Fuzzy ellipsoidal shell clustering algorithm and detection of elliptical shapes

Rajesh N. Dave; Kalpesh J. Patel

doi:10.1117/12.25164

1 February 1991 Fuzzy ellipsoidal shell clustering algorithm and detection of elliptical shapes

Rajesh N. Dave, Kalpesh J. Patel

Proceedings Volume 1381, Intelligent Robots and Computer Vision IX: Algorithms and Techniques; (1991) https://doi.org/10.1117/12.25164
Event: Advances in Intelligent Robotics Systems, 1990, Boston, MA, United States

Abstract

Fuzzyc-Efflpsoidal Shell (FCES) algorithm that utilizes hyper-ellipsoidal-shells as cluster prototypes is proposed. FCES is a generalization of the Fuzzy Shell Clustering (FSC) algorithm. The generalization is achieved by allowing the distances measured through a norm inducing matrix that is symmetric positive definite. In case offixed known norms the extension of FcS to FCS is straightforward. Two different strategies are recommended when the norm is unknown. The first strategy considers use of non-linear least-squared fit approach with fuzzy memberships as weights. The second approach considers norm inducing matrix as a variable of optimization thus making FCES an adaptive norm type algorithm. An adaptive norm theorem is presented. The results of first approach is used to detect ellipses having unequal sizes and orientations in two-dimensional data-sets. Non-linear equations of the FCES algorithm are more complex than those of the FSC algorithm. Numerical issues related to both the FCES algorithm and the FSC algorithm are discussed.

Citation Download Citation

Rajesh N. Dave and Kalpesh J. Patel "Fuzzy ellipsoidal shell clustering algorithm and detection of elliptical shapes", Proc. SPIE 1381, Intelligent Robots and Computer Vision IX: Algorithms and Techniques, (1 February 1991); https://doi.org/10.1117/12.25164

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