Application of the \texttt{DIRECT} algorithm to searching for an optimal \(k\)-partition of the set \(\mathcal {A}\subset \mathbb {R}^n\) and its application to the multiple circle detection problem

DOI10.1007/s10898-019-00743-8zbMath1461.65185OpenAlexW2912803520MaRDI QIDQ2423794

Rudolf Scitovski, Kristian Sabo

Publication date: 20 June 2019

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-019-00743-8

zbMATH Keywords

\(k\)-meansincremental algorithmdirectglobally optimal partitionmultiple circles detection problem

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Nonconvex programming, global optimization (90C26) Derivative-free methods and methods using generalized derivatives (90C56) Combinatorial optimization (90C27)

Related Items (5)

Incremental method for multiple line detection problem -- iterative reweighted approach ⋮ The DIRECT algorithm: 25 years later ⋮ A combination of \texttt{RANSAC} and \texttt{DBSCAN} methods for solving the multiple geometrical object detection problem ⋮ The adaptation of the \(k\)-means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm. ⋮ A combination of \(k\)-means and \texttt{DBSCAN} algorithm for solving the multiple generalized circle detection problem

Uses Software

• flexclust
• SIGOA
• SymDIRECT

Cites Work

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• Circular and Linear Regression
• Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola
• Advantages of simplicial partitioning for Lipschitz optimization problems with linear constraints

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