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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)

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)

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 Clif-ford algebra R 5,0 that codes color (RGB) and geometric structures information. Using geometric calculus, a notion of local color phase is introduced, generalizing the one for… (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)

The number of non isomorphic solutions of the eikonal equation can be infinite. We show that there can exist a whole family of non isomorphic solutions, indexed by a continuous parameter. This implies, first, that the general problem of shape from shading can be ill-posed when no additional condition on the shape is imposed. This is in contradiction with… (More)