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3rd international conference on scale space and variational methods in computer vision

作者： Duan, Yuping Wang, Yu Tai, Xue-Cheng Hahn, Jooyoung Nanyang Technol Univ Sch Phys & Math Sci Div Math Sci Singapore Singapore Technion Dept Comp Sci IL-32000 Haifa Israel Univ Bergen Dept Mat N-5007 Bergen Norway Graz Univ Inst Math & Sci Comp A-8010 Graz Austria

ISBN: (纸本)9783642247842

In this paper, a fast algorithm for Euler's elastica functional is proposed, in which the Euler's elastica functional is reformulated as a constrained minimization problem. Combining the augmented Lagrangian method and operator splitting techniques, the resulting saddle-point problem is solved by a serial of sub-problems. To tackle the nonlinear constraints arising in the model, a novel fixed-point-based approach is proposed so that all the sub-problems either are linear problems or have closed form solutions. Numerical examples are provided to demonstrate the performance of the proposed method.

关键词： Numerical methods

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3D Curve Evolution Algorithm with Tangential Redistribution for a Fully Automatic Finding of an Ideal Camera Path in Virtual Colonoscopy

3D Curve Evolution Algorithm with Tangential Redistribution ...

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3rd international conference on scale space and variational methods in computer vision

作者： Mikula, Karol Urban, Jozef Slovak Univ Technol Bratislava Dept Math & Descript Geometry Bratislava 81368 Slovakia

ISBN: (纸本)9783642247842

In this paper we develop new method, based on 3D evolving curves, for finding the optimal trajectory of the camera in the virtual colonoscopy - the medical technology dealing with colon diagnoses by computer. The proposed method consists of three steps: 3D segmentation of the colon from CT images, finding an initial trajectory guess inside the segmented 3D subvolumes, and driving the initial 3D curve to its optimal position. To that goal, the new fast and stable 3D curve evolution algorithm is developed in which the initial curve is driven by the velocity field in the plane normal to the evolving curve, the evolution is regularized by curvature and accompanied by the suitable choice of tangential velocity. Thanks to the asymtotically uniform tangential redistribution of grid points, originally introduced in this paper for 3D evolving curves, and to the fast and stable semi-implicit scheme for solving our proposed intrinsic advection-diffusion PDE, we end up in fast and robust way with the smooth uniformly discretized 3D curve representing the ideal path of the camera in virtual colonoscopy.

关键词： Virtual colonoscopy evolving 3D curves tangential velocity asymptotically uniform redistribution distance function segmentation

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Novel Schemes for Hyperbolic PDEs Using Osmosis Filters from Visual Computing

Novel Schemes for Hyperbolic PDEs Using Osmosis Filters from...

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3rd international conference on scale space and variational methods in computer vision

作者： Hagenburg, Kai Breuss, Michael Weickert, Joachim Vogel, Oliver Univ Saarland Math Image Anal Grp Fac Math & Comp Sci D-66041 Saarbrucken Germany

ISBN: (纸本)9783642247842

Recently a new class of generalised diffusion filters called osmosis filters has been proposed. Osmosis models are useful for a variety of tasks in visual computing. In this paper, we show that these filters are also beneficial outside image processing and computer graphics: We exploit their use for the construction of better numerical schemes for hyperbolic partial differential equations that model physical transport phenomena. Our novel osmosis-based algorithm is constructed as a two-step, predictor-corrector method. The predictor scheme is given by a Markov chain model of osmosis that captures the hyperbolic transport in its advection term. By design, it also incorporates a discrete diffusion process. The corresponding terms can easily be identified within the osmosis model. In the corrector step, we subtract a stabilised version of this discrete diffusion. We show that the resulting osmosis-based method gives correct, highly accurate resolutions of shock wave fronts in both linear and nonlinear test cases. Our work is an example for the usefulness of visual computing ideas in numerical analysis.

