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Abstract: Hough transform (HT) has been the most common method for circle detection, exhibiting robustness but adversely demanding a considerable computational load and large storage. Alternative approaches for multiple circle detection include heuristic methods built over iterative optimization procedures which confine the search to only one circle per optimization cycle yielding longer execution times. On the other hand, artificial immune systems (AIS) mimic the behavior of the natural immune system for solving complex optimization problems. The clonal selection algorithm (CSA) is arguably the most widely employed AIS approach. It is an effective search method which optimizes its response according to the relationship between patterns to be identified, i.e. antigens (Ags) and their feasible solutions also known as antibodies (Abs). Although CSA converges to one global optimum, its incorporated CSA-Memory holds valuable information regarding other local minima which have emerged during the optimization process. Accordingly, the detection is considered as a multi-modal optimization problem which supports the detection of multiple circular shapes through only one optimization procedure. The algorithm uses a combination of three non-collinear edge points as parameters to determine circles candidates. A matching function determines if such circle candidates are actually present in the image. Guided by the values of such function, the set of encoded candidate circles are evolved through the CSA so the best candidate (global optimum) can fit into an actual circle within the edge map of the image. Once the optimization process has finished, the CSA-Memory is revisited in order to find other local optima representing potential circle candidates. The overall approach is a fast multiple-circle detector despite considering complicated conditions in the image. [Copyright &y& Elsevier]

Abstract: Unsupervised clustering for datasets with severe outliers inside is a difficult task. In this approach, we propose a cluster-dependent multi-metric clustering approach which is robust to severe outliers. A dataset is modeled as clusters each contaminated by noises of cluster-dependent unknown noise level in formulating outliers of the cluster. With such a model, a multi-metric Lp-norm transformation is proposed and learnt which maps each cluster to the most Gaussian distribution by minimizing some non-Gaussianity measure. The approach is composed of two consecutive phases: multi-metric location estimation (MMLE) and multi-metric iterative chi-square cutoff (ICSC). Algorithms for MMLE and ICSC are proposed. It is proved that the MMLE algorithm searches for the solution of a multi-objective optimization problem and in fact learns a cluster-dependent multi-metric Lq-norm distance and/or a cluster-dependent multi-kernel defined in data space for each cluster. Experiments on heavy-tailed alpha-stable mixture datasets, Gaussian mixture datasets with radial and diffuse outliers added respectively, and the real Wisconsin breast cancer dataset and lung cancer dataset show that the proposed method is superior to many existent robust clustering and outlier detection methods in both clustering and outlier detection performances. [Copyright &y& Elsevier]