A Variational Approach to Reconstructing Images Corrupted by Poisson Noise

We propose a new variational model to denoise an image corrupted by Poisson noise. Like the ROF model described in [1] and [2], the new model uses total-variation regularization, which preserves edges. Unlike the ROF model, our model uses a data-fidelity term that is suitable for Poisson noise. The result is that the strength of the regularization is signal dependent, precisely like Poisson noise. Noise of varying scales will be removed by our model, while preserving low-contrast features in regions of low intensity. Funded by the Department of Energy under contract W-7405ENG-36. Triet M. Le received his Ph.D. in Mathematics from the University of California, Los Angeles, in 2006. He is now a Gibbs Assistant Professor in the Mathematics Department at Yale University. His research interests are in applied harmonic analysis and function spaces with application to image analysis and inverse problems. Rick Chartrand received a Ph.D. in Mathematics from UC Berkeley in 1999, where he studied functional analysis. He now works as an applied mathematician at Los Alamos National Laboratory. His research interests are image and signal processing, inverse problems, and classification. Tom Asaki is a staff member in the Computer and Computational Science Division at Los Alamos National Laboratory. He obtained his doctorate in physics from Washington State University. His interests are mixed-variable and direct-search optimization, applied inverse problems, and quantitative tomography.     

Centroidal Voronoi Tessellation Algorithms for Image Compression, Segmentation, and Multichannel Restoration

Centroidal Voronoi tessellations (CVT's) are special Voronoi tessellations for which the generators of the tessellation are also the centers of mass (or means) of the Voronoi cells or clusters. CVT's have been found to be useful in many disparate and diverse settings. In this paper, CVT-based algorithms are developed for image compression, image segmenation, and multichannel image restoration applications. In the image processing context and in its simplest form, the CVT-based methodology reduces to the well-known k-means clustering technique. However, by viewing the latter within the CVT context, very useful generalizations and improvements can be easily made. Several such generalizations are exploited in this paper including the incorporation of cluster dependent weights, the incorporation of averaging techniques to treat noisy images, extensions to treat multichannel data, and combinations of the aforementioned. In each case, examples are provided to illustrate the efficiency, flexibility, and effectiveness of CVT-based image processing methodologies. Qiang Du is a Professor of Mathematics at the Pennsylvania State University. He received his Ph.D. from the Carnegie Mellon University in 1988. Since then, he has held academic positions at several institutions such as the University of Chicago and the Hong Kong University of Science and Technology. He has published over 100 papers on numerical algorithms and their various applications. His recent research works include studies of bio-membranes, complex fluids, quantized vortices, micro-structure evolution, image and data analysis, mesh generation and optimization, and approximations of partial differential equations. Max Guzburger is the Frances Eppes Professor of Computational Science and Mathematics at Florida State University. He received his Ph.D. degree from New York University in 1969 and has held positions at the University of Tennessee, Carnegie Mellon University, Virginia Tech, and Iowa State University. He is the author of five books and over 225 papers. His research interest include computational methods for partial differential equations, control of complex systems, superconductivity, data mining, computational geometry, image processing, uncertainty quantification, and numerical analysis. Lili Ju is an Assistant Professor of Mathematics at the University of South Carolina, Columbia. He received a B.S. degree in Mathematics from Wuhan University in China in 1995, a M.S. degree in Computational Mathematics from the Chinese Academy of Sciences in 1998, and a Ph.D. in Applied Mathematics from Iowa State University in 2002. From 2002 to 2004, he was an Industrial Postdoctoral Researcher at the Institute of Mathematics and Its Applications at the University of Minnesota. His research interests include numerical analysis, scientific computation, parallel computing, and medical image processing. Xiaoqiang Wang is a graduate student in mathematics at the Pennsylvania State University, working under the supervision of Qiang Du. Starting in September 2005, he will be an Industrial Postdoctoral Researcher at the Institute of Mathematics and its Applications at the University of Minnesota. His research interests are in the fields of applied mathematics and scientific computation. His work involves numerical simulation and analysis, algorithms for image processing and data mining, parallel algorithms, and high-performance computing.     