关键词： diffusion filtering osmosis diffusion-advection drift-diffusion hyperbolic conservation laws finite difference methods predictor-corrector schemes stabilised inverse diffusion

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From High Definition Image to Low space Optimization

From High Definition Image to Low Space Optimization

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3rd international conference on scale space and variational methods in computer vision

作者： Feigin, Micha Feldman, Dan Sochen, Nir Tel Aviv Univ Deparment Math IL-69978 Tel Aviv Israel CALTECH Ctr Math Informat Pasadena CA USA

ISBN: (纸本)9783642247842

Signal and image processing have seen in the last few years an explosion of interest in a new form of signal/image characterization via the concept of sparsity with respect to a dictionary. An active field of research is dictionary learning: Given a large amount of example signals/images one would like to learn a dictionary with much fewer atoms than examples on one hand, and much more atoms than pixels on the other hand. The dictionary is constructed such that the examples are sparse on that dictionary i.e each image is a linear combination of small number of atoms. This paper suggests a new computational approach to the problem of dictionary learning. We show that smart non-uniform sampling, via the recently introduced method of coresets, achieves excellent results, with controlled deviation from the optimal dictionary. We represent dictionary learning for sparse representation of images as a geometric problem, and illustrate the coreset technique by using it together with the K-SVD method. Our simulations demonstrate gain factor of up to 60 in computational time with the same, and even better, performance. We also demonstrate our ability to perform computations on larger patches and high-definition images, where the traditional approach breaks down.

关键词： Sparsity dictionary learning K-SVD coresets

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scale space and variational methods in computer vision - Third international conference, SSVM 2011, Revised Selected Papers

Scale Space and Variational Methods in Computer Vision - Thi...

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3rd international conference on scale space and variational methods in computer vision, SSVM 2011

ISBN: (纸本)9783642247842

The proceedings contain 66 papers. The topics discussed include: fiber enhancement in diffusion-weighted MRI;numerical schemes for linear and non-linear enhancement of DW-MRI;a variational approach for exact histogram specification;from a modified Ambrosio-Tortorelli to a randomized part hierarchy tree;robust edge detection using Mumford-Shah model and binary level set method;Sulci detection in photos of the human cortex based on learned discriminative dictionaries;an efficient and effective tool for image segmentation, total variations and regularization;theoretical foundations of Gaussian convolution by extended box filtering;curvature minimization for surface reconstruction with features;fast PDE-based image analysis in your pocket;a correspondence-less approach to matching of deformable shapes;and 3D curve evolution algorithm with tangential redistribution for a fully automatic finding of an ideal camera path in virtual colonoscopy.

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Joint ToF Image Denoising and Registration with a CT Surface in Radiation Therapy

Joint ToF Image Denoising and Registration with a CT Surface...

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3rd international conference on scale space and variational methods in computer vision

作者： Bauer, Sebastian Berkels, Benjamin Hornegger, Joachim Rumpf, Martin Univ Erlangen Nurnberg Dept Comp Sci Pattern Recognit Lab Martensstr 3 D-91058 Erlangen Germany Univ Erlangen Nurnberg Erlangen Grad Sch Adv Opt Tech D-91058 Erlangen Germany Univ S Carolina Interdisciplinary Math Inst Columbia SC 29208 USA Univ Bonn Inst Numer Simulat D-53115 Bonn Germany

ISBN: (纸本)9783642247842

The management of intra-fractional respiratory motion is becoming increasingly important in radiation therapy. Based on in advance acquired accurate 3D CT data and intra-fractionally recorded noisy time-of-flight (ToF) range data an improved treatment can be achieved. In this paper, a variational approach for the joint registration of the thorax surface extracted from a CT and a ToF image and the denoising of the ToF image is proposed. This enables a robust intra-fractional full torso surface acquisition and deformation tracking to cope with variations in patient pose and respiratory motion. Thereby, the aim is to improve radiotherapy for patients with thoracic, abdominal and pelvic tumors. The approach combines a Huber norm type regularization of the ToF data and a geometrically consistent treatment of the shape mismatch. The algorithm is tested and validated on synthetic and real ToF/CT data and then evaluated on real ToF data and 4D CT phantom experiments.

关键词： Radiotherapy

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Deblurring space-Variant Blur by Adding Noisy Image

Deblurring Space-Variant Blur by Adding Noisy Image

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3rd international conference on scale space and variational methods in computer vision

作者： Klapp, Iftach Sochen, Nir Mendlovic, David Tel Aviv Univ Dept Phys Elect IL-69978 Tel Aviv Israel Tel Aviv Univ Dept Mat IL-69978 Tel Aviv Israel

ISBN: (纸本)9783642247842

Imaging restoration is an essential step in hybrid optical and image processing system which relays on poor optics. The poor optics makes the blur ill-conditioned and turns the deblurring process difficult and unstable. Recently the idea of parallel optics (PO) was introduced. In the parallel optics setup the optical system is composed of a main system and an auxiliary system. The auxiliary system is designed to improve the stability of the deblurring process by improving the condition number of the blurring operator. In this paper we show that in one such system the post processing acts as a noise filter hence allows to work with noisy data in the auxiliary channel. Using the singular value decomposition we derive analytical limit for the difference in SNR requirements of the auxiliary channel relative to that of the main channel. The gap between the SNR requirements of the two systems is analyzed theoretically and proved to be as large as 27.68 [db]. Image restoration comparison on simulations is performed between a blurred/noisy pair with average SNR gap of 20 [db] and a system without an auxiliary system. The average Mean Square Error Improvement Factor (MSEIF) achieved by the blurred/noisy pair, was 13.9 [db] higher than the system without a noisy auxiliary system.

