A method for solving the multiple ellipses detection problem. (December 2016) - Grbić, Ratko; Grahovac, Danijel; Scitovski, Rudolf
Abstract: In this paper, the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance is considered. An ellipse is considered as a Mahalanobis circle with some positive definite matrix. A very efficient method for solving this problem is proposed. This method very successfully combines the well-known direct least squares method and the RANSAC algorithm with a realistic statistical model of multiple ellipses in the plane. The method is illustrated and tested on numerous synthetic and real-world applications. The method was also compared with other similar methods. In the case when a data points set comes from a number of ellipses with clear edges, the proposed method gives results similar to other known methods. However, when a data points set comes from a number of ellipses with noisy edges, the proposed method performs significantly better than the other methods. We should emphasize the advantage and utility of the proposed methods in a variety of applications such as: medical image analysis and ultrasound image segmentation. Abstract : Highlights: RANSAC-based method for solving the multiple ellipses detection problem is proposed. The proposed method shows high efficiency. The method has the potential to solve real time applications. Data is considered as a realization of a realistic statistical model. Pseudocodes of all proposed algorithms are provided.