All Publications:


  Efficient Minimal-Surface Regularization of Perspective Depth Maps in Variational Stereo paper       software      
  Gottfried Graber, Jonathan Balzer, Stefano Soatto, Thomas Pock       CVPR 2015  
paper We propose a method for dense three-dimensional surface reconstruction that leverages the strengths of shapebased approaches, by imposing regularization that respects the geometry of the surface, and the strength of depthmap-based stereo, by avoiding costly computation of surface topology. The result is a near real-time variational reconstruction algorithm free of the staircasing artifacts that affect depth-map and plane-sweeping approaches. This is made possible by exploiting the gauge ambiguity to design a novel representation of the regularizer that is linear in the parameters and hence amenable to be optimized with state-of-the-art primal-dual numerical schemes.
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  Bi-level Optimization for Support Vector Machines paper              
  Teresa Klatzer       Master's Thesis  
paper This thesis deals with an efficient approach for learning the optimal hyper-parameters for Support Vector Machines (SVMs). The common method to determine hyper-parameters is grid search. Grid search typically involves the definition of a discretized "grid" of possible parameter values with a certain resolution and a search for the values that result in the minimal validation error of the learned model. A major limitation of grid search is that the search space grows exponentially in the parameters which makes the approach only practical for determining very few hyper-parameters.
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  Learning fast and effective image restoration models paper              
  Yunjin Chen       PhD Thesis  
paper Up to now, image restoration remains an active research topic, and many new approaches are constantly emerging. However, many newly proposed algorithms achieve the state-of-the-art performance, at the expense of computation time. The goal of this thesis is to develop effective image restoration approaches with both high computational efficiency and recovery quality. To that end, we focus on variational models and some related models derived from them, e.g., nonlinear diffusion processes, due to their effectiveness for many generally ill-posed computer vision problems...
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  On learning optimized reaction diffusion processes for effective image restoration paper       software   links  
  Yunjin Chen, Wei Yu, Thomas Pock       CVPR 2015  
paper For several decades, image restoration remains an active research topic in low-level computer vision and hence new approaches are constantly emerging. However, many recently proposed algorithms achieve state-of-the-art performance only at the expense of very high computation time, which clearly limits their practical relevance. In this work, we propose a simple but effective approach with both high computational efficiency and high restoration quality. We extend conventional nonlinear reaction diffusion models by several parametrized linear filters as well as several parametrized influence functions.
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  Bilevel Optimization with Nonsmooth Lower Level Problems paper              
  Peter Ochs, Rene Ranftl, Thomas Brox, Thomas Pock       SSVM 2015 (Preprint)  
paper We consider a bilevel optimization approach for parameter learning in nonsmooth variational models. Existing approaches solve this problem by applying implicit differentiation to a sufficiently smooth approximation of the nondifferentiable lower level problem. We propose an alternative method based on differentiating the iterations of a nonlinear primal-dual algorithm. Our method computes exact (sub)gradients and can be applied also in the nonsmooth setting. We show preliminary results for the case of multi-label image segmentation.
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  Continuous Hyper-parameter Learning for Support Vector Machines paper              
  Teresa Klatzer, Thomas Pock       CVWW 2015  
paper In this paper, we address the problem of determining optimal hyper-parameters for support vector machines (SVMs). The standard way for solving the model selection problem is to use grid search. Grid search constitutes an exhaustive search over a pre-defined discretized set of possible parameter values and evaluating the cross-validation error until the best is found. We developed a bi-level opti-mization approach to solve the model selection problem for linear and kernel SVMs, including the extension to learn several kernel parameters.
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  A Remark on Accelerated Block Coordinate Descent for Computing the Proximity Operators of a Sum of Convex Functions paper              
  Antonin Chambolle, Thomas Pock       Preprint  
paper We analyze alternating descent algorithms for minimizing the sum of a quadratic function and block separable non-smooth functions. In case the quadratic interactions between the blocks are pairwise, we show that the schemes can be accelerated, leading to improved convergence rates with respect to related accelerated parallel proximal descent. As an application we obtain very fast algorithms for computing the proximity operator of the 2D and 3D total variation.
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  Scene Flow Estimation from Light Fields via the Preconditioned Primal-Dual Algorithm paper              
  Stefan Heber, Thomas Pock       GCPR 2014  
paper In this paper we present a novel variational model to jointly estimate geometry and motion from a sequence of light fields captured with a plenoptic camera. The proposed model uses the so-called sub-aperture representation of the light field. Sub-aperture images represent images with slightly different viewpoints, which can be extracted from the light field. The sub-aperture representation allows us to formulate a convex global energy functional, which enforces multi-view geometry consistency, ...
