The Experts below are selected from a list of 174 Experts worldwide ranked by ideXlab platform

S Banerjee - One of the best experts on this subject based on the ideXlab platform.

  • detecting Parameterized Curve segments using mdl and the hough transform
    Computer Vision and Pattern Recognition, 1992
    Co-Authors: J Sheinvald, Byron Dom, W Niblack, S Banerjee
    Abstract:

    A method for detecting Curve segments in a digital image is described. The method takes as input a set of edges, and produces as output the number of and parameters for the segments. The method is robust, requiring no thresholds. In place of thresholds, a model class must be provided. Using the information-theoretic minimum description length (MDL) principle, it evaluates each model in the model class, computing the optimal parameters for that model, and selects the best model as the one that gives the shortest encoding of the data and the model. Typical of such methods, the search space is extremely large. It is shown how the Hough transform (HT) may be used to reduce this search space greatly, yielding an efficient (although suboptimal) search. The result is an algorithm in which MDL overcomes standard problems with the HT, while the HT overcomes problems with MDL, and which produces a pleasing set of line segments. >

  • CVPR - Detecting Parameterized Curve segments using MDL and the Hough transform
    Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1
    Co-Authors: J Sheinvald, Byron Dom, W Niblack, S Banerjee
    Abstract:

    A method for detecting Curve segments in a digital image is described. The method takes as input a set of edges, and produces as output the number of and parameters for the segments. The method is robust, requiring no thresholds. In place of thresholds, a model class must be provided. Using the information-theoretic minimum description length (MDL) principle, it evaluates each model in the model class, computing the optimal parameters for that model, and selects the best model as the one that gives the shortest encoding of the data and the model. Typical of such methods, the search space is extremely large. It is shown how the Hough transform (HT) may be used to reduce this search space greatly, yielding an efficient (although suboptimal) search. The result is an algorithm in which MDL overcomes standard problems with the HT, while the HT overcomes problems with MDL, and which produces a pleasing set of line segments. >

Maria Siopacha - One of the best experts on this subject based on the ideXlab platform.

  • Strong Taylor approximation of stochastic differential equations and application to the L\'evy LIBOR model
    2010
    Co-Authors: Antonis Papapantoleon, Maria Siopacha
    Abstract:

    In this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by L\'evy processes or general semimartingales. The main ingredients of our method is the perturbation of the SDE and the Taylor expansion of the resulting Parameterized Curve. We apply this method to develop strong approximation schemes for LIBOR market models. In particular, we derive fast and precise algorithms for the valuation of derivatives in LIBOR models which are more tractable than the simulation of the full SDE. A numerical example for the L\'evy LIBOR model illustrates our method.

  • STRONG TAYLOR APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS AND APPLICATION TO THE L EVY LIBOR MODEL
    arXiv: Probability, 2009
    Co-Authors: Antonis Papapantoleon, Maria Siopacha
    Abstract:

    In this article we consider the strong approximation of sto- chastic dierential equations driven by L evy processes or general semi- martingales. The main ingredients of our method is the perturbation of the SDE and the Taylor expansion of the resulting Parameterized Curve. We apply this method to develop strong approximation schemes for LIBOR market models. In particular, we derive fast and precise algo- rithms for the valuation of derivatives in LIBOR models which are more tractable than the simulation of the full SDE. A numerical example for the L evy LIBOR model illustrates our method.

Aurélie Fischer - One of the best experts on this subject based on the ideXlab platform.

  • Parameter Selection for Principal Curves
    IEEE Transactions on Information Theory, 2012
    Co-Authors: Gérard Biau, Aurélie Fischer
    Abstract:

    Principal Curves are nonlinear generalizations of the notion of first principal component. Roughly, a principal Curve is a Parameterized Curve in which passes through the “middle” of a data cloud drawn from some unknown probability distribution. Depending on the definition, a principal Curve relies on some unknown parameters (number of segments, length, turn, etc.) which have to be properly chosen to recover the shape of the data without interpolating. In this paper, we consider the principal Curve problem from an empirical risk minimization perspective and address the parameter selection issue using the point of view of model selection via penalization. We offer oracle inequalities and implement the proposed approach to recover the hidden structures in both simulated and real-life data.

  • Parameter selection for principal Curves
    2011
    Co-Authors: Gérard Biau, Aurélie Fischer
    Abstract:

    Principal Curves are nonlinear generalizations of the notion of first principal component. Roughly, a principal Curve is a Parameterized Curve in Rd which passes through the "middle" of a data cloud drawn from some unknown probability distribution. Depending on the definition, a principal Curve relies on some unknown parameters (number of segments, length, turn. . . ) which have to be properly chosen to recover the shape of the data without interpolating. In the present paper, we consider the principal Curve problem from an empirical risk minimization perspective and address the parameter selection issue using the point of view of model selection via penalization. We offer oracle inequalities and implement the proposed approaches to recover the hidden structures in both simulated and real-life data.

J. Diebolt - One of the best experts on this subject based on the ideXlab platform.

  • On the density of the maximum of smooth Gaussian processes
    The Annals of Probability, 1996
    Co-Authors: C. Posse, J. Diebolt
    Abstract:

    We obtain an integral formula for the density of the maximum of smooth Gaussian processes. This expression induces explicit nonasymptotic lower and upper bounds which are in general asymptotic to the density. Moreover, these bounds allow us to derive simple asymptotic formulas for the density with rate of approximation as well as accurate asymptotic bounds. In particular, in the case of stationary processes, the latter upper bound improves the well-known bound based on Rice's formula. In the case of processes with variance admitting a finite number of maxima, we refine recent results obtained by Konstant and Piterbarg in a broader context, producing the rate of approximation for suitable variants of their asymptotic formulas. Our constructive approach relies on a geometric representation of Gaussian processes involving a unit speed Parameterized Curve embedded in the unit sphere.

  • Nonasymptotic Formulae for the Distribution of the Maximum of Smooth Gaussian Processes
    1994
    Co-Authors: J. Diebolt, C. Posse
    Abstract:

    Abstract : We derive an integral formula for the density of the maximum of smooth Gaussian processes. This expression induces explicit lower and upper bounds which are in general asymptotic to the density. Our constructive approach relies on a geometric representation of Gaussian processes involving a unit speed Parameterized Curve embedded in the unit sphere.

Chen Jian-hong - One of the best experts on this subject based on the ideXlab platform.

  • Automatic Identification Algorithm for Complicated Regions of Parameterized Curve Set
    Computer Engineering, 2010
    Co-Authors: Chen Jian-hong
    Abstract:

    According to the automation and general requirements of Parameterized Curve set regions identification algorithm,spatial organization of regions generated by Parameterized Curve set is represented using multi-tree structure.Based on the establishment of directional closed loops,a new method for identification of complex regions is proposed for the automation and general applicability.Compared with the other methods,this method is effective for regions with holes and islands.It has wide adaptability and is easy to implement.

  • Method for target region identification based on graph theory from Parameterized Curve set
    Computer Engineering and Applications, 2010
    Co-Authors: Chen Jian-hong
    Abstract:

    Identification for region generated by Parameterized Curve set in plane is the base of pattern filling.At present,several algorithms for area-filling in raster graphics field are proposed,but there are difficulties of detection for region generated by Parameterized Curve set.Based on the spatial theory,some issues about the region identification are studied.The main researches concentrate on representation and relations of regions.Based on the concepts and property of directional closed loop,this paper proposes an algorithm for region identification and plane Parameterized Curve set.Experiments show this algorithm has wide adaptability and is easy to implement,and has been applied in Dimine software.