View article

Geometric model fitting is a typical chicken-&-egg problem: data points should be clustered based on geometric proximity to models whose unknown parameters must be estimated at the same time. Most existing methods, including generalizations of RANSAC, greedily search for models with most inliers (within a threshold) ignoring overall classification of points. We formulate geometric multi-model fitting as an optimal labeling problem with a global energy function balancing geometric errors and regularity of inlier clusters. Regularization based on spatial coherence (on some near-neighbor graph) and/or label costs is NP hard. Standard combinatorial algorithms with guaranteed approximation bounds (e.g. α-expansion) can minimize such regularization energies over a finite set of labels, but they are not directly applicable to a continuum of labels, e.g. in line fitting. Our proposed approach (PEaRL …