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.     

Error Analysis for Image Inpainting

Image inpainting refers to restoring a damaged image with missing information. In recent years, there have been many developments on computational approaches to image inpainting problem [2, 4, 6, 9, 11–13, 27, 28]. While there are many effective algorithms available, there is still a lack of theoretical understanding on under what conditions these algorithms work well. In this paper, we take a step in this direction. We investigate an error bound for inpainting methods, by considering different image spaces such as smooth images, piecewise constant images and a particular kind of piecewise continuous images. Numerical results are presented to validate the theoretical error bounds. Tony F. Chan received the B.S. degree in engineering and the M.S. degree in aerospace engineering in 1973, from the California Institute of Technology, and the Ph.D. degree in computer science from Stanford University in 1978. He is Professor of Mathematics and currently also Dean of the division of Physical science at University of California, Los Angeles, where he has been a Professor since 1986. His research interests include mathematical and computational methods in image processing, multigrid, domain decomposition algorithms, iterative methods, Krylov subspace methods, and parallel algorithms. Sung Ha Kang received the Ph.D. degree in mathematics in 2002, from University of California, Los Angeles, and currently is Assistant Professor of Mathematics at University of Kentucky since 2002. Her research interests include mathematical and computational methods in image processing and computer vision.     

Neural network algorithms for analyzing multidimensional time series for predicting events and their application to study of Sun-Earth relations

In the paper, an original neural network algorithm for analysis of time series is presented. This algorithm allows predicting the occurrence of a certain event and finding a time interval to which a phenomenon (a precursor or a cause of the event) belongs. The characteristics of the algorithm functioning are investigated applied to the study of the solar-terrestrial relationship. Yu. V. Orlov. Candidate in Physics and Mathematics. Researcher at the Institute of Nuclear Physics, Moscow State University. Scientific interests: neural networks, genetic algorithms, algorithms of pattern recognition and image analysis. Yu. S. Shugai. Researcher at the Institute of Nuclear Physics, Moscow State University. Scientific interests: neural networks, genetic algorithms, algorithms of pattern recognition and image analysis, algorithms of classification and prediction. I. G. Persiantsev. Professor, Doctor in Mathematics and Physics. Head of the Laboratory, Leading Researcher at the Institute of Nuclear Physics, Moscow State University Scientific interests: neural networks, genetic algorithms, algorithms of pattern recognition and image analysis, algorithms of classification and prediction, inverse problems. Laureate of the USSR State Prize. S. A. Dolenko. Candidate in Physics and Mathematics. Senior Researcher at the Institute of Nuclear Physics, Moscow State University. Scientific interests: neural networks, genetic algorithms, algorithms of pattern recognition and image analysis, algorithms of classification and prediction, inverse problems.     

Construction and Application of Hybrid Wavelet and Other Parametric Orthogonal Transforms

We introduce new methods for construction and implementation of various parametric and hybrid orthogonal transforms, including generalized Haar-like, Daubechies, and Coiflet wavelet transforms. The corresponding fast algorithms of computations are briefly discussed and the variance properties of these transforms in analyzing 1-st order Markov processes are investigated. The designed hybrid transforms can be useful in various specific signal processing applications where combining properties of Hadamard and wavelet transforms may be of particular benefit. We also present some numerical results pertaining to image zonal and threshold coding using these hybrid transforms and compare their efficacy with those of traditional orthogonal transforms.Hakob Sarukhanyan received his M.S. degree in Applied Mathematics from Yerevan State University in 1973, and his Ph.D. and D.Sc. degrees in Technical Sciences from the National Armenian Academy of Sciences (NAAS) in 1982 and 1999 accordingly. He has worked as a faculty in the Department of Applied Mathematics at Yerevan State University in 1968–73, and as a junior and senior researcher in the Laboratory of Image Processing Systems at the Institute for Informatics and Automation Problems (IIAP) of the NAAS in 1973–93. He has been the Head of the above Laboratory since 1993 and has been elected a member of the Doctoral Council at IIAP in 2000. He has been a visiting professor at the Tampere Institute of Technology, Finland, in 1999–2001. He is a recipient of research grants from various European funding agencies as well as from the US Civilian and Research Foundation (sponsored by the NSF and the US Department of State). His main research interests are in construction of Hadamard matrices and their applications in wireless communications, combinatorics theory, and fast orthogonal transforms for image processing. He is the author of more than 70 scientific publications in major scientific media.Arthur Petrosian received his M.S. Summa Cum Laude degree in Mathematics from Moscow State University in 1983, and a Ph.D. in Applied Mathematics from the Institute for Problems of Informatics & Automation of the National Armenian Academy of Sciences in 1989. He was a visiting scientist at the Institute of General and Physical Chemistry at Belgrade University, Yugoslavia (1991), an NIH supported postdoctoral fellow at the University of Michigan, Ann Arbor (1992–93), and a research instructor at the Medical College of Ohio, Toledo (1993–94). He joined Texas Tech University Health Sciences Center as an Assistant Professor in 1994, and was appointed as an Adjunct Professor of Mathematics and Electrical and Computer Engineering at Texas Tech University in 1995. He was promoted to the Associate Professor level at Texas Tech University Health Sciences Center in 2000. While at Texas Tech, he received a number of research grant awards to conduct research in EEG signal processing and in biomedical signal/image compression, including from the Federal Administration on Aging, Alzheimers Association, and the US Civilian and Research Foundation (sponsored by the NSF and the US Department of State, to promote cooperative research between the wavelet theory groups in United States and ex-USSR). He is a Senior Member of IEEE and a past member of the New York Academy of Sciences. He is currently a Scientific Review Administrator in the Surgery, Biomedical Imaging, and Bioengineering integrated review group at the National Institutes of Health, US Department of Health and Human Services.     

