A stabilizer mahalanobis distance applied to ellipses extraction using the fuzzy clustering

In this paper we are interested to extract ellipses using a fuzzy clustering algorithm. In literature, the will-known fuzzy clustering algorithms are based on the Euclidean distance, which can only be used to extract circular or spherical clusters, to overcome this problem, Gustafson-Kessel have extended the measure distance to the Mahalanobis distance, which can be used to extract clusters with different geometrical shapes. However, this new distance has two major problems, to overcome them and achieve our goal we propose a modified version of the FCM algorithm based on two solutions. To evaluate our algorithm, we compare its results with those of the FCM based on Euclidean distance. In order to do that, we test the both algorithms with the same datasets of 2D points and under the same clustering parameters. After a comparative study between the results of both algorithms, using an ellipse fitting algorithm, we notice the efficiency of the proposed algorithm to extract elliptical clusters.