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  A Deep Variational Model for Image Segmentation paper           links  
  Rene Ranftl, Thomas Pock       GCPR 2014  
paper In this paper we introduce a novel model that combines Deep Convolutional Neural Networks with a global inference model. Our model is derived from a convex variational relaxation of the minimum s-t cut problem on graphs, which is frequently used for the task of image segmentation. We treat the outputs of Convolutional Neural Networks as the unary and pairwise potentials of a graph and derive a smooth approximation to the minimum s-t cut problem. During training, this approximation facilitates the adaptation of the Convolutional Neural Network to the smoothing that is induced by the global model.
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  On the ergodic convergence rates of a first-order primal-dual algorithm paper              
  Antonin Chambolle, Thomas Pock       Preprint  
paper We revisit the proofs of convergence for a first order primal-dual algorithm for convex optimization which we have studied a few years ago. In particular, we prove rates of convergence for a more general version, with simpler proofs and more complete results.
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  Shape from Light Field meets Robust PCA paper              
  Stefan Heber, Thomas Pock       European Conference on Computer Vision 2014  
paper In this paper we propose a new type of matching term for multi-view stereo reconstruction. Our model is based on the assumption, that if one warps the images of the various views to a common warping center and considers each warped image as one row in a matrix, then this matrix will have low rank. This also implies, that we assume a certain amount of overlap between the views after the warping has been performed. Such an assumption is obviously met in the case of light field data ...
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  Non-Local Total Generalized Variation for Optical Flow Estimation paper              
  Rene Ranftl, Kristian Bredies, Thomas Pock       European Conference on Computer Vision 2014  
paper In this paper we introduce a novel higher-order regularization term. The proposed regularizer is a non-local extension of the popular second-order Total Generalized variation, which favors piecewise affine solutions and allows to incorporate soft-segmentation cues into the regularization term. These properties make this regularizer especially appealing for optical flow estimation, where it offers accurately localized motion boundaries and allows to resolve ambiguities in the matching term.
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  A higher-order MRF based variational model for multiplicative noise reduction paper       software      
  Yunjin Chen, Wensen Feng, Rene Ranftl, Hong Qiao, Thomas Pock       IEEE Signal Processing Letters  
paper The Fields of Experts (FoE) image prior model, a filter-based higher-order Markov Random Fields (MRF) model, has been shown to be effective for many image restoration problems. Motivated by the successes of FoE-based approaches, in this letter we propose a novel variational model for multiplicative noise reduction based on the FoE image prior model. The resulting model corresponds to a non-convex minimization problem, which can be efficiently solved by a recently published non-convex optimization algorithm.
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  A Comparison of First-order Algorithms for Machine Learning paper       software      
  Yu Wei, Thomas Pock       OAGM/AAPR Workshop 2014  
paper Using an optimization algorithm to solve a machine learning problem is one of mainstreams in the field of science. In this work, we demonstrate a comprehensive comparison of some state-of-the-art first-order optimization algorithms for convex optimization problems in machine learning. We concentrate on several smooth and non-smooth machine learning problems with a loss function plus a regularizer. The overall experimental results show the superiority of primal-dual algorithms in solving a machine learning problem from the perspectives of the ease to construct, running time and accuracy.
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  An iteratively reweighted Algorithm for Non-smooth Non-convex Optimization in Computer Vision paper              
  Peter Ochs, Alexey Dosovitskiy, Thomas Brox, Thomas Pock       Technical Report  
paper Natural image statistics indicate that we should use non-convex norms for most regularization tasks in image processing and computer vision. Still, they are rarely used in practice due to the challenge of optimization. Recently, iteratively reweighed \ell_1 minimization (IRL1) has been proposed as a way to tackle a class of non-convex functions by solving a sequence of convex \ell_2 - \ell_1 problems. We extend the problem class to the sum of a convex function and a (non-convex) non-deceasing function applied to another convex function.
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  iPiasco: Inertial Proximal Algorithm for strongly convex Optimization paper              
  Peter Ochs, Thomas Brox, Thomas Pock       Technical Report  
paper In this paper, we present a forward-backward splitting algorithm with additional inertial term for solving a strongly convex optimization problem of a certain type. The strongly convex objective function is assumed to be a sum of a non-smooth convex and a smooth convex function. This additional knowledge is used for deriving a convergence rate for the proposed algorithm. It is proved to be an optimal algorithm with linear rate of convergence. For certain problems this linear rate of convergence is better than the provably optimal rate of convergence for smooth strongly convex functions.