One-bit algorithms

Many algorithms in distributed systems assume that the size of a single message depends on the number of processors. In this paper, we assume in contrast that messages consist of a single bit. Our main goal is to explore how the one-bit translation of unbounded message algorithms can be sped up by pipelining. We consider two problems. The first is routing between two processors in an arbitrary network and in some special networks (ring, grid, hypercube). The second problem is coloring a synchronous ring with three colors. The routing problem is a very basic subroutine in many distributed algorithms; the three coloring problem demonstrates that pipelining is not always useful. Amotz Bar-Noy received his B.Sc. degree in Mathematics and Computer Science in 1981, and his Ph.D. degree in Computer Science in 1987, both from the Hebrew University of Jerusalem, Israel. Between 1987 and 1989 he was a post-doctoral fellow in the Department of Computer Science at Stanford University. He is currently a visiting scientist at the IBM Thomas J. Watson Research Center. His current research interests include the theoretical aspects of distributed and parallel computing, computational complexity and combinatorial optimization. Joseph (Seffi) Naor received his B.A. degree in Computer Science in 1981 from the Technion, Israel Institute of Technology. He received his M.Sc. in 1983 and Ph.D. in 1987 in Computer Science, both from the Hebrew University of Jerusalem, Israel. Between 1987 and 1988 he was a post-doctoral fellow at the University of Southern California, Los Angeles, CA. Since 1988 he has been a post-doctoral fellow in the Department of Computer Science at Stanford University. His research interests include combinatorial optimization, randomized algorithms, computational complexity and the theoretical aspects of parallel and distributed computing. Moni Naor received his B.A. in Computer Science from the Technion, Israel Institute of Technology, in 1985, and his Ph.D. in Computer Science from the University of California at Berkeley in 1989. He is currently a visiting scientist at the IBM Almaden Research Center. His research interests include computational complexity, data structures, cryptography, and parallel and distributed computation.Supported in part by a Weizmann fellowship and by contract ONR N00014-85-C-0731Supported by contract ONR N00014-88-K-0166 and by a grant from Stanford's Center for Integrated Systems. This work was done while the author was a post-doctoral fellow at the University of Southern California, Los Angeles, CAThis work was done while the author was with the Computer Science Division, University of California at Berkeley, and Supported by NSF grant DCR 85-13926     

Trends in agent-based computational modeling of macroeconomics

Based on the 50 papers surveyed in Reference,²⁾ this paper addresses general research trends in agent-based macroeconomics. On the aspect ofagent engineering, we highlight two major developments: first, the extensive applications of computational intelligence tools in modeling adaptive behavior, and second the grounding of these applications in the cognitive sciences. Shu-Heng Chen, Ph.D.: He is a professor in the Department of Economics of the National Chengchi University. He now serves as the director of the AI-ECON Research Center, National Chengchi University, the editor-in-chief of the forthcoming journal “Fuzzy Mathematics and Natural Computing” (World Scientific) and a member of the Editorial Board of The Journal of Management and Economics. Dr. Chen holds a M.A. degree in mathematics and a Ph.D. in Economics from the University of California at Los Angeles. His research interests are mainly on the applications of computational intelligence to the agent-based computational economics and finance.     

A Variational Model for Capturing Illusory Contours Using Curvature

Illusory contours, such as the classical Kanizsa triangle and square [9], are intrinsic phenomena in human vision. These contours are not completely defined by real object boundaries, but also include illusory boundaries which are not explicitly present in the images. Therefore, the major computational challenge of capturing illusory contours is to complete the illusory boundaries. In this paper, we propose a level set based variational model to capture a typical class of illusory contours such as Kanizsa triangle. Our model completes missing boundaries in a smooth way via Euler’s elastica, and also preserves corners by incorporating curvature information of object boundaries. Our model can capture illusory contours regardless of whether the missing boundaries are straight lines or curves. We compare the choice of the second order Euler’s elastica used in our model and that of the first order Euler’s elastica developed in Nitzberg-Mumford-Shiota’s work on the problem of segmentation with depth [15, 16]. We also prove that with the incorporation of curvature information of objects boundaries our model can preserve corners as completely as one wants. Finally we present the numerical results by applying our model on some standard illusory contours. This work has been supported by ONR contract N00014-03-1-0888, NSF contract DMS-9973341 and NIH contract P20 MH65166. Wei Zhu received the B.S. degree in Mathematics from Tsinghua University in 1994, the M.S. degree in Mathematics from Peking University in 1999, and the Ph.D. degree in Applied Mathematics from UCLA in 2004. He is currently a Postdoc at Courant Institute, New York University. His research interests include mathematical problems in image processing and visual neuroscience. Tony Chan received the B.S. degree in engineering and the M.S. degree in aerospace engineering, both in 1973, from the California Institute of Technology, Pasadena, and the Ph.D. degree in computer science from Stanford University, Stanford, CA, in 1978. Heis currently the Dean of the Division of Physical Science and College of Letters and Science, UCLA, where he has been a Professor in the Department of Mathematics since 1986. His research interests include PDE methods for image processing, multigrid, and domain decomposition algorithms, iterative methods, Krylov subspace methods, and parallel algorithms.     

