Search results for "Transform"
showing 10 items of 3975 documents
Kolmogorov Superposition Theorem and Wavelet Decomposition for Image Compression
2009
International audience; Kolmogorov Superposition Theorem stands that any multivariate function can be decomposed into two types of monovariate functions that are called inner and external functions: each inner function is associated to one dimension and linearly combined to construct a hash-function that associates every point of a multidimensional space to a value of the real interval $[0,1]$. These intermediate values are then associated by external functions to the corresponding value of the multidimensional function. Thanks to the decomposition into monovariate functions, our goal is to apply this decomposition to images and obtain image compression. We propose a new algorithm to decomp…
Roughness evaluation of vine leaf by image processing
2013
International audience; The study of leaf surface roughness is very important in the domain of precision spraying. It is one of the parameters that allow to reduce costs and losses of phytosanitary prod- ucts and to improve the spray accuracy. Moreover, the leaf roughness is related to adhesion mechanisms of liquid on a surface. It can be used to define leaf nature surface (hy- drophilic/hydrophobic). The main goal of this study is thus to estimate and to follow the evolution of leaf roughness using image processing and computer vision. The develop- ment and application of computer vision for measurement of surface leaf roughness using artificial neural networks will be described. The syste…
Darboux curves on surfaces I
2017
International audience; In 1872, G. Darboux defined a family of curves on surfaces of $\mathbb{R}^3$ which are preserved by the action of the Mobius group and share many properties with geodesics. Here, we characterize these curves under the view point of Lorentz geometry and prove that they are geodesics in a 3-dimensional sub-variety of a quadric $\Lambda^4$ contained in the 5-dimensional Lorentz space $\mathbb{R}^5_1$ naturally associated to the surface. We construct a new conformal object: the Darboux plane-field $\mathcal{D}$ and give a condition depending on the conformal principal curvatures of the surface which guarantees its integrability. We show that $\mathcal{D}$ is integrable w…
Categorical action of the extended braid group of affine type $A$
2017
Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.
Spectral approach to D-bar problems
2017
We present the first numerical approach to D-bar problems having spectral convergence for real analytic, rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.© 2017 Wiley Periodicals, Inc.
Automatic detection of P, QRS and T patterns in 12 leads ECG signal based on CWT
2016
International audience; In this paper, a new method based on the continuous wavelet transform is described in order to detect the QRS, P and T waves. QRS, P and T waves may be distinguished from noise, baseline drift or irregular heartbeats. The algorithm, described in this paper, has been evaluated using the Computers in Cardiology (CinC) Challenge 2011 database and also applied on the MIT-BIH Arrhythmia database (MITDB). The data from the CinC Challenge 2011 are standard 12 ECG leads recordings with full diagnostic bandwidth compared to the MITDB which only includes two leads for each ECG signal. Firstly, our algorithm is validated using fifty 12 leads ECG samples from the CinC collection…
Contribution à l'estimation non paramétrique des quantiles géométriques et à l'analyse des données fonctionnelles
2008
In this dissertation we study the nonparametric geometric quantile estimation, conditional geometric quantiles estimation and functional data analysis. First, we are interested to the definition of geometric quantiles. Different simulations show that Transformation-Retransformation technique should be used to estimate geometric quantiles when the distribution is not spheric. A real study shows that, data are better modelized by geometric quantiles than by marginal one's, especially when variables that make up the random vector are correlated. Then we estimate geometric quantiles when data are obtained by survey sampling techniques. First, we propose an unbaised estimator, then using lineari…
Asymptotics of accessibility sets along an abnormal trajectory
2001
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer $\gamma$ into two sectors, bordered by the first Pontryagin's cone along $\gamma$, called the $\xLinfty$-sector and the $\xLtwo$-sector. Moreover we find again necessary and sufficient conditions of optimality of an abnormal trajectory for such systems, for any optimization problem.
Computation of conjugate times in smooth optimal control: the COTCOT algorithm
2006
Conjugate point type second order optimality conditions for extremals associated to smooth Hamiltonians are evaluated by means of a new algorithm. Two kinds of standard control problems fit in this setting: the so-called regular ones, and the minimum time singular single-input affine systems. Conjugate point theory is recalled in these two cases, and two applications are presented: the minimum time control of the Kepler and Euler equations.
On the high resolution spectroscopy and intramolecular potential function of SO2
2009
Abstract Two weak stretching bands, ν 1 + 3 ν 3 and 3 ν 1 + ν 3 , of the sulfur dioxide molecule have been recorded at high resolution and analyzed for the first time with using a Fourier transform Bruker IFS-120 HR interferometer. About 1000 transitions with J max . = 51, K a max . = 16 , and 900 transitions with J max . = 53, K a max . = 16 have been assigned to the bands ν 1 + 3 ν 3 and 3 ν 1 + ν 3 , respectively. Analysis of the recorded spectra was made using the model of isolated vibrational states. Parameters obtained from the fit reproduce the initial experimental ro-vibrational energies with the rms deviation of 0.0006 and 0.0012 cm −1 for the bands, 3 ν 1 + ν 3 and ν 1 …