关键词： deblurring parallel optics blurred and noisy image pair

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Should We Search for a Global Minimizer of Least Squares Regularized with an l₀ Penalty to Get the Exact Solution of an under Determined Linear System?

Should We Search for a Global Minimizer of Least Squares Reg...

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3rd international conference on scale space and variational methods in computer vision

作者： Nikolova, Mila CMLA CNRS ENS Cachan UniverSud F-94235 Cachan France

ISBN: (纸本)9783642247842

We study objectives F-d combining a quadratic data-fidelity and an l(0) regularization. Data d are generated using a full-rank M x N matrix A with N > M. Our main results are listed below. Minimizers (u) over cap of F-d are strict if and only if length(support((u) over cap)) <= M and the submatrix of A whose columns are indexed by support((u) over cap) is full rank. Their continuity in data is derived. Global minimizers are always strict. We adopt a weak assumption on A and show that it holds with probability one. Data read d = A(u) over dot where length(support(u) double over dot) <= M - 1 and the submatrix whose columns are indexed by support((u) double over dot) is full rank. Among all strict (local) minimizers of F-d with support shorter than Al 1, the exact solution (u) over cap = (u) double over dot is the unique vector that cancels the residual. The claim is independent of the regularization parameter. This (u) over cap = (u) double over dot is usually a strict local minimizer where F-d does not reach its global minimum. Global minimization of F-d can then prevent the recovery of U. A numerical example (A is 5 x 10) illustrates our main results.

关键词： under-determined systems of linear equations variational methods l(0) regularization linear programming sparse representation solution analysis exact recovery global minimizers

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Fiber enhancement in diffusion-weighted MRI

Fiber enhancement in diffusion-weighted MRI

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3rd international conference on scale space and variational methods in computer vision, SSVM 2011

作者： Duits, Remco Dela Haije, Tom C. J. Ghosh, Arpan Creusen, Eric Vilanova, Anna Ter Haar Romeny, Bart Eindhoven University of Technology Department of Mathematics and Computer Science Netherlands Eindhoven University of Technology Department of Biomedical Engineering Netherlands

ISBN: (纸本)9783642247842

Diffusion-Weighted MRI (DW-MRI) measures local water diffusion in biological tissue, which reflects the underlying fiber structure. In order to enhance the fiber structure in the DW-MRI data we consider both (convection-)diffusions and Hamilton-Jacobi equations (erosions) on the space of 3D-positions and orientations, embedded as a quotient in the group SE(3) of 3D-rigid body movements. These left-invariant evolutions are expressed in the frame of left-invariant vector fields on SE(3), which serves as a moving frame of reference attached to fiber fragments. The linear (convection-)diffusions are solved by a convolution with the corresponding Green's function, whereas the Hamilton-Jacobi equations are solved by a morphological convolution with the corresponding Green's function. Furthermore, we combine dilation and diffusion in pseudo-linear scale spaces on 3 S2. All methods are tested on DTI-images of the brain. These experiments indicate that our techniques are useful to deal with both the problem of limited angular resolution of DTI and the problem of spurious, non-aligned crossings in HArdI. © 2012 Springer-Verlag.

关键词： Diffusion

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Lecture Notes in computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface

Lecture Notes in Computer Science (including subseries Lectu...

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Lecture Notes in computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2012年 6667 LNCS卷 VI页

作者： Bruckstein, Alfred M. Romeny, Bart Ter Haar Bronstein, Alexander M. Bronstein, Michael M. Technion - Israel Institute of Technology Computer Science Department 718 Taub Building Technion Haifa 32000 Israel Eindhoven University of Technology Department of Biomedical Engineering Biomedical Image Analysis and Interpretation Den Dolech 2 - WH 2.101 5600 MB Eindhoven Netherlands Tel Aviv University Faculty of Engineering School of Electrical Engineering Ramat Aviv 69978 Israel Università Della Svizzera Italiana Institute of Computational Science Faculty of Informatics SI-109 Via Giuseppe Buffi 13 6904 Lugano Switzerland

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