Nonlinear Projection Recovery in Digital Inpainting for Color Image Restoration

This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized color image inpainting problem and the restoration of digital signals. In particular, we discuss the problem of reconstructing a digital signal/image from very few, sparse, and complete information and from a substantially incomplete information, which will be assumed as the result of a nonlinear distortion. Differently from well known inpainting applications for the recovery of gray images, the proposed techniques apply to color images embedding blanks where only gray level information is given. As a typical and inspiring example, we illustrate the concrete problem of the color restoration of a destroyed art fresco from its few known fragments and some gray picture taken prior to the damage. Numerical implementations are included together with several examples and numerical results to illustrate the proposed method. The numerical experience suggests furthermore that a particular system of coupled Hamilton-Jacobi equations is well-posed. Massimo Fornasier received his Ph.D. degree in Computational Mathematics on February 2003 at the University of Padova, Italy. Within the European network RTN HASSIP (Harmonic Analysis and Statistics for Signal and Image Processing) HPRN-CT-2002-00285, he cooperated as PostDoc with NuHAG (the Numerical Harmonic Analysis Group), Faculty of Mathematics of the University of Vienna, Austria and the AG Numerical/Wavelet-Analysis Group of the Department of Mathematics and Computer Science of the Philipps-University in Marburg, Germany (2003). Since June 2003 he is research assistant at the Department of Mathematical Methods and Models for the Applied Science at the University of Rome “La Sapienza”. Since May 2004 he is Individual Marie Curie Fellow (project FTFDORF-FP6-501018) at NuHAG. His research interests include applied harmonic analysis with particular emphasis on time-frequency analysis and decompositions for applications in signal and image processing. Since 1998, he developed with Domenico Toniolo the Mantegna Project (http://www.pd.infn.it/~labmante/) at the University of Padova and the local laboratory for image processing and applications in art restoration. Recently he has focused his attention on adaptive and dynamical schemes for the numerical solution of (pseudo) differential equations and inverse problems in digital signal processing.     

Shape Estimation from Support and Diameter Functions

We address the problem of reconstructing a planar shape from a finite number of noisy measurements of its support function or its diameter function. New linear and non-linear algorithms are proposed, based on the parametrization of the shape by its Extended Gaussian Image. This parametrization facilitates a systematic statistical analysis of the problem via the Cramér-Rao lower bound (CRLB), which provides a fundamental lower bound on the performance of estimation algorithms. Using CRLB, we also generate confidence regions which conveniently display the effect of parameters like eccentricity, scale, noise, and measurement direction set, on the quality of the estimated shapes, as well as allow a performance analysis of the algorithms. Supported in part by U.S. National Science Foundation grants CCR-9984246 and DMS-0203527. Amyn Poonawala received the B.E. degree from the University of Mumbai, India, in 2001, and the M.S. degree from the University of California, Santa Cruz (UCSC), in 2004, both in computer engineering. He is currently pursuing the Ph.D. degree in computer engineering at UCSC. His technical interests include statistical signal and image processing and inverse problems in microlithography. Peyman Milanfar received the B.S. degree in electrical engineering/mathematics from the University of California, Berkeley, in 1988, and the S.M., E.E., and Ph.D. degrees in electrical engineering from the Massachusetts Institute of Technology, in 1990, 1992, and 1993, respectively. Until 1999, he was a Senior Research Engineer at SRI International, Menlo Park, CA. He is currently Associate Professor of Electrical Engineering at the University of California, Santa Cruz. He was a Consulting Assistant Professor of computer science at Stanford University from 1998-2000, and a visiting Associate Professor there in 2002. His technical interests are in statistical signal and image processing, and inverse problems. He won a National Science Foundation CAREER award in 2000, was associate editor for the IEEE Signal Processing Letters from 1998 to 2001, and is a Senior member of the IEEE. Richard Gardner holds B.Sc. and Ph.D. degrees in mathematics from University College London and was awarded a D.Sc. degree from the University of London in 1988 for contributions to measure theory and convex geometry. He has held positions at universities and research institutions in several countries and has been Professor of Mathematics at Western Washington University since 1991. He founded geometric tomography, an area of geometric inverse problems involving data concerning sections by and projections on lines or planes, and published a book on the subject in 1995.     

Recent Progress on Selected Topics in Database Research ——-A Report by Nine Young Chinese Researchers Working in the United States

The study on database technologies, or more generally, the technologies of data and information management, is an important and active research field. Recently, many exciting results have been reported. In this fast growing field, Chinese researchers play more and more active roles. Research papers from Chinese scholars, both in China and abroad,appear in prestigious academic forums.In this paper,we, nine young Chinese researchers working in the United States, present concise surveys and report our recent progress on the selected fields that we are working on.Although the paper covers only a small number of topics and the selection of the topics is far from balanced, we hope that such an effort would attract more and more researchers,especially those in China,to enter the frontiers of database research and promote collaborations. For the obvious reason, the authors are listed alphabetically, while the sections are arranged in the order of the author list.     

