Notícias

Palestra 'Image Processing by Polynomial Computations'

may 5th | 11h00 | Room I-105 DEEC

Image Processing by Polynomial Computations :: Joab Winkler, Department of Computer Science :: The University of Sheffield, United Kingdom Image deblurring - the removal of blur from an image - is one of the most important problems in image processing. Much research effort has been devoted to it, and many methods have been developed. It is usually assumed that the degradation process that causes the blur is not known, in which case image deblurring reduces to the problem of blind image deconvolution. It is shown in this talk that blind image deconvolution can be performed by polynomial computations, such that the Fourier and wavelet transforms are not required. In this polynomial approach to image deblurring, the blurred image and point spread function (PSF) are represented by bivariate polynomials. It will be shown that the PSF can be computed from greatest common divisor (GCD) computations on two regions of the given blurred image, where the GCD computations are performed using the Sylvester resultant matrix. The deblurred image is then obtained by deconvolving the PSF from the blurred image. The effectiveness of this method of deblurring relies on extensive use of structured matrices. The talk will include a complete derivation of the equivalence between image deblurring and bivariate polynomial deconvolution, and the role of the Sylvester resultant matrix for the computation of the PSF will be included. Examples of blind image deconvolution will be presented, including comparisons with the deconvolution methods in the image processing toolbox in Matlab. The talk will conclude with a discussion of future work. Biography of Joab Winkler :: Department of Computer Science, The University of Sheffield Education and research JoabWinkler obtained his undergraduate (BSc) and postgraduate (PhD) degrees at Imperial College of Science and Technology, and University College London, respectively. He worked in industry for a few years after graduation, and he then returned to academia. In particular, he joined the University of Sheffield in 1997, where he is now a Reader (Associate Professor) in The Department of Computer Science. Joab's main research interest is algebraic and numerical problems of curves and surfaces in geometric modelling and computer aided design systems. He has worked extensively on computational problems associated with resultant matrices, which are used for the calculation of the points of intersection of curves and surfaces. The main technical challenge is the ill-posed nature of these problems, which implies that advanced numerical methods are required to obtain computationally reliable solutions, that is, solutions that are insensitive to noise. This is an important requirement for practical problems because of the uncertainty that is associated with the data in these problems. In the course of this work, he and his research students developed a polynomial root solver for the computation of multiple roots of a polynomial, which is important in geometric modelling because multiple roots of polynomials are associated with smooth (tangential) intersections of curves and surfaces. Joab has recently carried out research in image deblurring, which is an important problem in image processing. Many methods have been developed for the solution of this problem, but Joab showed that the mathematical methods required for the solution of important problems in geometric modelling and computer aided design systems can be used to deblur an image. In particular, an image is considered a bivariate polynomial, from which it follows that operations that arise frequently in polynomial computations, for example, greatest common divisor computations and deconvolution, can be applied to deblur an image. The main advantage of this method of image deblurring with respect to other methods is that less information is required. In particular, the point spread function is calculated and it is not assumed that it is known, and similarly, it is not assumed that the noise level is known. The absence of the need to specify these quantities arises because advanced methods of computational linear algebra are used to perform the polynomial operations. Joab has published extensively in academic journals, including Journal of Computational and Applied Mathematics, Computer Aided Geometric Design, Linear Algebra and Its Applications and SIAM J. Numerical Analysis. He has also reviewed papers for these and other journals in computational and applied mathematics. Lectures, awards and conference organization Joab has lectured abroad extensively, including New York University, USA, City University of New York, USA, The University of Pisa, Italy, Charles University Prague, Czech Republic, The Czech Technical University, Prague, Czech Republic, The Mathematics Division of The Czech Academy of Sciences, Prague, Czech Republic, The University of Athens, Greece, The Technion Haifa, Israel, and Tel Aviv University, Israel. In 2007, Joab organised a Summer School, held at Oxford University, on polynomial and greatest common divisor computations (http://ml.dcs.shef.ac.uk/summer−school/). This School provided a series of lectures and computer laboratory classes to postgraduate students and new academics on new methods of polynomial computations. Also, he and colleagues from Greece (University of Athens), Italy (University of Pisa) and Belgium (Catholic University of Leuven) are organising a conference, to be held in September 2014, on structured matrices (http://noether.math.uoa.gr/conferences/sla2014/). Joab was awarded a Global Research Award by The Royal Academy of Engineering (http://www.raeng.org.uk/) in 2010, which allowed him to spend three months at The City University of New York, USA, working with Professor Victor Pan. Joab used this award to carry out further work on computationally robust operations on polynomials. :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Disclose your events and projects by e-mail noticias@fe.up.pt. Find out more about our services in SICC site.