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  Maximum Persistency in Energy Minimization paper           links  
  Alexander Shekhovtsov       CVPR 2014  
paper We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, max-sum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is intractable, determining optimal values for a part of variables is an interesting possibility. Existing methods are based on different sufficient conditions. We propose a new sufficient condition for partial optimality...
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  An accelerated forward-backward algorithm for monotone inclusions paper              
  Dirk Lorenz, Thomas Pock       Preprint  
paper In this paper, we propose a new accelerated forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method of Nesterov, but can be applied to a much larger class of problems including convex-concave saddle point problems and general monotone inclusions. We prove convergence of the algorithm in a Hilbert space setting and show that several recently proposed first-order methods can be obtained as special cases of the general algorithm.
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  Insights into analysis operator learning: From patch-based sparse models to higher-order MRFs paper       software      
  Yunjin Chen, Rene Ranftl, Thomas Pock       Preprint  
paper This paper addresses a new learning algorithm for the recently introduced co-sparse analysis model. First, we give new insights into the co-sparse analysis model by establishing connections to filter-based MRF models, such as the Field of Experts (FoE) model of Roth and Black. For training, we introduce a technique called bi-level optimization to learn the analysis operators. Compared to existing analysis operator learning approaches, our training procedure has the advantage that it is unconstrained with respect to the analysis operator.
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  iPiano: Inertial Proximal Algorithm for Non-Convex Optimization paper              
  Peter Ochs, Yunjin Chen, Thomas Brox, Thomas Pock       Accepted to SIAM Journal on Imaging Sciences  
paper In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly non-convex) and a convex (possibly non-differentiable) function. The algorithm combines forward-backward splitting with an inertial force. A rigorous analysis of the algorithm for the proposed class of problems yields global convergence of the function values and the arguments. This makes the algorithm robust for usage on non-convex problems. The convergence result is obtained based on the Kurdyka-Lojasiewicz inequality.
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  A Convex, Lower Semi-Continuous Approximation of Euler's Elastica energy paper              
  Kristian Bredies, Thomas Pock, Benedikt Wirth       Preprint  
paper We propose a convex, lower semi-continuous, coercive approximation of Euler's elastica energy for images, which is thus very well-suited as a regularizer in image processing. The approximation is not quite the convex relaxation, and we discuss its close relation to the exact convex relaxation as well as the difficulties associated with computing the latter. Interestingly, the convex relaxation of the elastica energy reduces to constantly zero if the total variation part of the elastica energy is neglected.
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  Variational Shape from Light Field paper              
  Stefan Heber, Rene Ranftl, Thomas Pock       EMMCVPR 2013  
paper In this paper we propose an efficient method to calculate a high-quality depth map from a single raw image captured by a light field or plenoptic camera. The proposed model combines the main idea of Active Wavefront Sampling (AWS) with the light field technique, i.e. we extract so-called sub-aperture images out of the raw image of a plenoptic camera, in such a way that the virtual view points are arranged on circles around a fixed center view.
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  A Convex Approach for Image Hallucination paper       software      
  Peter Innerhofer, Thomas Pock       OAGM/AAPR Workshop 2013  
paper In this paper we propose a global convex approach for image hallucination. Altering the idea of classical multi image super resolution (SU) systems to single image SU, we incorporate aligned images to hallucinate the output. Our work is based on the paper of Tappen et al. where they use a non-convex model for image hallucination. In comparison we formulate a convex primal optimization problem and derive a fast converging primal-dual algorithm with a global optimal solution.
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  Revisiting loss-specific training of filter-based MRFs for image restoration paper       software      
  Yunjin Chen, Thomas Pock, Rene Ranftl, Horst Bischof       GCPR 2013  
paper It is now well known that Markov random fields (MRFs) are particularly effective for modeling image priors in low-level vision. Recent years have seen the emergence of two main approaches for learning the parameters in MRFs: (1) probabilistic learning using sampling-based algorithms and (2) loss-specific training based on MAP estimate. After investigating existing training approaches, it turns out that the performance of the loss-specific training has been significantly underestimated in existing work.