On Semismooth Newton’s Methods for Total Variation Minimization

In [2], Chambolle proposed an algorithm for minimizing the total variation of an image. In this short note, based on the theory on semismooth operators, we study semismooth Newton’s methods for total variation minimization. The convergence and numerical results are also presented to show the effectiveness of the proposed algorithms. The research of this author is supported in part by Hong Kong Research Grants Council Grant Nos. 7035/04P and 7035/05P, and HKBU FRGs. The research of this author is supported in part by the Research Grant Council of Hong Kong. This work was started while the author was visiting Department of Applied Mathematics, The Hong Kong Polytechnic University. The research of this author is supported in part by The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme and the National Science Foundation of China (No. 60572114). Michael Ng is a Professor in the Department of Mathematics at the Hong Kong Baptist University. As an applied mathematician, Michael’s main research areas include Bioinformatics, Data Mining, Operations Research and Scientific Computing. Michael has published and edited 5 books, published more than 140 journal papers. He is the principal editor of the Journal of Computational and Applied Mathematics, and the associate editor of SIAM Journal on Scientific Computing. Liqun Qi received his B.S. in Computational Mathematics at Tsinghua University in 1968, his M.S, and Ph.D. degree in Computer Sciences at University of Wisconsin-Madison in 1981 and 1984, respectively. Professor Qi has taught in Tsinghua University, China, University of Wisconsin-Madison, USA, University of New South Wales, Australia, and The Hong Kong Polytechnic University. He is now Chair Professor of Applied Mathematics at The Hong Kong Polytechnic University. Professor Qi has published more than 140 research papers in international journals. He established the superlinear and quadratic convergence theory of the generalized Newton method, and played a principal role in the development of reformulation methods in optimization. Professor Qi’s research work has been cited by the researchers around the world. According to the authoritative citation database ISIHighlyCited.com, he is one of the world’s most highly cited 300 mathematicians during the period from 1981 to 1999. Yu-Fei Yang received the B.Sc., M.S. and Ph.D. degrees in mathematics from Hunan University, P. R. China, in 1987, 1994 and 1999, respectively. From 1999 to 2001, he stayed at the University of New South Wales, Australia as visiting fellow. From 2002 to 2005, he held research associate and postdoctoral fellowship positions at the Hong Kong Polytechnic University. He is currently professor in the College of Mathematics and Econometrics, at Hunan University, P. R. China. His research interests includes optimization theory and methods, and partial differential equations with applications to image analysis. Yu-Mei Huang received her M.Sc. in Computer science from Lanzhou University in 2000. She is now pursuing her doctoral studies in computational mathematics in Hong Kong Baptist University. Her research interests are in image processing and numerical linear algebra.     

Identification of stable description elements using an active sensor

A two-phase method for the pattern-driven recognition of objects in images is presented, implemented, and tested numerically. The method is based on the use of an active sensor. Possibilities for development are envisaged. This approach was shown to have advantages in solving the object-background separation problem and a high recognition rate was achieved with slow learning. Dmitrii I. Mednikov. Born in 1987. Fifth-year student at the Faculty of Mathematics and Mechanics of Moscow State University. Scientific interests include image recognition and image processing. Author of one paper. Alexei Milovidov. Born in 1986. Graduated from the Faculty of Mathematics and Mechanics of Moscow State University in 2008. Scientific interests include image recognition. Author of 3 papers. Semen Yu. Sergunin. Born in 1980. Graduated from the Faculty of Mathematics and Mechanics of Moscow State University in 2002. Postgraduate student at the same faculty. Scientific interests include image recognition. Author of five papers. Mikhail I. Kumskov. Born in 1956. Graduated from the Faculty of Computational Mathematics and Cybernetics of Moscow State University in 1978. Received his candidate’s degree in Physics and Mathematics in 1981 and doctoral degree in 1997. Professor at the Department of Computational Mathematics of the Faculty of Mathematics and Mechanics of Moscow State University. Scientific interests include the prediction of properties of chemical compounds, optimization of structural objects representation for classification problems, and image processing. Author of more than 50 papers.     

