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Journal Article
Energy-Based Geometric Multi-model Fitting
2012
Overview
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
) 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
.
Publisher
Springer US,Springer,Springer Nature B.V
Subject
Algorithmics. Computability. Computer arithmetics
/ Analysis
/ Combinatorics. Ordered structures
/ Computer science; control theory; systems
/ Energy
/ Exact sciences and technology
/ Fittings
/ Image Processing and Computer Vision
/ Information retrieval. Graph
/ Labels
/ Noise
/ Pattern Recognition and Graphics
/ Sampling
/ Sciences and techniques of general use
/ Studies
/ Vision
