial-based geometric model representations, when used with RANSAC, offer accurate transformation parameters, therefore are used for a diverse set of problems [12,17,30,20]. Globally optimal methods [10,33,42,2,15,3,23,49], which overcome limitations of RANSAC, further bolster the importance of maximizing consensus. However, most methods that seek consensus maximization solely depend upon the geometric models.…”