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Abstract: In the paper an iteratively unsupervised image segmentation algorithm is developed, which is based on our proposed multiphase multiple piecewise constant (MMPC) model and its graph cuts optimization. The MMPC model use multiple constants to model each phase instead of one single constant used in Chan and Vese (CV) model and cartoon limit so that heterogeneous image object segmentation can be effectively dealt with. We show that the multiphase optimization problem based on our proposed model can be approximately solved by graph cuts methods. Four-Color theorem is used to relabel the regions of image after every iteration, which makes it possible to represent and segment an arbitrary number of regions in image with only four phases. Therefore, the computational cost and memory usage are greatly reduced. The comparison with some typical unsupervised image segmentation methods using a large number of images from the Berkeley Segmentation Dataset demonstrates the proposed algorithm can effectively segment natural images with a good performance and acceptable computational time. [Copyright &y& Elsevier]

Abstract: Nearest neighbor classification is one of the most used and well known methods in data mining. Its simplest version has several drawbacks, such as low efficiency, high storage requirements and sensitivity to noise. Data reduction techniques have been used to alleviate these shortcomings. Among them, prototype selection and generation techniques have been shown to be very effective. Positioning adjustment of prototypes is a successful trend within the prototype generation methodology. Evolutionary algorithms are adaptive methods based on natural evolution that may be used for searching and optimization. Positioning adjustment of prototypes can be viewed as an optimization problem, thus it can be solved using evolutionary algorithms. This paper proposes a differential evolution based approach for optimizing the positioning of prototypes. Specifically, we provide a complete study of the performance of four recent advances in differential evolution. Furthermore, we show the good synergy obtained by the combination of a prototype selection stage with an optimization of the positioning of prototypes previous to nearest neighbor classification. The results are contrasted with non-parametrical statistical tests and show that our proposals outperform previously proposed methods. [Copyright &y& Elsevier]

Abstract: In this paper we introduce an adaptive image thresholding technique via minimax optimization of a novel energy functional that consists of a non-linear convex combination of an edge sensitive data fidelity term and a regularization term. While the proposed data fidelity term requires the threshold surface to intersect the image surface only at places with large image gradient magnitude, the regularization term enforces smoothness in the threshold surface. To the best of our knowledge, all the previously proposed energy functional-based adaptive image thresholding algorithms rely on manually set weighting parameters to achieve a balance between the data fidelity and the regularization terms. In contrast, we use minimax principle to automatically find this weighting parameter value, as well as the threshold surface. Our conscious choice of the energy functional permits a variational formulation within the minimax principle leading to a globally optimum solution. The proposed variational minimax optimization is carried out by an iterative gradient descent with exact line search technique that we experimentally demonstrate to be computationally far more attractive than the Fibonacci search applied to find the minimax solution. Our method shows promising results to preserve edge/texture structures in different benchmark images over other competing methods. We also demonstrate the efficacy of the proposed method for delineating lung boundaries from magnetic resonance imagery (MRI). [Copyright &y& Elsevier]