Geo-located image categorization and location recognition

Image categorization is undoubtedly one of the most recent and challenging problems faced in Computer Vision. The scientific literature is plenty of methods more or less efficient and dedicated to a specific class of images; further, commercial systems are also going to be advertised in the market. Nowadays, additional data can also be attached to the images, enriching its semantic interpretation beyond the pure appearance. This is the case of geo-location data that contain information about the geographical place where an image has been acquired. This data allow, if not require, a different management of the images, for instance, to the purpose of easy retrieval from a repository, or of identifying the geographical place of an unknown picture, given a geo-referenced image repository. This paper constitutes a first step in this sense, presenting a method for geo-referenced image categorization, and for the recognition of the geographical location of an image without such information available. The solutions presented are based on robust pattern recognition techniques, such as the probabilistic Latent Semantic Analysis, the Mean Shift clustering and the Support Vector Machines. Experiments have been carried out on a couple of geographical image databases: results are actually very promising, opening new interesting challenges and applications in this research field. The article is published in the original. Marco Cristani received the Laurea degree in 2002 and the Ph.D. degree in 2006, both in Computer Science from the University of Verona, Verona, Italy. He was a visiting Ph.D. student at the Computer Vision Lab, Institute for Robotics and Intelligent Systems School of Engineering (IRIS), University of Southern California, Los Angeles, in 2004–2005. He is now an Assistant Professor with the Department of Computer Science, University of Verona, working with the Vision, Image Processing and Sounds (VIPS) Lab. His main research interests include statistical pattern recognition, generative modeling via graphical models, and non-parametric data fusion techniques, with applications on surveillance, segmentation and image and video retrieval. He is the author of several papers in the above subjects and a reviewer for several international conferences and journals. Alessandro Perina received the BD and MS degrees in Information Technologies and Intelligent and Multimedia Systems from the University of Verona, Verona, Italy, in 2004 and 2006, respectively. He is currently a Ph.D. candidate in the Computer Science Department at the University of Verona. His research interests include computer vision, machine learning and pattern recognition. He is a student member of the IEEE. Umberto Castellani is Ricercatore (i.e., Research Assistant) of Department of Computer Science at University of Verona. He received his Dottorato di Ricerca (Ph.D.) in Computer Science from the University of Verona in 2003 working on 3D data modelling and reconstruction. During his Ph.D., he had been Visiting Research Fellow at the Machine Vision Unit of the Edinburgh University, in 2001. In 2007 he has been an Invited Professor for two months at the LASMEA laboratory in Clermont-Ferrand, France. In 2008, he has been Visiting Researcher for two months at the PRIP laboratory of the Michigan State University (USA). His main research interests concern the processing of 3D data coming from different acquisition systems such as 3D models from 3D scanners, acoustic images for the vision in underwater environment, and MRI scans for biomedical applications. The addressed methodologies are focused on the intersections among Machine Learning, Computer Vision and Computer Graphics. Vittorio Murino received the Laurea degree in electronic engineering in 1989 and the Ph.D. degree in electronic engineering and computer science in 1993, both from the University of Genoa, Genoa, Italy. He is a Full Professor with the Department of Computer Science, University of Verona. From 1993 to 1995, he was a Postdoctoral Fellow in the Signal Processing and Understanding Group, Department of Biophysical and electronic Engineering, University of Genoa, where he supervised of research activities on image processing for object recognition and pattern classification in underwater environments. From 1995 to 1998, he was an Assistant Professor of the Department of Mathematics and Computer Science, University of Udine, Udine, Italy. Since 1998, he has been with the University of Verona, where he founded and is responsible for the Vision, Image processing, and Sound (VIPS) Laboratory. He is scientifically responsible for several national and European projects and is an Evaluator for the European Commission of research project proposals related to different scientific programmes and frameworks. His main research interests include computer vision and pattern recognition, probabilistic techniques for image and video processing, and methods for integrating graphics and vision. He is author or co-author of more than 150 papers published in refereed journals and international conferences. Dr. Murino is a referee for several international journals, a member of the technical committees for several conferences (ECCV, ICPR, ICIP), and a member of the editorial board of Pattern Recognition, IEEE Transactions on Systems, Man, and Cybernetics, Pattern Analysis and Applications and Electronic Letters on Computer Vision and Image Analysis (ELCVIA). He was the promotor and Guest Editor off our special issues of Pattern Recognition and is a Fellow of the IAPR.     

划痕图像的连分式插值修补算法

目的 图像修复在图像处理中起着举足轻重的地位,针对目前大部分图像修补算法在修复划痕时存在纹理修复不够突出的缺陷,提出了两种基于连分式插值的修补算法,可以较好保持图像纹理的特性。方法 该算法基于连分式插值理论,采用图像破损点周围像素信息来插值出破损点的像素值。根据插值函数和插值窗口的不同,提出了两种插值方法,即Thiele型修补算法与Newton-Thiele型修补算法,解决不同纹理类型图像的划痕修补问题,并对插值过程中出现的奇异点问题和平移问题提出了行之有效的解决办法。结果 对大量的划痕图像进行实验测试,并通过主观评价和客观评价进行评估。客观评价包括峰值信噪比（PSNR）和运行时间的比较。相对于目前流行的一些修补方法来说,本文算法有更好的视觉效果,更高的峰值信噪比和更短的运行时间,峰值信噪比为44.79 dB,运行时间为0.53 s。结论 Thiele型修补算法更加擅长处理纹理垂直于划痕的图像,而Newton-Thiele型修补算法适用于复杂纹理的图像。     

