Laurent Mascarilla

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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 propose new sets of Fourier-Mellin descriptors for color images. They are constructed using the Clifford Fourier Transform of Batard et al. (2010) and are an extension of the classical Fourier-Mellin descriptors for grayscale images. These are invariant under direct similarity transformations (translations, rotations, scale) and marginal treatment of(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)
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)
This article deals with the combination of pattern classifiers with two reject options. Such classifiers operate in two steps and differ on the managing of ambiguity and distance rejection (independently or not). We propose to combine the first steps of these classifiers using concepts from the theory of evidence. We propose some intelligent basic(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)
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 aim of this paper is to define an extension of the analytic signal for a color image. We generalize the construction of the so-called monogenic signal to mappings with values in the vectorial part of the Clifford algebra ℝ5,0. Solving a Dirac equation in this context leads to a multiscale signal (relatively to the Poisson scale-space) which contains(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)