Energy-Based Geometric Multi-model Fitting |
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Authors: | Hossam Isack Yuri Boykov |
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Affiliation: | 1. Computer Science Department, University of Western Ontario, London, Ontario, Canada
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Abstract: | 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. R2{\mathcal{R}}^{2} in line fitting. Our proposed approach (PEaRL) combines model sampling from data points as in RANSAC with iterative re-estimation of inliers and models’ parameters based on a global regularization functional. This technique
efficiently explores the continuum of labels in the context of energy minimization. In practice, PEaRL converges to a good quality local minimum of the energy automatically selecting a small number of models that best explain
the whole data set. Our tests demonstrate that our energy-based approach significantly improves the current state of the art
in geometric model fitting currently dominated by various greedy generalizations of RANSAC. |
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