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共 291 条记录，以下是211-220 订阅

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Nonlocal variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise

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2nd international conference on scale space and variational methods in computer vision

作者： Jung, Miyoun Vese, Luminita A. Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA

ISBN: (纸本)9783642022555

We wish to recover an image corrupted by blur and Gaussian or impulse noise, in a variational framework. We use two data-fidelity terms depending oil the noise, and several local and nonlocal regularizers. Inspired by Buades-Coll-Morel, Gilboa-Osher, and other nonlocal models, we propose nonlocal versions of the Ambrosio-Tortorelli and Shah approximations to Mumford-Shah-like regularizing functionals, with applications to image deblurring in the presence of noise. In the case of impulse noise model, we propose a necessary preprocessing step for the computation of the weight function. Experimental results show that these nonlocal MS regularizers yield better results than the corresponding local ones (proposed for deblurring by Bar et al.) in both noise models;moreover, these perform better than the nonlocal total variation in the presence of impulse noise. Characterization of minimizers is also given.

关键词： Impulse noise

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A scale-space Approach to Landmark Constrained Image Registration

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2nd international conference on scale space and variational methods in computer vision

作者： Haber, Eldad Heldmann, Stefan Modersitzki, Jan Emory Univ Dept Math & Comp Sci Atlanta GA 30322 USA Univ Lubeck Inst Math Lubeck Germany McMaster Univ Dept Comp & Software Hamilton ON Canada

ISBN: (纸本)9783642022555

Adding external knowledge improves the results for ill-posed problems. In this paper we present a new multi-level optimization framework for image registration when adding landmark constraints oil the transformation. Previous approaches are based oil a fixed discretization and lack of allowing for continuous landmark positions that are not oil grid points. Our novel approach overcomes these problems such that we can apply multi-level methods which have been proven being crucial to avoid local minima in the course of optimization. Furthermore, for our numerical method we are able to use constraint elimination such that we trace back the landmark constrained problem to a unconstrained optimization leading to all efficient algorithm.

关键词： Image registration

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Momentum Based Optimization methods for Level Set Segmentation

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2nd international conference on scale space and variational methods in computer vision

作者： Lathen, Gunnar Andersson, Thord Lenz, Reiner Borga, Magnus Linkoping Univ Dept Sci & Technol S-58183 Linkoping Sweden Linkoping Univ Dept Biomed Engn Linkoping Sweden Linkoping Univ Ctr Med Image Sci & Visual Linkoping Sweden

ISBN: (纸本)9783642022555

Segmentation of images is often posed as a variational problem. As such, it is solved by formulating an energy functional depending on a contour and other image derived terms. The solution of the segmentation problem is the contour which extremizes this functional. The standard way of solving this optimization problem is by gradient descent search in the solution space, which typically suffers from many unwanted local optima and poor convergence. Classically, these problems have been circumvented by modifying the energy functional. In contrast, the focus of this paper is on alternative methods for optimization. Inspired by ideas from the machine learning community, we propose segmentation based on gradient descent with momentum. Our results show that typical models hampered by local optima solutions can be further improved by this approach. We illustrate the performance improvements using the level set framework.

关键词： Optimization

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Theoretical Foundations for Discrete Forward-and-Backward Diffusion Filtering

引用

2nd international conference on scale space and variational methods in computer vision

作者： Welk, Martin Gilboa, Guy Weickert, Joachim Univ Saarland Math Image Anal Grp Fac Math & Comp Sci Campus E1-1 D-66041 Saarbrucken Germany 3DV Syst IL-20692 Yokneam Israel

ISBN: (纸本)9783642022555

Forward-and-backward (FAB) diffusion is a method for sharpening blurry images (Gilboa et al. 2002). It combines forward diffusion with a positive diffusivity and backward diffusion where negative diffusivities are used. The well-posedness properties of FAB diffusion are unknown, and it has been observed that standard discretisations can violate a maximum-minimum principle. We show that for a novel nonstandard space discretisation which pays specific attention to image extrema, one can apply a modification of the space-discrete well-posedness and scale-space framework of Weickert (1998). This allows to establish well-posedness and a maximum-minimum principle for the resulting dynamical system. In the fully discrete 1-D case with an explicit time discretisation, a maximum-minimum principle and total variation reduction are proven in spite of the fact that negative diffusivities may appear. This provides a theoretical justification for applying FAB diffusion to digital images.

关键词： Diffusion

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Bregman-EM-TV methods with Application to Optical Nanoscopy

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2nd international conference on scale space and variational methods in computer vision

作者： Brune, Christoph Sawatzky, Alex Burger, Martin Univ Munster Inst Numer & Angew Math D-48149 Munster Germany

ISBN: (纸本)9783642022555

Measurements in nanoscopic imaging suffer from blurring effects concerning different point spread functions (PSF). Some apparatus even have PSFs that are locally dependent. oil phase shifts. Additionally, raw data are affected by Poisson noise resulting from laser sampling and "photon counts" in fluorescence microscopy. In these applications standard reconstruction methods (EM, filtered back projection) deliver unsatisfactory and noisy results. Starting from a statistical modeling in terms of a MAP likelihood estimation we combine the iterative EM algorithm with TV regularization techniques to make an efficient, use of a-priori information. Typically, TV-based methods deliver reconstructed cartoon-images suffering from contrast reduction. We propose an extension to EM-TV, based on Bregman iterations and inverse scale space methods, in order to obtain improved imaging results by simultaneous contrast enhancement. We illustrate our techniques by synthetic and experimental biological data.

