December 6: 09:45-10:00 Registration and coffee 10:00-10:15 Introductory remarks 10:15-10:45 Sgallari 10:45-11:15 Morigi 11:15-11:45 Mørken 11:45-12:15 Rahman 12:15-13:05 Lunch 13:05-13:50 Heyden 13:50-14:20 Lundervold 14:30-15:30 Carlsson (Aud. Pi, Math institute) 15:30-15:40 Break 15:40-16:10 Hodneland 16:10-16:40 Clausen 16:40-17:10 Rasmussen 17:10-17:40 Floater Program (final) invited speakers underlined
Geometrical partial differential equations:
numerics and applications
Bergen 6-7 December 2006
 
December 7: 09:00-09:45 Schertzer 09:45-10:15 Li 10:15-10:45 Break 10:45-11:30 Didas 11:30-12:00 Mannseth 12:00-13:00 Lunch 13:00-13:45 louze 13:45-14:15 Rahman 14:14-14:45 Seland 14:45-15:15 Break 15:15-15:45 Anderlik 15:45-16:15 Zoellner 16:15-16:45 Heimsund 16:45-17:15 Nygaard 17:15-17:30 Concluding remarks
Alfatih Ali Unversity of Bergen email : Alfatih.Ali@student.uib.no Anderlik, Andrea University of Bergen email: Andreea.Anderlik@biomed.uib.no Bae, Egil Mathematics - University of Bergen email: egil.bae@student.uib.no Brox, Ivan UiB email: ivan.brox@student.uib.no Christiansen, Oddvar UiB email : oddvar@mi.uib.no Clausen, Sigmund SINTEF ICT email : sigmund.clausen@sintef.no Talk: Automatic segmentation of overlapping fish using shape priors Abstract: We present results from a study where we attempt to segment fish in images taken within fish cages. The ultimate goal is to use this information to extract the size distribution of the fish within the cages. Statistical shape knowledge is added to the Mumford-Shah functional following Cremers et. al. The fish shape is represented by a polygonial curve and the energy minimization is done by gradient descent. The images represent many challenges with a highly cluttered background, inhomogeneous lighting and several overlapping objects. We obtain good segmentation results for "silhouette-like" images containing releatively few fish. In this case the fish appears dark on a light background and the image energy is well behaved. In cases with more difficult ligthing conditions the contours evolve slowly and often get trapped in local minima.   Cremers D., Tischhäuser F., Weickert J., Scnörr C. Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah functional. International Journal of Computer Vision 50(3), 295-313, 2002. Espedal, Magne S. CIPR email : magne.espedal@mi.uib.no Floater, Michael Institutt for informatikk, UiO email : michaelf@ifi.uio.no Talk : Web-splines for solving PDE's Abstract: We give an introduction to the use of web-splines (Weighted Extended B-splines) for solving elliptic PDE's via a finite element method, due to Hollig, Reif, and Wipper. The method requires a "weight" function that behaves like the distance to the boundary of the domain but should be smoother. We describe a new approach to the latter, based on mean value interpolation. This is joint work with Christopher Dyken. Heimsund, Bjørn-Ove Center for Integrated Petroleum Research email: Bjorn-Ove.Heimsund@uib.no Talk : Meshing of domains with complex internal geometries Hodneland, Erlend University of Bergen email: erlend.hodneland@biomed.uib.no Talk : Level set methods for watershed image segmentation Abstract: We propose a marker-controlled and regularized watershed segmentation. Only a few previous studies address the task of regularizing the obtained watershed lines from the traditional marker-controlled watershed segmentation. In the present formulation, the to-pographical distance function is applied in a level set formulation to perform the segmentation, and the regularization is easily accomplished by regularizing the level set functions. Based on the well-known Four-Color theorem, a mathematical model is developed for the proposed ideas. With this model, it is possible to segment any 2D image with an arbitrary number of phases with as few as one or two level set functions. The algorithm has been tested on real 2D fluorescence microscopy images displaying rat cancer cells, and the algorithm has also been compared to a standard watershed segmentation as it is implemented in MATLAB. For a fixed set of markers and a fixed set of challenging images, the comparison of these two methods shows that the present level set formulation performs better than a standard watershed segmentation. Johannsen, Klaus BCCS, UiB, Bergen, Norway email : klaus.johannsen@bccs.uib.no Knudsen, Ørjan Institute for Mathematics, University of Bergen email : oek002@student.uib.no Li, Hongwei Center for Integrated Petroleum Research, UiB. email : hongwei.li@cipr.uib.no Talk: Permeability