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  An iterated l1 Algorithm for Non-smooth Non-convex Optimization in Computer Vision paper              
  Peter Ochs, Alexey Dosovitskiy, Thomas Brox, Thomas Pock       CVPR 2013  
paper Natural image statistics indicate that we should use non-convex norms for most regularization tasks in image processing and computer vision. Still, they are rarely used in practice due to the challenge to optimize them. Recently, iteratively reweighed l1 minimization has been proposed as a way to tackle a class of non-convex functions by solving a sequence of convex l2 - l1 problems. Here we extend the problem class to linearly constrained optimization of a Lipschitz continuous function, which is the sum of a convex function and a function being concave and increasing on the non-negative orthant (possibly non-convex and non-concave on the whole space).
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  Minimizing TGV-based Variational Models with Non-Convex Data Terms paper              
  Rene Ranftl, Thomas Pock, Horst Bischof       SSVM 2013  
paper We introduce a method to approximately minimize variational models with Total Generalized Variation regularization (TGV) and non-convex data terms. Our approach is based on a decomposition of the functional into two subproblems, which can be both solved globally optimal. Based on this decomposition we derive an iterative algorithm for the approximate minimization of the original non-convex problem. We apply the proposed algorithm to a state-of-the-art stereo model that was previously solved using coarse-to-fine warping, where we are able to show significant improvements in terms of accuracy.
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  Learning l1-based analysis and synthesis sparsity priors using bi-level optimization paper              
  Yunjin Chen, Thomas Pock, Horst Bischof       Workshop on Analysis Operator Learning vs. Dictionary Learning, NIPS 2012  
paper We consider the analysis operator and synthesis dictionary learning problems based on the the l1 regularized sparse representation model. We reveal the internal relations between the l1 -based analysis model and synthesis model. We then introduce an approach to learn both analysis operator and synthesis dictionary simultaneously by using a unified framework of bi-level optimization. Our aim is to learn a meaningful operator (dictionary) such that the minimum energy solution of the analysis (synthesis)-prior based model is as close as possible to the groundtruth.
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  Convex Optimization for Image Segmentation paper              
  Markus Unger       Phd Thesis 2012  
paper Segmentation is one of the fundamental low level problems in computer vision. Extracting objects from an image gives rise to further high level processing as well as image composing. A segment not always has to correspond to a real world object, but can fulfill any coherency criterion (e.g. similar motion). Segmentation is a highly ambiguous task, and usually requires some prior knowledge. This can either be obtained by interactive user input in an supervised manner, or completely unsupervised using strong prior knowledge. In this thesis we use continuous energy minimization to tackle all of these problems.
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  Realtime 3D Reconstruction paper   videos   software      
  Gottfried Graber       Masters Thesis  
paper Reconstruction of 3D geometry from 2D images is one of the most fundamental challenges in computer vision. In the past decade, numerous algorithms have been developed to solve this problem in an offline fashion. Only recently, the availability of cheap processing power in the form of GPUs and appropriate parallel algorithms made it possible to tackle this problem in a novel way and present results to the user in realtime.
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  Approximate Envelope Minimization for Curvature Regularity paper              
  Stefan Heber, Rene Ranftl, Thomas Pock       Workshop on Higher-Order Models and Global Constraints in Computer Vision, ECCV 2012  
paper We propose a method for minimizing a non-convex function, which can be split up into a sum of simple functions. The key idea of the method is the approximation of the convex envelopes of the simple functions, which leads to a convex approximation of the original function. A solution is obtained by minimizing this convex approximation. Cost functions, which fulfill such a splitting property are ubiquitous in computer vision, ...
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  Convex Approaches for High Performance Video Processing paper              
  Manuel Werlberger       Phd Thesis 2012  
paper Accurate and robust motion estimation in image sequences is essential for high quality video processing and digital film restoration. The ability to deal with strong outliers and large impaired regions is especially important for restoring historical film. Typical artifacts like brightness changes, noise, scratches or other forms of missing data may cause the algorithms to fail. Even in situations without disturbance and only changing illuminationsthe algorithms often have problems to compute the correct motion.
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  A bilevel optimization approach for parameter learning in variational models paper              
  Karl Kunisch, Thomas Pock       SIAM Journal on Imaging Sciences  
paper In this work we consider the problem of parameter learning for variational image denoising models. The learning problem is formulated as a bilevel optimization problem, where the lower level problem is given by the variational model and the higher level problem is expressed by means of a loss function that penalizes errors between the solution of the lower level problem and the ground truth data. We consider a class of image denoising models incorporating p -norm based analysis priors using a fixed set of linear operators.