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.     

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 Numerical Scheme for the Curvature Equation Near the Singularities

In this paper we propose a modification in the usual numerical method for computing the solutions of the curvature equation in the plane . This modification takes place near the singularities of the image. We propose to use zero as the vertical speed at a saddle point and, at an extremum, the geometric mean of the eigenvalues of the Hessian matrix. This modification is theoretically justified and the preliminary experimental results show that it makes the algorithm more reliable.Marcos Craizer has a degree in mathematics from UFRJ (Rio de Janeiro), a M.Sc. from IMPA (Rio de Janeiro) and received his Ph.D. in mathematics also from IMPA, in 1989. His research interests in image processing includes image representation, curve evolution and PDE applications. Since 1988, he has been working at the math department of PUC-Rio, Brazil.Sinésio Pesco is an Assistant Professor of the Department of Mathematics at Pontifical Catholic University of Rio de Janeiro (PUCRio). He received his Ph.D. and MS degree in Applied Mathematics at PUC-Rio and a B.S. degree in mathematics from State University of Maringa Brasil. He has visiting positions at Lawrence Livermore National Laboratory, CSE/OGI School of Science and Engineering (Oregon Health & Science University) and Scientific Computation and Imaging Insititute (University of UTAH). His main research interests are in Computational Topology, Image Processing and Scientific Visualization. Since 1991, he has been working in the development of a CAD system for petroleum reservoir modeling.Ralph Teixeira has a degree in Computer Engineering from IME (in Rio), a M.Sc. from IMPA (also in Rio) and received his Ph.D. in Mathematics from Harvard University in 1998. His research interests in Computer Vision include shape representations by skeletons (medial axis and similar objects), curve evolutions and PDE applications. Since 2001, he has been working at Fundação Getulio Vargas in Rio de Janeiro, Brazil.     

Digital Products, Wedges, and Covering Spaces

The paper [9] introduces the important tool of the digital covering space for studying the digital fundamental group. From a classical construction of algebraic topology [16,17,19], we show the existence of digital universal covering spaces and their significance for the study of the digital fundamental group. 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 received a Bachelor’s in Mathematics from the University of Michigan at Ann Arbor; Master’s and PhD in Mathematics from the University of Illinois at Urbana-Champaign; and Master’s in Computer Science from the State University of New York at Buffalo. Dr. Boxer’s research interests are in the fields of algorithms and digital topology. He is co-author of Algorithms Sequential and Parallel: A Unified Approach, an innovative textbook whose second edition is published by Charles River Media.     

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.     

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.     

