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.
DOI10.21136/AM.2019.0262-18OpenAlexW2982518314MaRDI QIDQ2280464
Rudolf Scitovski, Kristian Sabo
Publication date: 18 December 2019
Published in: Applications of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.21136/am.2019.0262-18
DIRECT\(k\)-meansLipschitz continuous functionglobally optimal \(k\)-partitionmultiple ellipses detection problem
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) Symmetric functions and generalizations (05E05) Combinatorial optimization (90C27)
Uses Software
Cites Work
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- A modification of the \texttt{DIRECT} method for Lipschitz global optimization for a symmetric function
- Interpretation and optimization of the \(k\)-means algorithm.
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- ElliFit: an unconstrained, non-iterative, least squares based geometric ellipse fitting method
- 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
- Simplicial Global Optimization
- Multiple ellipse fitting by center-based clustering
- Least-squares fitting of circles and ellipses
- Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola
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