In this paper, the standard hard C-means (HCM) clustering approach to image segmentation is modified by incorporating weighted membership Kullback–Leibler (KL) divergence and local data information into the HCM objective function. The membership KL divergence, used for fuzzification, measures the proximity between each cluster membership function of a pixel and the locally-smoothed value of the membership in the pixel vicinity. The fuzzification weight is a function of the pixel to cluster-centers distances. The used pixel to a cluster-center distance is composed of the original pixel data distance plus a fraction of the distance generated from the locally-smoothed pixel data. It is shown that the obtained membership function of a pixel is proportional to the locally-smoothed membership function of this pixel multiplied by an exponentially distributed function of the minus pixel distance relative to the minimum distance provided by the nearest cluster-center to the pixel. Therefore, since incorporating the locally-smoothed membership and data information in addition to the relative distance, which is more tolerant to additive noise than the absolute distance, the proposed algorithm has a threefold noise-handling process. The presented algorithm, named local data and membership KL divergence based fuzzy C-means (LDMKLFCM), is tested by synthetic and real-world noisy images and its results are compared with those of several FCM-based clustering algorithms.
In this paper a new approach in human identification is introduced, in which the use of the Vectorcardiogram (VCG) main loop as a biometric feature is investigated. The advantage of using VCG over the Electrocardiogram (ECG) is that the shape of the VCG is independent of the heart rate. A test set of 550 VCG's recorded from 22 healthy individuals measured at different times and with a wide range of heart rate values is used to validate the system. The proposed system uses only the main loop of the VCG for identification. Two different algorithms are used. In the first one, coefficients from specially developed descriptor (the Equal Distance descriptor) are used for identification, and in the second, selected Fourier Descriptor coefficients of the main loop of the VCG are used as biometric data. In both methods Feed Forward Neural Networks are used as classifiers giving identification rates of 99.454% and 95% respectively.
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