Mobile geoinformation systems

The geoinformation system for handheld computers (PDAs) makes it possible to solve a wide range of geographically dispersed data (GDD) processing problems. The developed program software (PS) based on effective models and GDD processing methods has allowed significantly increasing the GDD processing rate in PDAs. Yurii G. Vasin was born in 1940 and graduated from Gor’kii State University in 1962. He received his doctoral (doctor of science) degree in 1988 and was a recipient of the Prize of the Council of Ministers of the USSR in 1990. He is the director of the Research Institute of Applied Mathematics and Cybernetics of the State University of Nizhni Novgorod. His scientific interests include theoretical and applied computer science, pattern recognition and image processing, and information technologies, and he is the author of more than 100 publications. Sergei V. Zherzdev was born in 1976 and graduated from the State University of Nizhni Novgorod in 1999. He is a software engineer at the Research Institute of Applied Mathematics and Cybernetics of the State University of Nizhni Novgorod. His scientific interests include theoretical and applied computer science and data compression techniques. He is the author of 7 publications. Andrei A. Egorov was born in 1982 and graduated from the State University of Nizhni Novgorod in 2006. He is a programmer at the Research Institute of Applied Mathematics and Cybernetics of the State University of Nizhni Novgorod, and his scientific interests include hierarchical structures of data storage on mobile platforms. He is the author of 2 inventions and 7 publications.     

Automatic transaction of signal via statistical modeling

The statistical information processing can be characterized by the likelihood function defined by giving an explicit form for an approximation to the true distribution. This mathematical representation, which is usually called a model, is built based on not only the current data but also prior knowledge on the object and the objective of the analysis. Akaike^2,3) showed that the log-likelihood can be considered as an estimate of the Kullback-Leibler (K-L) information which measures the similarity between the predictive distribution of the model and the true distribution. Akaike information criterion (AIC) is an estimate of the K-L information and makes it possible to evaluate and compare the goodness of many models objectively. In consequence, the minimum AIC procedure allows us to develop automatic modeling and signal extraction procedures. In this article, we give a simple explanation of statistical modeling based on the AIC and demonstrate four examples of applying the minimum AIC procedure to an automatic transaction of signals observed in the earth sciences. Genshiro, Kitagawa, Ph.D.: He is a Professor in the Department of Prediction and Control at the Institute of Statistical Mathematics. He is currently Deputy Director of the Institute of Statistical Mathematics and Professor of Statistical Science at the Graduate University for Advanced Study. He obtained his Ph.D. from the Kyushu University in 1983. His primary research interests are in time series analysis, non-Gaussian nonlinear filtering, and statistical modeling. He has published over 50 research papers. He was awarded the 2nd Japan Statistical Society Prize in 1997. Tomoyuki Higuchi, Ph.D.: He is an Associate Professor in the Department of Prediction and Control at the Institute of Statistical Mathematics. He is currently an Associate Professor of Statistical Science at the Graduate University for Advanced Study. He obtained his Ph.D. from the University of Tokyo in 1989. His research interests are in statistical modeling of space-time data, stochastic optimization techniques, and data mining. He has published over 30 research papers.     

Properties of Digital Homotopy

Several recent papers have adapted notions of geometric topology to the emerging field of digital topology. An important notion is that of digital homotopy. In this paper, we study a variety of digitally-continuous functions that preserve homotopy types or homotopy-related properties such as the digital fundamental group.Laurence Boxer is Professor 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 received his Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign. His research interests are computational geometry, parallel algorithms, and digital topology. Dr. Boxer is co-author, with Russ Miller, of Algorithms Sequential and Parallel, A Unified Approach, a recent textbook published by Prentice Hall.     

On the suitability of Biological structure determination by electron microscopy to Grid Computing

