Abstract
In this Chapter, we address the problem of identifying and fitting more than one ellipse simultaneously, from a set of data points in the plane. This problem is an active research area with many applications in engineering and biology. Numerous studies attempted to solve this problem by detecting, fitting, and extracting the ellipses in a one-by-one approach from the set of data points. Although the one-by-one approach is effective and useful for many applications, recent studies have show that this approach is ill posed which led to the proposal of novel methods such as PEARL. PEARL is a multi-model fitting algorithm which minimizes an energy function. The PEARL algorithm requires to be initialized with random solutions. In this work we show that the performance of the PEARL algorithm, to solve the multi-ellipse fitting problem, can be improved by initializing it in a smarter way with solutions taken from a multi-objective genetic algorithm. Numerical results show that our approach can solve challenging data points instances, with high amount of outliers, and also with overlapping and nested ellipses.
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Cruz Hernández, H., de la Fraga, L.G. (2019). Fitting Multiple Ellipses with PEARL and a Multi-objective Genetic Algorithm. In: Trujillo, L., Schütze, O., Maldonado, Y., Valle, P. (eds) Numerical and Evolutionary Optimization – NEO 2017. NEO 2017. Studies in Computational Intelligence, vol 785. Springer, Cham. https://doi.org/10.1007/978-3-319-96104-0_4
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