Colloquium/Seminar

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Event(s) on April 2014


  • Thursday, 3rd April, 2014

    Title: CMIV Colloquium - Signal Denoising and Shape-from-shading using Mean Curvature
    Speaker: Dr. Andy YIP, Department of Mathematics, National University of Singapore, Singapore
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, we present two applications of curvature regularization. First, we consider the problem of signal denoising. Total variation regularization has been widely studied and used because of its ability to preserve edges and discontinuities. However, the reconstructed signals often exhibit staircase artifacts and reduced contrast. Various researchers have shown that using curvature to regularize signals can overcome many of these drawbacks. Unfortunately, the resulting optimality condition is 4th-order nonlinear PDE which is more difficult to solve than the 2nd-order PDE arising from total variation. We propose a numerical method to solve the problem efficiently. Motivated by the work of Chan, Golub and Mulet, we introduce some auxiliary variables to linearize some of the equations. While a direct application of the Newton's method often fails to converge, we propose a modification which improves the convergence significantly. In our extensive experiments, quadratic convergence is observed. Second, we consider the problem of Shape-from-shading. We demonstrate that the use mean curvature regularization allows better reconstruction of various interesting features compared to classical models. Computing numerical solution of shape-from-shading problem is often very difficult because the fitting term has too many global minimizers. We demonstrate how we overcome this difficulty with some carefully designed initialization procedure.


  • Wednesday, 23rd April, 2014

    Title: The Relation Construction of TM-modes and Its Application for Nonhomogeneous Waveguides Terminated by PMLs
    Speaker: Prof. Jianxin ZHU, Department of Mathematics, Zhejiang University, China
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The modal computation with high-precision is an important issue for wave propagation in the optical waveguides when the eigenmode expansion method is applied. For an open waveguide, it is terminated by two perfectly matched layers. Then, by differential transfer matrix method, a nonlinear relation of modes for TM case is proposed for the complex waveguides with varied refractive index along the transverse direction. For the gradually varied waveguides, a higher approximation is provided and some asymptotic formulae of leaky modes are created, which may be used as the better initial values for some iteration methods. Numerical examples illustrate that our treatment is more feasible and effective.