estimation for two-phase porous media flow by using a piecewise constant level set method Abstract: We consider the permeability estimation problem in two-phase porous media flow. Lie, Johan UiB email : johanl@mi.uib.no Lie, Knut-Andreas SINTEF ICT, Department of Applied Mathematics email: Knut-Andreas.Lie@sintef.no Lien, Martha CIPR email : martha.lien@cipr.uib.no Losnegård, Are Matematisk institutt, Universitetet i Bergen email: Are.Losnegard@student.uib.no Lundervold, Alexander Department of Mathematics, University of Bergen email : alexander.lundervold@student.uib.no Lundervold, Arvid University of Bergen email : arvid.lundervold@biomed.uib.no Talk: The role of mathematics in biomedical imaging In this talk there will be given examples how central fields of mathematics related to quantity (e.g. complex numbers and quaternions), structure (e.g. abstract algebra and group theory), space (e.g. differential geometry, topology, and fractal geometry), and change (e.g. calculus and differential equations) are increasingly important in the field of biomedical imaging. On the other hand, there are also examples on how practical problems in brain imaging can turn out to be a challenge in theoretical mathematics, blending aspects of topology and graph theory (i.e. the "spherical homeomorphism conjecture"). Mannseth, Trond CIPR email: trond.mannseth@cipr.uib.no Talk : Coarse-scale representation of level-set functions for solving inverse problems with low data density Abstract: In image segmentation and other applications, the ability to represent virtually any shape is a strong feature of level-set representation. With a discrete level-set function on a fine computational grid, a large number of function values are, however, required to fully utilize the flexibility offered. For many inverse problems, the data density is sparse, allowing for identification of only a very restricted number of parameters. This talk will consider use of level-set representation of the unknown parameter function for such inverse problems. The focus will be on how one can design a representation controlled by few parameters, but without giving up too much flexibility. This talk is based on a joint work with Inga Berre, Martha Lien, Trond Mannseth Munthe-Kaas, Hans Matematisk institutt, Universitet i Bergen email: hans@mi.uib.no Mørken, Knut Institutt for informatikk, Universitet i Oslo email: knutm@ifi.uio.no Talk : Some challenges in medical imaging and related areas Abstract : In this talk I will discuss some mathematical challenges that are encountered in practical applications of medical imaging. All the problems stem from research that is conducted at the Interventional Centre at the Rikshospitalet Hospital in Oslo. Nygaard, Jens Olav SINTEF applied mathematics Talk: Experiences from attempting to do non-rigid registration with splines email : Jens.O.Nygaard@sintef.no Oppedal, Ketil Department of Biomedicine, University of Bergen email : ketil.oppedal@student.uib.no Talal Rahman Department of Mathematics email: talal.rahman@mi.uib.no Talk: Denoising digital images with the TV Stokes algorithm Abstract: In this talk, we present a two-step algorithm for denoising digital images with additive noise. Observing that the isophote directions of an image correspond to an incompressible velocity field, we impose the constraint of zero divergence on the tangential field. Combined with an energy minimization problem corresponding to the smoothing of tangential vectors, this constraint gives rise to a nonlinear Stokes equation. Once the isophote directions are found, an image is reconstructed that fits those directions by solving another nonlinear partial differential equation. In both steps, we use finite difference schemes to solve. We present several numerical examples to show the effectiveness of our approach. Talal Rahman Department of Mathematics, University of Bergen email: talal.rahman@mi.uib.no Talk: PDE based image processing on the GPU Abstract: Recently, more and more scientific problems are being solved on programmable graphical units (GPU), entirely or partly together with the CPU. In many scientific applications it has been evident that a simulation on a GPU can be much faster than on a CPU. In this talk we give a brief introduction to computing on the GPU with application to image processing. Rasmussen, Atgeirr Flø CMA, UiO email: atgeirr@math.uio.no Talk : Reparametrization of surfaces using PDE methods First, a short introduction will be given to parametric surfaces and their properties. The remainder of the talk