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4 pages; International audience; In [1], the authors have approached the sphere-like surfaces using the tensor product of an algebraic cubic spline quasiinterpolant with a 2¼-periodic Uniform Algebraic Trigonometric B-splines (UAT B-splines) of order four. In this paper, we improve the results given in [1], by introducing a new quasi-interpolant based on the tensor product of an algebraic cubic spline quasi-interpolant with a periodic cubic spline quasi-interpolant, obtained by the periodization of an algebraic cubic spline quasi-interpolant. Our approach allows us to obtain an approximating surface which is of class C2 and with an approximation order O(h4). We show that this method is particularly well designed to render 3D closed surfaces, and it has been successfully applied to reconstruct human organs such as the left ventricle of the heart.

International audience; In this chapter, starting from fractional Brownian motion of unique parameter H (0 < H < 1), we propose two variants which extend the classical fBm. First, the piece-wise fractional Brownian motion model of parameters $H_o$, $H_i$ and $\gamma$ presents two spectral regimes: it behaves like fBm of parameter $H_o$ for low frequencies $|f| < \gamma$ and like fBm of parameter $H_i$ for high frequencies $|f| > \gamma$. Second, the nth-order fractional Brownian motion enables the H parameter to be within the range $]n-1, n[$, where $n$ is any strictly positive integer. The properties of these two processes are investigated. Special interest is given to their increments, which extend fractional Gaussian noises. Synthesis of realizations of such processes is discussed. Finally, an application of such processes for the characterization of trabecular bone radiographs is presented. The overall objective of this application is to provide methods helping in the early diagnosis of osteoporosis for elderly people.

Publication in the conference proceedings of EUSIPCO, Florence, Italy, 2006

Publication in the conference proceedings of EUSIPCO, Florence, Italy, 2006

Publication in the conference proceedings of EUSIPCO, Viena, Austria, 2004

Publication in the conference proceedings of EUSIPCO, Rhodes, Greece, 1998

Publication in the conference proceedings of EUSIPCO, Trieste, Italy, 1996

This paper describes a three complementary images processing method. The three images are coming from a scanning electron microscope (SEM) during the analysis of a particular stone: the Tuffeau used in most monuments of the Loire valley (France). The goal is to separate two classes of particles (calcareous and siliceous) from the porosity to give more information to experts who evaluate the damage of weathering on monuments. A specific process is developed: a first threshold on the good quality image allows separation of particles from porosity. Then, the complementarity of the three images gives the two other thresholds. Granulometry, percentages of components, and anisotropy of the porosity are precious information that can be derived from the three segmented image.