Geometric Analysis of Particle Motion in a Vector Image Field

This paper proposes a geometrical model for the Particle Motion in a Vector Image Field (PMVIF) method. The model introduces a c-evolute to approximate the edge curve in the gray-level image. The c-evolute concept has three major novelties: (1) The locus of Particle Motion in a Vector Image Field (PMVIF) is a c-evolute of image edge curve; (2) A geometrical interpretation is given to the setting of the parameters for the method based on the PMVIF; (3) The gap between the image edge’s critical property and the particle motion equations appeared in PMVIF is padded. Our experimental simulation based on the image gradient field is simple in computing and robust, and can perform well even in situations where high curvature exists. Chenggang Lu received his Bachelor of Science and PhD degrees from Zhejiang University in 1996 and 2003, respectively. Since 2003, he has been with VIA Software (Hang Zhou), Inc. and Huawei Technology, Inc. His research interests include image processing, acoustic signaling processing, and communication engineering. Zheru Chi received his BEng and MEng degrees from Zhejiang University in 1982 and 1985 respectively, and his PhD degree from the University of Sydney in March 1994, all in electrical engineering. Between 1985 and 1989, he was on the Faculty of the Department of Scientific Instruments at Zhejiang University. He worked as a Senior Research Assistant/Research Fellow in the Laboratory for Imaging Science and Engineering at the University of Sydney from April 1993 to January 1995. Since February 1995, he has been with the Hong Kong Polytechnic University, where he is now an Associate Professor in the Department of Electronic and Information Engineering. Since 1997, he has served on the organization or program committees for a number of international conferences. His research interests include image processing, pattern recognition, and computational intelligence. Dr. Chi has authored/co-authored one book and nine book chapters, and published more than 140 technical papers. Gang Chen received his Bachelor of Science degree from Anqing Teachers College in 1983 and his PhD degree in the Department of Applied Mathematics at Zhejiang University in 1994. Between 1994 and 1996, he was a postdoctoral researcher in electrical engineering at Zhejiang University. From 1997 to 1999, he was a visiting researcher in the Institute of Mathematics at the Chinese University of Hong Kong and the Department of Electronic and Information Engineering at The Hong Kong Polytechnic University. Since 2001, he has been a Professor at Zhejiang University. He has been the Director of the Institute of DSP and Software Techniques at Ningbo University since 2002. His research interests include applied mathematics, image processing, fractal geometry, wavelet analysis and computer graphics. Prof. Chen has co-authored one book, co-edited five technical proceedings and published more than 80 technical papers. (David) Dagan Feng received his ME in Electrical Engineering & Computing Science (EECS) from Shanghai JiaoTong University in 1982, MSc in Biocybernetics and Ph.D in Computer Science from the University of California, Los Angeles (UCLA) in 1985 and 1988 respectively. After briefly working as Assistant Professor at the University of California, Riverside, he joined the University of Sydney at the end of 1988, as Lecturer, Senior Lecturer, Reader, Professor and Head of Department of Computer Science/School of Information Technologies, and Associate Dean of Faculty of Science. He is Chair-Professor of Information Technology, Hong Kong Polytechnic University; Honorary Research Consultant, Royal Prince Alfred Hospital, the largest hospital in Australia; Advisory Professor, Shanghai JiaoTong University; Guest Professor, Northwestern Polytechnic University, Northeastern University and Tsinghua University. His research area is Biomedical & Multimedia Information Technology (BMIT). He is the Founder and Director of the BMIT Research Group. He has published over 400 scholarly research papers, pioneered several new research directions, made a number of landmark contributions in his field with significant scientific impact and social benefit, and received the Crump Prize for Excellence in Medical Engineering from USA. More importantly, however, is that many of his research results have been translated into solutions to real-life problems and have made tremendous improvements to the quality of life worldwide. He is a Fellow of ACS, HKIE, IEE, IEEE, and ATSE, Special Area Editor of IEEE Transactions on Information Technology in Biomedicine, and is the current Chairman of IFAC-TC-BIOMED.     

Naming symmetric processes using shared variables

Summary Implementations of inter-process communication and synchronization in distributed systems usually rely on the existence of unique ids for the processes. We consider the problem of generating such ids for identical processes in a shared-variable system. A randomized protocol that assigns distinct ids to the processes within an expected polynomial number of rounds using a polynomial number of boolean atomic variables is presented. Ömer Eeciolu obtained his Ph.D. degree in mathematics from the University of California, San Diego in 1984. At present he is an Associate Professor in the Computer Science department of the University of California, Santa Barbara, where he has been on the faculty since 1985. His principal areas of research are parallel algorithms, bijective and enumerative combinatorics, and combinatorial algorithms. His current interest in parallel algorithms involve approximation and numerical techniques on distributed memory systems while his combinatorial interests center around computational geometry, bijective methods, and ranking algorithms for combinatorial structures. Ambuj K. Singh is an Assistant Professor in the Department of Computer Science at the University of California, Santa Barbara. He received a Ph.D. in Computer Science from the University of Texas at Austin in 1989, an M.S. in Computer Science from Iowa State University in 1984, and a B. Tech. from the Indian Institute of Technology at Kharagpur in 1982. His research interests are in the areas of adaptive resource allocation, concurrent program development, and distributed shared memory.Work supported in part by NSF grants CCR-9008628 and CCR-9223094     