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  Joint Motion Estimation and Segmentation of Complex Scenes with Label Costs and Occlusion Modeling paper              
  Markus Unger, Manuel Werlberger, Thomas Pock, Horst Bischof       CVPR 2012, Providence, Rhode Island  
paper We propose a unified variational formulation for joint motion estimation and segmentation with explicit occlusion handling. This is done by a multi-label representation of the flow field, where each label corresponds to a parametric representation of the motion. We use a convex formulation of the multi-label Potts model with label costs and show that the asymmetric map-uniqueness criterion can be integrated into our formulation by means of convex constraints.
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  Pushing the Limits of Stereo Using Variational Stereo Estimation paper   videos          
  Rene Ranftl, Stefan Gehrig, Thomas Pock, Horst Bischof       IEEE Intelligent Vehicles Symposium 2012  
paper We examine high accuracy stereo estimation for binocular sequences that where obtained from a mobile platform. The ultimate goal is to improve the range of stereo systems without altering the setup. Based on a well-known variational optical flow model, we introduce a novel stereo model that features a second-order regularization, which both allows sub-pixel accurate solutions and piecewise planar disparity maps.
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  Online 3D reconstruction using Convex Optimization paper   videos          
  Gottfried Graber, Thomas Pock, Horst Bischof       1st Workshop on Live Dense Reconstruction From Moving Cameras, ICCV 2011  
paper We present a system that is capable of interactively reconstructing a scene from a single live camera. We use a dense volumetric representation of the surface, which means there are no constraints concerning the 3D-scene topology. Reconstruction is based on range image fusion using a total variation formulation, where the surface is represented implicitly by a signed distance function.
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  A convex approach to minimal partitions (revised version) paper              
  Antonin Chambolle, Daniel Cremers, Thomas Pock       SIAM Journal on Imaging Sciences  
paper We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically, we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct numerical approximation of the optimal solution.
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  Convex relaxation of a class of vertex penalizing functionals paper              
  Kristian Bredies, Thomas Pock, Benedikt Wirth       Journal of Mathematical Imaging and Vision  
paper We investigate a class of variational problems that incorporate in some sense curvature information of the level lines. The functionals we consider incorporate metrics defined on the orientations of pairs of line segments that meet in the vertices of the level lines. We discuss two particular instances: One instance that minimizes the total number of vertices of the level lines and another instance that minimizes the total sum of the absolute exterior angles between the line segments.
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  Neural Process Reconstruction from Sparse User Scribbles paper           links  
  Mike Roberts, Won-Ki Jeong, Amelio Vazquez-Reina, Markus Unger, Horst Bischof, Jeff Lichtman, Hanspeter Pfister       Medical Image Computing and Computer Assisted Intervention (MICCAI) 2011  
paper We present a novel semi-automatic method for segmenting neural processes in large, highly anisotropic EM (electron microscopy) image stacks. Our method takes advantage of sparse scribble annotations provided by the user to guide a 3D variational segmentation model, thereby allowing our method to globally optimally enforce 3D geometric constraints on the segmentation.
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  Global Relabeling for Continuous Optimization in Binary Image Segmentation paper              
  Markus Unger, Thomas Pock, Horst Bischof       EMMCVPR 2011, Saint Petersburg, Russia  
paper Recently, continuous optimization methods have become quite popular since they can deal with a variety of non-smooth convex problems. They are inherently parallel and therefore well suited for GPU implementations. Most of the continuous optimization approaches have in common that they are very fast in the beginning, but tend to get very slow as the solution gets close to the optimum...
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  Diagonal preconditioning for first order primal-dual algorithms in convex optimization paper              
  Thomas Pock, Antonin Chambolle       International Conference on Computer Vision (ICCV 2011), To Appear  
paper In this paper we study preconditioning techniques for the first-order primal-dual algorithm proposed in [7]. In particular, we propose simple and easy to compute diagonal preconditioners for which convergence of the algorithm is guaranteed without the need to compute any step size parameters...
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  Optical Flow Guided TV-L1 Video Interpolation and Restoration paper              
  Manuel Werlberger, Thomas Pock, Markus Unger, Horst Bischof       EMMCVPR 2011, Saint Petersburg, Russia  
paper The ability to generate intermediate frames between two given images in a video sequence is an essential task for video restoration and video post-processing. In addition, restoration requires robust denoising algorithms, must handle corrupted frames and recover from impaired frames accordingly.
