Finding the Smallest Ellipse Containing a Point Set based on Genetic Algorithms

Abstract

Finding one of the smallest non-standard ellipse containing a given point set, is very useful in image and picture labeling. The paper presents an approach to seek the ellipse. The paper was not going to seek the equation of the ellipse, it solved the 5 elliptical parameters (the long axis a, the short axis b, the elliptical center and the rotation k) for determining the ellipse, instead. In order to reduce the problem complexity, the search of non-standard ellipse was turned into the standard ellipse's search through spatial coordinate transformation. And the genetic algorithms are adopted to optimize the ultimate aim to solve the smallest non-standard ellipse. The experiment results show that the approach is effective.