Variational Image Binarization and its Multi-Scale Realizations

A variational approach for image binarization is discussed in this paper. The approach is based on the interpolation of surface. This interpolation is computed using edge points as interpolating points and minimizing an energy functional which interpolates a smooth threshold surface. A globally convergent Sequential Relaxation Algorithm (SRA) is proposed for solving the optimization problem. Moreover, our algorithm is also formulated in a multi-scale framework. The performance of our method is demonstrated on a variety of real and synthetic images and compared with traditional techniques. Examples show that our method gives promising results.This research is partially supported by HKBU Faculty Research Grant FRG/02-03/II-04 and NSF of China Grant. C.S. Tong received a BA degree in Mathematics and a Ph.D. degree (on Mathematical Modelling of Intermolecular Forces) both from Cambridge University. After graduation, he joined the Signal and Image Processing division of GEC-Marconis Hirst Research Centre as a Research Scientist, working on image restoration and fractal image compression. He then moved to the Department of Mathematics at Hong Kong Baptist University in 1992, becoming Associate Professor since 2002.He is a member of the IEEE, a Fellow of the Institute of Mathematics and Its Application, and a Chartered Mathematician. His current research interests include image processing, fractal image compression, and neural networks. Yongping Zhang received the M. S. degree from Department of Mathematics at Shaanxi Normal University, Xian, China, in 1988 and received the Ph.D. degree from The Institute of Artificial Intelligence and Robotics at Xian Jiaotong University, Xian, China, in 1998.In 1988 he joined Department of Mathematics at Shaanxi Normal University, where he became Associate Professor in July 1987. He held postdoctoral position at Northwestern Polytechnic University during the 1999–2000 academic years. Currently he is a research associate in the Bioengineering Institute at the University of Auckland, New Zealand. His research interests are in Computer Vision and Pattern Recognition, and include Wavelets, Neural Networks, PDE methods and variational methods for image processing. Nanning Zheng received the M.S. degree from Xian Jiaotong University, Xian, China, in 1981 and the Ph.D. degree from Keio University, Japan, in 1985. He is an academician of Chinese Engineer Academy, and currently a Professor at Xian Jiaotong University. His research interest includes Signal Processing, Machine Vision and Image Processing, Pattern Recognition and Virtual Reality.This revised version was published online in June 2005 with correction to CoverDate     

A Cortical Based Model of Perceptual Completion in the Roto-Translation Space

We present a mathematical model of perceptual completion and formation of subjective surfaces, which is at the same time inspired by the architecture of the visual cortex, and is the lifting in the 3-dimensional rototranslation group of the phenomenological variational models based on elastica functional. The initial image is lifted by the simple cells to a surface in the rototranslation group and the completion process is modeled via a diffusion driven motion by curvature. The convergence of the motion to a minimal surface is proved. Results are presented both for modal and amodal completion in classic Kanizsa images. The work was supported by University of Bologna: founds for selected research topics. Giovanna Citti is full professor of Mathematical Analysis at University of Bologna, and she is coordinator, together with A.Sarti, of the local interdipartimental group of “Neuromathematics and Visual Cognition”. Her principal research interests are existence and regularity of solution of nonlinear subelliptic equations represented as sum of squares of vector fields, whose associated geometry is subriemannian. Besides she is interested in applications of instruments of real analysis in Lie Groups and subriemannian geometry to visual perception, and to the study of the functionality of the visual cortex. Alessandro Sarti received the Ph.D. degree in bioengineering from the University of Bologna in 1996. From 1997 to 2000 he was appointed with a Postdoc position at the Mathematics Department of the University of California, Berkeley, and the Mathematics Department of the Lawrence Berkeley National Laboratory in Berkeley. Since 2001 he got a permanent position at the University of Bologna. He is associate to CREA, Ecole Polytechnique, Paris, France. With Giovanna Citti, he is the scientific responsible of the interdipartimental group of “Neuromathematics and Visual Cognition.” In the last years he gave lectures at the University of Yale, University of California at Los Angeles, University of California at Berkeley, Freie Universitat Berlin, Ecole Normale Superieure Cachan, Ecole Polytechnique, Scuola Normale Superiore di Pisa.     

A content-based image authentication scheme based on singular value decomposition

In this paper, we propose an image authentication scheme in which image features are embedded for copyright protection and content-tampering detection. The features are based on the invariance of the relationship among SVD coefficients. The proposed method is sensitive to malicious manipulations and robust to lossy compressions or regular image operations, such as brightening, shifting, averaging, rotation, and so on. Several experiments demonstrated that the proposed scheme could efficiently detect locations which have been tampered with and effectively resist several types of attacks. Moreover, stego images based on our proposed method have high visual quality. The text was submitted by the authors in English. Tzu-Chuen Lu received the B.M. degree (1999) and MSIM degree (2001) in information management from Chaoyang University of Technology, Taiwan. She received her Ph.D. degree (2006) in computer engineering from National Chung Cheng University. Her current title is an Assistant Professor in Departament of Information Management from Chaoyang University of Technology. Her current research interests include data mining, image retrieval, image authentication, information hiding, and knowledge management. Chin-Chen Chang received his B.S. degree in applied mathematics in 1977 and the M.S. degree in computer and decision sciences in 1979, both from the National Tsing Hua University, Hsinchu, Taiwan. He received his Ph.D. in computer engineering in 1982 from the National Chiao Tung University, Hsinchu, Taiwan. From August 1995 to October 1997, he was the provost at the National Chung Cheng University. From September 1996 to October 1997, Dr. Chang was the Acting President at the Nationa Chung Cheng University. From July 1998 to June 2000, he was a director of the Ministry of Education of China. In addition, he has served as a consultant to several research institutes and government departments. His current research interests include database design, computer cryptography, image compression and data structures. Yi-Long Liu received the B.S. degree (2002) in the Department of Mathematics (Applied Mathematics Section) from the College of Science and Engineering at Fu-Jen Catholic University, Taiwan. Liu is now a Master student in National Chung Cheng University and is studying in the domain of image processing. His current research interests include data hiding, data compression, and progressive image transmission.     

