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Performance of any clustering algorithm depends critically on the number of clusters that are initialized. A practitioner might not know, a priori, the number of partitions into which his data should be divided; to address this issue many cluster validity indices have been proposed for finding the optimal number of partitions. In this paper, we propose a(More)
In pattern recognition, the membership of an object to classes is often measured by labels. This article mainly deals with the mathematical foundations of labels combination operators, built on t-norms, that extend previous ambiguity measures of objects by dealing not only with 2 classes ambiguities but also with k classes, k lying between 1 and the number(More)
The aim of this paper is to propose two different approaches for color object recognition, both using the recently defined color Clifford Fourier transform. The first one deals with so-called Generalized Fourier Descriptors, the definition of which relies on plane motion group actions. The proposed color extension leads to more compact descriptors, with(More)
This article relies on two recent developments of well known methods which are a color Fourier transform using geometric algebra [1] and Generalized Fourier descriptors defined from the group M<inf>2</inf> of the motion of the plane [2]. In this paper, new generalized color Fourier descriptors (GCFD) are proposed. They depend on the choice of a bivector B(More)
We use in this paper the formalism of Clifford algebras to define the so-called Color Monogenic Signal associated to a color image. It consists in a function with values in the Clifford algebra &#x211D;<inf>5,0</inf> that codes color (RGB) and geometric structures information. Using geometric calculus, a notion of local color phase is introduced,(More)