Finding Structure in Point Cloud Data with the Robust Isoperimetric Loss.

We present a new regularization method to find structure in point clouds corrupted by outliers. The method organizes points into a graph structure, and uses isoperimetric inequalities to craft a loss function that is minimized alternatingly to identify outliers, and annihilate their effect. It can operate in the presence of large amounts of outliers, and inlier noise. The approach is applicable to both low-dimensional point clouds, such as those obtained from stereo or structured light, as well as high-dimensional ones.