A method for solving the multiple ellipses detection problem

• 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.

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.