will deal with the issue of parametrization. Many surfaces used in industrial and other applications suffer from bad parametrizations. I will explain what we mean by a bad parametrization, what properties a good parametrization should have, and how we find such a parametrization by solving the Laplace-Beltrami PDE. Finally, I will show some numerical examples. Schulerud, Helene SINTEF email : hsc@sintef.no Seland, Johan Simon Center of Mathematics for Applications, Univ. of Oslo email: johans@cma.uio.no Talk: Real Time Algebraic Surface Visualization Abstract: Modern Graphics Hardware (aka GPUs) can be seen as high performance streaming co-processors, delivering tremendeous floating point performance, but demanding highly parallel and tuned algorithms in order to stay on the fast path. We present an overview of "the why's, how's, and why not's" of programming such streaming architechutures. We illustrate the programming model with an example, demonstraing how level sets of real algebraic surfaces can be visualized at interactive framerates. Xue-Cheng Tai Department of Mathematics, University of Bergen email: tai@mi.uib.no Talk : TBA Yao, Changhui CIPR, UIB email: changhui.yao@cipr.uib.no Talk : Finite Element Approximation for TV Regularization Abstract: In this paper, we will develop the convergence of the solution of the TV-regularization equations with regularized parameter $\varepsilon$ in $BV(\Omega)$ and extend this result to TV-regularization equations on the implicit surfaces whose situation will be discussed in the extension Sobolev space $BV_P(\Omega)$. Originated from the effects of regularized parameter $\varepsilon$, the error rate of convergence of finite element approximation will be depend on a constant $O(\frac{1}{\varepsilon})$, as well as the TV-regularization equations on implicit surfaces. This work will suggest that we have to choose an appropriate mesh size in order to keep numerical methods convergent when we use finite element methods to solve the TV-regularization problems. Ystad, Martin Department of Biomedicine, University of Bergen email : martin.ystad@student.uib.no Zanna, Antonella Matematisk institutt, University of Bergen email: anto@mi.uib.no Frank Zoellner University of Bergen email: frank.zoellner@biomed.uib.no Talk : Assessment of Total Kidney Volume in 3D DCE-MRI Time Series using Active Countours Abstract: In our work we have applied an active contour ("snake'') model to segment the total kidney volume. In contrast to most other snake models, the procedure is not dependent on a user for contour initialisation, as we take advantage of the segmentation results from a previous clustering step. To better adopt the model to our data, we have implemented a special image energy term that takes voxel time-course information into account. mailto:Alfatih.Ali@student.uib.nomailto:Andreea.Anderlik@biomed.uib.nomailto:egil.bae@student.uib.nomailto:ivan.brox@student.uib.nomailto:oddvar@mi.uib.nomailto:sigmund.clausen@sintef.nomailto:magne.espedal@mi.uib.nomailto:michaelf@ifi.uio.nomailto:Bjorn-Ove.Heimsund@uib.nomailto:erlend.hodneland@biomed.uib.nomailto:klaus.johannsen@bccs.uib.nomailto:oek002@student.uib.nomailto:hongwei.li@cipr.uib.nomailto:johanl@mi.uib.nomailto:Knut-Andreas.Lie@sintef.nomailto:martha.lien@cipr.uib.nomailto:Are.Losnegard@student.uib.nomailto:alexander.lundervold@student.uib.nomailto:arvid.lundervold@biomed.uib.nomailto:trond.mannseth@cipr.uib.nomailto:hans@mi.uib.nomailto:knutm@ifi.uio.nomailto:Jens.O.Nygaard@sintef.nomailto:ketil.oppedal@student.uib.nomailto:talal.rahman@mi.uib.nomailto:talal.rahman@mi.uib.nomailto:atgeirr@math.uio.nomailto:hsc@sintef.nomailto:johans@cma.uio.nomailto:tai@mi.uib.nomailto:changhui.yao@cipr.uib.nomailto:martin.ystad@student.uib.nomailto:anto@mi.uib.nomailto:frank.zoellner@biomed.uib.noshapeimage_4_link_0shapeimage_4_link_1shapeimage_4_link_2shapeimage_4_link_3shapeimage_4_link_4shapeimage_4_link_5shapeimage_4_link_6shapeimage_4_link_7shapeimage_4_link_8shapeimage_4_link_9shapeimage_4_link_10shapeimage_4_link_11shapeimage_4_link_12shapeimage_4_link_13shapeimage_4_link_14shapeimage_4_link_15shapeimage_4_link_16shapeimage_4_link_17shapeimage_4_link_18shapeimage_4_link_19shapeimage_4_link_20shapeimage_4_link_21shapeimage_4_link_22shapeimage_4_link_23shapeimage_4_link_24shapeimage_4_link_25shapeimage_4_link_26shapeimage_4_link_27shapeimage_4_link_28shapeimage_4_link_29shapeimage_4_link_30shapeimage_4_link_31shapeimage_4_link_32shapeimage_4_link_33
Registered participants  and  abstracts contributed talks:
 
CIPR-CMA workshop