Fundamental Groups of Unbounded Digital Images

Recent papers have discussed homotopy properties of digital images. Most of the papers concerned with this topic restrict their attention to bounded digital images, and there are significant errors in some of the literature concerned with unbounded digital images. In this paper, we examine fundamental groups of unbounded digital images. Laurence Boxer is Professor, and past Chair, of Computer and Information Sciences at Niagara University, and Research Professor of Computer Science and Engineering at the State University of New York at Buffalo. He holds a Bachelor’s degree in Mathematics from the University of Michigan; Master’s and PhD in Mathematics from the University of Illinois; and a Master’s in Computer Science from the State University of New York at Buffalo. Dr. Boxer’s research interests are in digital topology and algorithms.     

Two fusion predictors for discrete-time linear systems with different types of observations

New fusion predictors for linear dynamic systems with different types of observations are proposed. The fusion predictors are formed by summation of the local Kalman filters/predictors with matrix weights depending only on time instants. The relationship between fusion predictors is established. Then, the accuracy and computational efficiency of the fusion predictors are demonstrated on the first-order Markov process and the GMTI model with multisensor environment. Recommended by Editorial Board member Lucy Y. Pao under the direction of Editor Young Il Lee. This work was partially supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MOST), No. R01-2007-000-20227-0 and the Center for Distributed Sensor Network at GIST. Ha-Ryong Song received the B.S. degree in Control and Instrumentation Engineering from the Chosun University, Korea, in 2006, the M.S. degree in School of Information and Mechatronics from the Gwangju Institute of Science and Technology, Korea, in 2007. He is currently a Ph.D. candidate in Gwangju Institute of Science and Technology. His research interests include estimation, target tracking systems, data fusion, nonlinear filtering. Moon-Gu Jeon received the B.S. degree in architectural engineering from the Korea University, Korea in 1988. He then received both the M.S. and Ph.D. degrees in computer science and scientific computation from the University of Minnesota in 1999 and 2001, respectively. Currently, he is an Associate Professor at the School of Information and Mechatronics of the Gwangju Institute of Science and Technology (GIST). His current research interests are in machine learning and pattern recognition and evolutionary computation. Tae-Sun Choi received the B.S. degree in Electrical Engineering from the Seoul National University, Seoul, Korea, in 1976, the M.S. degree in Electrical Engineering from the Korea Advanced Institute of Science and Technology, Seoul, Korea, in 1979, and the Ph.D. degree in Electrical Engineering from the State University of New York at Stony Brook, in 1993. He is currently a Professor in the School of Information and Mechatronics at Gwangju Institute of Science and Technology, Korea. His research interests include image processing, machine/robot vision, and visual communications. Vladimir Shin received the B.Sc. and M.Sc. degrees in Applied Mathematics from Moscow State Aviation Institute, in 1977 and 1979, respectively. In 1985 he received the Ph.D. degree in Mathematics at the Institute of Control Science, Russian Academy of Sciences, Moscow. He is currently an Associate Professor at Gwangju Institute of Science and Technology, South Korea. His research interests include estimation, filtering, tracking, data fusion, stochastic control, identification, and other multidimensional data processing methods.     

Edge-Forming Methods for Image Zooming

The article is concerned with edge-forming methods to be applied as a post-process for image zooming. Image zooming via standard interpolation methods often produces the so-called checkerboard effect, in particular, when the magnification factor is large. In order to remove the artifact and to form reliable edges, a nonlinear semi-discrete model and its numerical algorithm are suggested along with anisotropic edge-forming numerical schemes. The algorithm is analyzed for stability and choices of parameters. For image zooming by integer factors, a few iterations of the algorithm can form clear and sharp edges for gray-scale images. Various examples are presented to show effectiveness and efficiency of the newly-suggested edge-forming strategy. The work of this author is supported in part by NSF grant DMS–0312223. Youngjoon Cha received his B.Sc. (1988) and M.Sc. (1990) from Mathematics, Seoul National University, Seoul, South Korea; and Ph.D. (1996) from Mathematics, Purdue University, working on mathematical epidemiology, under a guidance of Prof. Fabio Milner. He was a post-doctoral researcher at Purdue University, and Seoul National University, South Korea, from 1996 to 1997 and from 1997 to 1998, respectively. He is currently an associate professor in the Department of Applied Mathematics, Sejong University, South Korea. His research interests include image processing, mathematical and numerical modeling for waves, and mathematical epidemiology. Seongjai Kim received his B.Sc. (1988) and M.Sc. (1990) from Mathematics, Seoul National University, Seoul, South Korea; and Ph.D. (1995) from Mathematics, Purdue University, working on computational fluid dynamics, under a guidance of Prof. Jim Douglas, Jr. After two years of post-doctoral research on seismic inversion at Rice University, he worked for Shell E&P Tech. Co., Houston, for a year and the Department of Mathematics, University of Kentucky, for seven years. He is currently an associate professor in the Department of Mathematics and Statistics, Mississippi State University. His research interests are in mathematical and numerical modeling for wave propagation in highly heterogeneous media, seismology, and image processing for challenging images.