The present contribution describes a potential application of Grid Computing in Bioinformatics. High resolution structure determination of biological specimens is critical in BioSciences to understanding the biological function. The problem is computational intensive. Distributed and Grid Computing are thus becoming essential. This contribution analyzes the use of Grid Computing and its potential benefits in the field of electron microscope tomography of biological specimens. Jose-Jesus Fernandez, Ph.D.: He received his M.Sc. and Ph.D. degrees in Computer Science from the University of Granada, Spain, in 1992 and 1997, respectively. He was a Ph.D. student at the Bio-Computing unit of the National Center for BioTechnology (CNB) from the Spanish National Council of Scientific Research (CSIC), Madrid, Spain. He became an Assistant Professor in 1997 and, subsequently, Associate Professor in 2000 in Computer Architecture at the University of Almeria, Spain. He is a member of the supercomputing-algorithms research group. His research interests include high performance computing (HPC), image processing and tomography. Jose-Roman Bilbao-Castro: He received his M.Sc. degree in Computer Science from the University of Almeria in 2001. He is currently a Ph.D. student at the BioComputing unit of the CNB (CSIC) through a Ph.D. CSIC-grant in conjuction with Dept. Computer Architecture at the University of Malaga (Spain). His current research interestsinclude tomography, HPC and distributed and grid computing. Roberto Marabini, Ph.D.: He received the M.Sc. (1989) and Ph.D. (1995) degrees in Physics from the University Autonoma de Madrid (UAM) and University of Santiago de Compostela, respectively. He was a Ph.D. student at the BioComputing Unit at the CNB (CSIC). He worked at the University of Pennsylvania and the City University of New York from 1998 to 2002. At present he is an Associate Professor at the UAM. His current research interests include inverse problems, image processing and HPC. Jose-Maria Carazo, Ph.D.: He received the M.Sc. degree from the Granada University, Spain, in 1981, and got his Ph.D. in Molecular Biology at the UAM in 1984. He left for Albany, NY, in 1986, coming back to Madrid in 1989 to set up the BioComputing Unit of the CNB (CSIC). He was involved in the Spanish Ministry of Science and Technology as Deputy General Director for Research Planning. Currently, he keeps engaged in his activities at the CNB, the Scientific Park of Madrid and Integromics S.L. Immaculada Garcia, Ph.D.: She received her B.Sc. (1977) and Ph.D. (1986) degrees in Physics from the Complutense University of Madrid and University of Santiago de Compostela, respectively. From 1977 to 1987 she was an Assistant professor at the University of Granada, from 1987 to 1996 Associate professor at the University of Almeria and since 1997 she is a Full Professor and head of Dept. Computer Architecture. She is head of the supercomputing-algorithms research group. Her research interest lies in HPC for irregular problems related to image processing, global optimization and matrix computation.     

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.     

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.     

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.     

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.     

Dual-coding representations for robot vision programming in Tekkotsu

We describe complementary iconic and symbolic representations for parsing the visual world. The iconic pixmap representation is operated on by an extensible set of “visual routines” (Ullman, 1984; Forbus et al., 2001). A symbolic representation, in terms of lines, ellipses, blobs, etc., is extracted from the iconic encoding, manipulated algebraically, and re-rendered iconically. The two representations are therefore duals, and iconic operations can be freely intermixed with symbolic ones. The dual-coding approach offers robot programmers a versatile collection of primitives from which to construct application-specific vision software. We describe some sample applications implemented on the Sony AIBO. David S. Touretzky is a Research Professor in the Computer Science Department and the Center for the Neural Basis of Cognition at Carnegie Mellon University. He earned his B.A. in Computer Science from Rutgers University in 1978, and his M.S. (1979) and Ph.D. (1984) in Computer Science from Carnegie Mellon. Dr. Touretzky’s research interests are in computational neuroscience, particularly representations of space in the rodent hippocampus and related structures, and high level primitives for robot programming. He is presently developing an undergraduate curriculum in cognitive robotics based on the Tekkotsu software framework described in this article. Neil S. Halelamien earned a B.S. in Computer Science and a B.S. in Cognitive Science at Carnegie Mellon University in 2004, and is currently pursuing his Ph.D. in the Computation & Neural Systems program at the California Institute of Technology. His research interests are in studying vision from both a computational and biological perspective. He is currently using transcranial magnetic stimulation to study visual representations and information processing in visual cortex. Ethan J. Tira-Thompson is a graduate student in the Robotics Institute at Carnegie Mellon University. He earned a B.S. in Computer Science and a B.S. in Human-Computer Interaction in 2002, and an M.S. in Robotics in 2004, at Carnegie Mellon. He is interested in a wide variety of computer science topics, including machine learning, computer vision, software architecture, and interface design. Ethan’s research has revolved around the creation of the Tekkotsu framework to enable the rapid development of robotics software and its use in education. He intends to specialize in mobile manipulation and motion planning for the completion of his degree. Jordan J. Wales is completing a Master of Studies in Theology at the University of Notre Dame. He earned a B.S. in Engineering (Swarthmore College, 2001), an M.Sc. in Cognitive Science (Edinburgh, UK, 2002), and a Postgraduate Diploma in Theology (Oxford, UK, 2003). After a year as a graduate research assistant in Computer Science at Carnegie Mellon, he entered the master’s program in Theology at Notre Dame and is now applying to doctoral programs. His research focus in early and medieval Christianity is accompanied by an interest in medieval and modern philosophies of mind and their connections with modern cognitive science. Kei Usui is a masters student in the Robotics Institute at Carnegie Mellon University. He earned his B.S. in Physics from Carnegie Mellon University in 2005. His research interests are reinforcement learning, legged locomotion, and cognitive science. He is presently working on algorithms for humanoid robots to maintain balance against unexpected external forces.