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Event(s) on June 2006


  • Thursday, 1st June, 2006

    Title: Super-Resolution Reconstruction Using Haar Wavelet Estimation
    Speaker: Mr. Leung King Tai, Department of Mathematics, Hong Kong Baptist Univeristy, China
    Time/Place: 10:00  -  11:00
    FSC 1217
    Abstract: High resolution image reconstruction refers to the reconstruction of a high resolution image from a set of shifted, blurred low resolution images. Many methods have been developed, and most of them are iterative methods. In this paper, we present a direct method to obtain the reconstruction. Our method takes advantages of the properties of Haar wavelet transform of the high resolution image and its relationship with the low resolution images. Thus the coefficients of the Haar wavelet transform of the high resolution image can be estimated from the low resolution images. Our method is very simple to implement and is very efficient. Experiments showed that it is robust to boundary conditions and is superior to the least - squares method especially in the low-noise case.


  • Thursday, 1st June, 2006

    Title: CMIV - Using Multivariate Splines to Study Problems in Discrete Mathematics
    Speaker: Prof. Zhi-qiang Xu, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
    Time/Place: 14:30  -  15:30
    FSC 1217
    Abstract: It is well known that multivariate splines are an important tool in numerical analysis. In this talk, we shall show multivariate splines are also very useful for solving problems in discrete mathematics. We shall survey some results as follows about solving problems in discrete mathematics using multivariate splines. 1. By using multivariate splines, we shall give an explicit formulation for counting non-negative solutions for linear Diophantine equations. 2. We shall show the iterated formulation for computing multivariate cone splines can be used to compute the volume of convex polytopes. Hence, some famous formulations about volume computation of polytopes follow from the properties of multivariate cone splines. 3. According to multivariate Box splines, the famous Popoviciu's formulation in number theory is generalized. 4. An explicit formulation for Ehrhart polynomial which counts integer points in polytopes is also given. Finally, some challenging problems in this area are also raised.


  • Wednesday, 7th June, 2006

    Title: CMIV - Active Contour Method for Image Segmentation & Segmentation with Shape and Intensity Priors
    Speaker: Prof. Yunmei Chen, Department of Mathematics, University of Florida, USA
    Time/Place: 11:00  -  12:00
    FSC 1217
    Abstract: Lecture 1: Active Contour Method for Image Segmentation In this talk we first expose the basic idea of the active contour method for image segmentation by reviewing two typical variational models. One of them is the geodesic active contour, an edge based segmentation model that uses the image gradient information. The other one is the cartoon form of Mumford-Shah scheme, a region based model that uses regional statistics of the intensity distribution. Both parametric and implicit forms of the models are discussed to show the application of level set method in PDE based modelling. We also present some new development of these two models and our recent work in finding objects in the images with high noise level and intensity inhomogeneity.


  • Wednesday, 7th June, 2006

    Title: CMIV - Active Contour Method for Image Segmentation & Segmentation with Shape and Intensity Priors
    Speaker: Prof. Yunmei Chen, Department of Mathematics, University of Florida, USA
    Time/Place: 15:30  -  16:30
    FSC 1217
    Abstract: Lecture 2: Segmentation with Shape and Intensity Priors We present a coupled minimization problem for image segmentation using prior shape and intensity profile. One part of the model minimizes an image based energy and a shape related energy with a parameter that balances the influence from these two. The minimizer corresponding to a fixed parameter in this minimization gives a segmentation and an alignment between the segmentation and prior shape. The second part of this model optimizes the selection of the parameter by maximizing the mutual information of image geometry between the prior and the aligned novel image over all the alignments corresponding to different parameters in the first part. By this coupling the segmentation arrives at higher image gradient, forms a shape similar to the prior, and captures the prior intensity profile. We also propose using mutual information of image geometry to generate intensity model from a set of training images. Experimental results on cardiac ultrasound images are presented. These results indicate that the proposed model provides close agreement with expert traced borders, and the parameter determined in this model for one image can be used for images with similar properties.


  • Tuesday, 13th June, 2006

    Title: Dynamics of Firing Activities and Synchronization in Neuronal Systems
    Speaker: Prof. Qishao Lu, Department of Mathematics and Division of General mechanics,School of Science, Beijing University of Aeronautics and Astronautics, China
    Time/Place: 11:30  -  12:30
    FSC 1217
    Abstract: Neural firing is crucial to the information processing in the nervous system, and there are many complex firing patterns observed in neural experiments and numerical simulations. Since 1980s, a number of advances in the field of nonlinear science has provided some necessary theoretical concepts and powerful tools for deeper understanding of neural firing patterns. The concepts of nonlinear dynamics, such as chaos, bifurcation and stochastic resonance, were successfully employed to investigate the complex firing patterns and their generation mechanisms. Based on these advances, a combination of neuroscience and nonlinear science was developed rapidly in the last two decades, and its new results have been earned in recognition of the basic dynamics of neural firing. This presentation is organized into three parts: (1) Some basic knowledge about neuron systems is introduced. (2) Firing patterns of some famous neuron models and their dynamical mechanisms are analyzed by means of the bifurcation theory and fast/slow dynamics. (3) Several types of synchronization and their transitions in coupled neurons are studied in terms of theoretical analysis and numerical simulations.