关键词： Fluorescence microscopy

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A variational Approach for Volume-to-Slice Registration

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2nd international conference on scale space and variational methods in computer vision

作者： Heldmann, Stefan Papenberg, Nils Univ Lubeck Inst Math Lubeck Germany

ISBN: (纸本)9783642022555

In this work we present a new variational approach for image registration where part of the data is only known on a low-dimensional manifold. Our work is motivated by navigated liver surgery. Therefore, we need to register 3D volumetric CT data and tracked 2D ultrasound (US) slices. The particular problem is that the set of all US slices does not assemble a full 3D domain. Other approaches use so-called compounding techniques to interpolate a 3D volume from the scattered slices. Instead of inventing new data by interpolation here we only use the given data. Our variational formulation of the problem is based on a standard approach. We minimize a joint functional made up from a distance term and a regularizer with respect to a 3D spatial deformation field. In contrast to existing methods we evaluate the distance of the images only on the two-dimensional manifold where the data is known. A crucial point here is regularization. To avoid kinks and to achieve a smooth deformation it turns out that at least second order regularization is needed. Our numerical method is based on Newton-type optimization. We present. a detailed discretization and give some examples demonstrating the influence of regularization. Finally we show results for clinical data.

关键词： Numerical methods

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scale spaces on the 3D Euclidean Motion Group for Enhancement of HArdI Data

引用

2nd international conference on scale space and variational methods in computer vision

作者： Franken, Erik Duits, Remco Eindhoven Univ Technol Dept Biomed Engn NL-5600 MB Eindhoven Netherlands

ISBN: (纸本)9783642022555

In previous work we studied left-invariant diffusion on the 2D Euclidean motion group for crossing-preserving coherence-enhancing diffusion on 2D images. In this paper we study the equivalent three-dimensional case. This is particularly useful for processing High Angular Resolution Diffusion Imaging (HArdI) data, which earl be considered as 3D orientation scores directly. A complicating factor in 3D is that all practical 3D orientation scores are functions on a coset space of the 3D Euclidean motion group instead of on the entire group. We show that, conceptually, we can still apply operations on the entire group by requiring the operations to be a-right-invariant. Subsequently, we propose to describe the local structure of the 3D orientation score using left-invariant derivatives and we smooth 3D orientation scores using left-invariant diffusion. Finally, we show a number of results for linear diffusion on artificial HArdI data.

关键词： Diffusion

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Fast Shape from Shading for Phong-Type Surfaces

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2nd international conference on scale space and variational methods in computer vision

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

ISBN: (纸本)9783642022555

Shape from Shading (SfS) is one of the oldest problems in image analysis that is modelled by partial differential equations (PDEs). The goal of SfS is to compute from a single 2-D image a reconstruction of the depicted 3-D scene. To this end, the brightness variation in the image and the knowledge of illumination conditions are used. While the quality of models has reached maturity, there is still the need for efficient numerical methods that enable to compute sophisticated SfS processes for large images in reasonable time. In this paper we address this problem. We consider a so-called Fast Marching (FM) scheme,which is one of the most efficient numerical approaches available. However, the FM scheme is not trivial to use for modern non-linear SfS models. We show how this is done for a recent SfS model incorporating the non-Lambertian reflectance model of Phong. Numerical experiments demonstrate that without compromising quality - our FM scheme is two orders of magnitude faster than standard methods.

关键词： Numerical methods

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Augmented Lagrangian Method, Dual methods and Split Bregman Iteration for ROF Model

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2nd international conference on scale space and variational methods in computer vision

作者： Tai, Xue-Cheng Wu, Chunlin Nanyang Technol Univ Div Math Sci Sch Phys & Math Sci Singapore Singapore

ISBN: (纸本)9783642022555

In the recent decades the ROF model (total variation (TV) minimization) has made great successes in image restoration due to its good edge-preserving property. However, the non-differentiability of the minimization problem brings computational difficulties. Different techniques have been proposed to overcome this difficulty. Therein methods regarded to be particularly efficient include dual methods of CGM (Chan, Golub, and Mulet) [7] Chambolle [6] and split Bregman iteration [14], as well as splitting-and-penalty based method [28] [29]. In this paper, we show that most of these methods can be classified under the same framework. The dual methods and split Bregman iteration are just different iterative procedures to solve the same system resulted from a Lagrangian and penalty approach. We only show this relationship for the ROF model. However, it provides a uniform framework to understand these methods for other models. In addition, we provide some examples to illustrate the accuracy and efficiency of the proposed algorithm.

关键词： Image reconstruction

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Spatio-Featural scale-space

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2nd international conference on scale space and variational methods in computer vision

作者： Felsberg, Michael Linkoping Univ Comp Vis Lab S-58183 Linkoping Sweden

ISBN: (纸本)9783642022555

Linear scale-space theory is the fundamental building block for many approaches to image processing like pyramids or scale-selection. However, linear smoothing does not preserve image structures very well and thus non-linear techniques are mostly applied for image enhancement. A different perspective is given in the framework of channel-smoothing, where the feature domain is not considered as a linear space, but it is decomposed into local basis functions. One major drawback is the larger memory requirement for this type of representation, which is avoided if the channel representation is subsampled in the spatial domain. This general type of feature representation is called channel-Coded feature map (CCFM) in the literature and a special case using linear channels is the SIFT descriptor. For computing CCFMs the spatial resolution and the feature resolution need to be selected. In this paper, we focus on the spatio-featural scale-space from a scale-selection perspective. We propose a coupled scheme for selecting the spatial and the featural scales. The scheme is based on an analysis of lower bounds for the product of uncertainties, which is summarized in a theorem about a spatio-featural uncertainty relation. As a practical application of the derived theory, we reconstruct images from CCFMs with resolutions according to our theory. The results are very similar to the results of non-linear evolution schemes, but our algorithm has the fundamental advantage of being non-iterative. Any level of smoothing can be achieved with about the same computational effort.

关键词： Image enhancement

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