Search results for "INTERPOLATION"
showing 10 items of 331 documents
A Geometric Algorithm for Ray/Bézier Surfaces Intersection Using Quasi-Interpolating Control Net
2008
In this paper, we present a new geometric algorithm to compute the intersection between a ray and a rectangular Bezier patch. The novelty of our approach resides in the use of bounds of the difference between a Bezier patch and its quasi-interpolating control net. The quasi-interpolating polygon of a Bezier surface of arbitrary degree approximates the limit surface within a precision that is function of the second order difference of the control points, which allows for very simple projections and 2D intersection tests to determine sub-patches containing a potential intersection. Our algorithm is simple, because it only determines a 2D parametric interval containing the solution, and effici…
A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions
2010
Abstract In this paper, we establish the equivalence between the Hajlasz–Sobolev spaces or classical Triebel–Lizorkin spaces and a class of grand Triebel–Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ ( n / ( n + 1 ) , ∞ ) , we give a new characterization of the Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.
Évolution des températures observées en Bourgogne (1961-2011)
2014
International audience; Depuis un demi-siècle environ, l’augmentation des concentrations atmosphériques en gaz à effet de serre a entraîné une élévation de température qui peut être analysée selon des échelles emboîtées, allant de la planète aux territoires. Dans cette étude, les mesures effectuées sur le réseau de stations Météo-France sont mobilisées pour analyser la température en Bourgogne sur la période 1961-2011. Le réchauffement observé a des caractéristiques très proches des moyennes françaises. Il est plus fort que sur la moyenne planétaire. Il est marqué par une rupture nette délimitant deux périodes bien différentes : 1961-1987 et 1988-2011. Une interpolation par régression krige…
Multivariate data analysis and bivariate regression studies applied to comparison of two multi-elemental methods for analysing wine samples
2002
Two inductively coupled plasma mass spectrometry (ICP-MS) methods which permit multi-elemental analysis in wine samples have been compared following two strategies. First, a multivariate tool based on principal component analysis (PCA) was employed for a global (all analytes) qualitative comparison of the two methods. A single plot based on the confidence limits of the Q and T2 PCA model statistics corresponding to the ‘standard’ method results (calibration set) was used to check the comparability of the ‘candidate’ method (test samples). The residual matrix (after test matrix interpolation into the PCA model) gives qualitative information about the nature of the main errors. This approach …
Impulsive control of the bilinear Schrödinger equation: propagators and attainable sets
2019
International audience; We consider a linear Schrödinger equation with an unbounded bilinear control term. The control term is the derivative of function with bounded variations (impulsive control). Well-posedness results and regularity of the associated propagators follow from classical theory from Kato. As a byproduct, one obtains a topological obstruction to exact controllability of the system in the spirit of the results of Ball, Marsden and Slemrod.
Robustified smoothing for enhancement of thermal image sequences affected by clouds
2015
Obtaining radiometric surface temperature information with both high acquisition rate and high spatial resolution is still not possible through a single sensor. However, in several earth observation applications, the fusion of data acquired by different sensors is a viable solution for so called image sharpening. A related issue is the presence of clouds, which may impair the performance of the data fusion algorithms. In this paper we propose a robustified setup for the sharpening of thermal images in a non real-time scenario, capable to deal with missing thermal data due to cloudy pixels, and robust with respect to cloud mask misclassifications. The effectiveness of the presented technique…
A Generalised RBF Finite Difference Approach to Solve Nonlinear Heat Conduction Problems on Unstructured Datasets
2011
Radial Basis Functions have traditionally been used to provide a continuous interpolation of scattered data sets. However, this interpolation also allows for the reconstruction of partial derivatives throughout the solution field, which can then be used to drive the solution of a partial differential equation. Since the interpolation takes place on a scattered dataset with no local connectivity, the solution is essentially meshless. RBF-based methods have been successfully used to solve a wide variety of PDEs in this fashion. Such full-domain RBF methods are highly flexible and can exhibit spectral convergence rates Madych & Nelson (1990). However, in their traditional implementation the fu…
THE INFLUENCE OF CHROMATIC ABERRATION ON DEMOSAICKING
2014
International audience; The wide deployment of colour imaging devices owes much to the use of colour filter array (CFA). A CFA produces a mosaic image, and normally a subsequent CFA demosaick-ing algorithm interpolates the mosaic image and estimates the full-resolution colour image. Among various types of optical aberrations from which a mosaic image may suffer, chromatic aberration (CA) influences the spatial and spectral correlation through the artefacts such as blur and mis-registration, which demosaicking also relies on. In this paper we propose a simulation framework aimed at an investigation of the influence of CA on demosaicking. Results show that CA benefits de-mosaicking to some ex…
Remarks on the semivariation of vector measures with respect to Banach spaces.
2007
Suppose that and . It is shown that any Lp(µ)-valued measure has finite L2(v)-semivariation with respect to the tensor norm for 1 ≤ p < ∞ and finite Lq(v)-semivariation with respect to the tensor norm whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor norm for any 1 ≤ q < 2. It is also shown that the measure m (A) = χA has infinite Lq-semivariation with respect to the tensor norm if q < p.
Commutators of linear and bilinear Hilbert transforms
2003
Let α ∈ R \alpha \in \mathbb {R} , and let H α ( f , g ) ( x ) = 1 π p . v . ∫ f ( x − t ) g ( x − α t ) d t t H_\alpha (f,g)(x)=\frac {1}{\pi } p.v. \int f(x-t)g(x-\alpha t)\frac {dt}{t} and H f ( x ) = 1 π p . v . ∫ f ( x − t ) d t t Hf(x)= \frac {1}{\pi } p.v.\int f(x-t)\frac {dt}{t} denote the bilinear and linear Hilbert transforms, respectively. It is proved that, for 1 > p > ∞ 1>p>\infty and α 1 ≠ α 2 \alpha _1\ne \alpha _2 , H α 1 − H α 2 H_{\alpha _1}-H_{\alpha _2} maps L p × B M O L^p\times BMO into L p L^{p} and it maps B M O × L p BMO \times L^p into L p L^{p} if and only if sign ( α 1 ) = sign ( α 2 ) \operatorname {sign}(\alpha _1)=\operatorname {sign}(\alpha _2…