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第40届中国控制会议

作者： Ruichen Zhang Shaofeng Bian Bing Ji Department of Navigation Naval University of Engineering

Fourier series of linear complementarity is introduced into the field of bathymetric data fitting. Firstly, in data preprocessing, the principles of grid processing in bathymetry is given in the paper. And then, different methods of complementarity（none complementarity, direct complementarity and linear complementarity） are compared and analyzed, which shows that the Fourier Series of linear complementarity method can effectively improve the convergence speed of modeling. And the result futher illustrated that the Fourier series of linear complementarity has a wide application in the bathymetric data processing.

关键词： Fourier series linear complementarity bathymetric data processing

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Homotopy Continuation Method for linear complementarity Problems

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Northeastern Mathematical Journal 2004年第3期20卷 309-316页

作者：刘国新于波 School of Mathematics Jilin University Changchun 130012 Department of Applied Mathematics Dalian University of Technology Dalian 116024t is well known that a linear complementarity problem (LCP) can be formulated as a system of nonsmooth equations F(x) = 0 where F is a map from Rninto itself. Using the aggregate function we construct a smooth Newton homotopy H(xt) = 0. Under certain assumptions we prove the existence of a smooth path defined by the Newton homotopy which leads to a solution of the original problem and study limiting properties of the homotopy path.

It is well known that a linear complementarity problem (LCP) can be formulated as a system of nonsmooth equations F(x) = 0, where F is a map from Rninto itself. Using the aggregate function, we construct a smooth Newton homotopy H(x,t) = 0. Under certain assumptions, we prove the existence of a smooth path defined by the Newton homotopy which leads to a solution of the original problem, and study limiting properties of the homotopy path.

关键词： linear complementarity aggregate function homotopy method

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Application of the Level-Set Model with Constraints in Image Segmentation

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Numerical Mathematics(Theory,Methods and Applications) 2016年第1期9卷 147-168页

作者： Vladimiır Klement Tomas Oberhuber Daniel Sevcovic Department of Mathematics Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PragueTrojanova 13Praha 212000Czech Republic Department of Applied Mathematics and Statistics Comenius University84248 BratislavaSlovakia

We proposeand analyze a constrained level-set method forsemi-automatic image segmentation.Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects.Such a-priori information can be expressed in terms of upper and lower constraints prescribed for the level-set function.Constraints have the same conceptual meaning as initial seeds of the popular graph-cuts based meth-ods for image segmentation.A numerical approximation scheme is based on the complementary-finite volumes method combined with the Projected successive over-relaxation method adopted for solving constrained linear complementarity prob-lems.The advantage of the constrained level-set method is demonstrated on several artificial images as well as on cardiac MRI data.

关键词： linear complementarity image processing segmentation level-set method projected successive over-relaxation method

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