Search results for "Geometry"
showing 10 items of 4487 documents
OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS
2010
The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…
Needle-shape quality control by shadowgraphic image processing
2011
International audience; We propose a needle-shape quality-control method. To this end, we have devised a new acquisition system that combines a camera and a backlight. Needle measurements are carried out at a micrometric scale using shadowgraphic image processing. Our method not only distinguishes good needles from bad ones, but also allows classifying flawed needles into various categories of defects. This classification is important because some categories of defects can affect the entire production, whereas others do not. The results of our needle-shape quality-control method are validated using real samples directly off the manufacturing line. Needles are correctly classified at >97%, a…
Reaction-Diffusion Network For Geometric Multiscale High Speed Image Processing
2010
International audience; In the framework of heavy mid-level processing for high speed imaging, a nonlinear bi-dimensional network is proposed, allowing the implementation of active curve algorithms. Usually this efficient type of algorithm is prohibitive for real-time image processing due to its calculus charge and the inadequate structure for the use of serial or parallel architectures. Another kind of implementation philosophy is proposed here, by considering the active curve generated by a propagation phenomenon inspired from biological modeling. A programmable nonlinear reaction-diffusion system is proposed under front control and technological constraints. Geometric multiscale processin…
Validation of a 2D multispectral camera: application to dermatology/cosmetology on a population covering five skin phototypes
2011
International audience; This paper presents the validation of a new multispectral camera specifically developed for dermatological application based on healthy participants from five different Skin PhotoTypes (SPT). The multispectral system provides images of the skin reflectance at different spectral bands, coupled with a neural network-based algorithm that reconstructs a hyperspectral cube of cutaneous data from a multispectral image. The flexibility of neural network based algorithm allows reconstruction at different wave ranges. The hyperspectral cube provides both high spectral and spatial information. The study population involves 150 healthy participants. The participants are classif…
Cluster matching in time resolved imaging for VLSI analysis
2014
International audience; If scaling has the benefit of enabling manufacturers to design tomorrow's integrated circuits, from the failure analyst point of view it also has the drawback of making devices more complex. The test sequence for modern VLSI can be quite long, with thousands of vector. Dynamic photon emission databases can contain millions of photons representing thousands of state changes in the region of interest. Finding a candidate location where to perform physical analysis is quite challenging, especially if the fault occurs on a single vector. In this paper, we suggest a new methodology to find single vector fault in dynamic photon emission database. The process is applied at …
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…
AN APPROACH TO CORRECTING IMAGE DISTORTION BY SELF CALIBRATION STEREOSCOPIC SCENE FROM MULTIPLE VIEWS
2012
International audience; An important step in the analysis and interpretation of video scenes for recognizing scenario is the aberration corrections introduced during the image acquisition in order to provide and correct real image data. This paper presents an approach on distortion correction based on stereoscopic self calibration from images sequences by using a multi-camera system of vision (network cameras). This approach for correcting image distortion brings an elegant and robust technique with good accuracy. Without any knowledge of shooting conditions, the camera's parameters will be estimated. For this, the image key points of interest are extracted from different overlapping views …
Darboux systems with a cusp point and pseudo-abelian integrals
2018
International audience; We study pseudo-abelian integrals associated with polynomial deformations of Darboux systems having a cuspidal singularity. Under some genericity hypothesis we provide locally uniform boundedness of on the number of their zeros.
Computational approach to compact Riemann surfaces
2017
International audience; A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on…
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…