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  Efficient Minimization of the Non-Local Potts Model paper              
  Manuel Werlberger, Markus Unger, Thomas Pock, and Horst Bischof       SSVM 2011, Ein-Gedi, Israel  
paper The Potts model is a well established approach to solve different multi-label problems. The classical Potts prior penalizes the total interface length to obtain regular boundaries. Although the Potts prior works well for many problems, it does not preserve fine details of the boundaries.
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  TGV-Fusion paper              
  Thomas Pock and Lukas Zebedin and Horst Bischof       C.S. Calude, G. Rozenberg, A. Salomaa (Eds.): Maurer Festschrift, LNCS 6570  
paper Location awareness on the Internet and 3D models of our habitat (as produced by Microsoft (Bing) or Google (Google Earth)) are a major driving force for creating 3D models from image data. A key factor for these models are highly accurate and fully automated stereo matching pipelines producing highly accurate 3D point clouds that are possible due to the fact that we can produce images with high redundancy...
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  Interactive Multi-Label Segmentation paper              
  Jakob Santner       Phd Thesis 2010  
paper Interactive image segmentation deals with partitioning an image into multiple pairwise-disjoint regions based on input provided by a human operator. Being interactive means, that an algorithm has to quickly react on user input, which limits the computational complexity of the employed algorithms drastically. Therefore, many interactive segmentation methods represent these regions with simple models based on low-dimensional feature spaces...
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  Interactive Multi-Label Segmentation paper       software      
  Jakob Santner and Thomas Pock and Horst Bischof       Asian Conference on Computer Vision (ACCV) 2010  
paper This paper addresses the problem of interactive multi-label segmentation. We propose a powerful new framework using several color models and texture descriptors, Random Forest likelihood estimation as well as a multi-label Potts-model segmentation. We perform most of the calculations on the GPU and reach runtimes of less than two seconds, allowing for convenient user interaction...
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  A Convex Approach for Variational Super-Resolution paper              
  Markus Unger and Thomas Pock and Manuel Werlberger and Horst Bischof       DAGM 2010, Annual Symposium of the German Association for Pattern Recognition  
paper We propose a convex variational framework to compute high resolution images from a low resolution video. The image formation process is analyzed to provide to a well designed model for warping, blurring, downsampling and regularization. We provide a comprehensive investigation of the single model components. The super-resolution problem is modeled as a minimization problem in an unified convex framework...
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  Exploiting Redundancy for Aerial Image Fusion using Convex Optimization paper              
  Stefan Kluckner and Thomas Pock and Horst Bischof       DAGM 2010, Annual Symposium of the German Association for Pattern Recognition  
paper This paper proposes a variational formulation for a tight integration of redundant image data showing urban environments. We introduce an efficient wavelet regularization which enables a natural-appearing recovery of fine details in the images by performing joint inpainting and denoising from a given set of input observations ...
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  A fi rst-order primal-dual algorithm for convex problems with applications to imaging paper              
  Antonin Chambolle and Thomas Pock       Journal of Mathematical Imaging and Vision  
paper In this paper we study a first-order primal-dual algorithm for convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O(1/N) in finite dimensions, which is optimal for the complete class of non-smooth problems we are considering in this paper...
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  Fast reduction of undersampling artifacts in radial MR angiography with 3D total variation on graphics hardware paper              
  Florian Knoll and Markus Unger and Clemens Diwoky and Christian Clason and Thomas Pock and Rudolf Stollberger       Magnetic Resonance Materials in Physics, Biology and Medicine  
paper Objective Subsampling of radially encoded MRI acquisitions in combination with sparsity promoting methods opened a door to significantly increased imaging speed, which is crucial for many important clinical applications. In particular, it has been shown recently that total variation (TV) regularization efficiently reduces undersampling artifacts. The drawback of the method is the long reconstruction time which makes it impossible to use in daily clinical practice, especially if the TV optimization problem has to be solved repeatedly to select a proper regularization parameter. Materials and Methods The goal of this work was to show that for the case of MR Angiography, TV filtering can be performed as a post-processing step, in contrast to the common approach of integrating TV penalties in the image reconstruction process. With this approach, it is possible to use TV algorithms with data fidelity terms in image space, which can be implemented very ef?ciently on graphic processing units (GPUs). The combination of a special radial sampling trajectory and a full 3D formulation of the TV minimization problem is crucial for the effectiveness of the artifact elimination process.
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  Total Generalized Variation paper              
  Kristian Bredies, Karl Kunisch, Thomas Pock       Accepted to SIIMS  
paper The novel concept of total generalized variation of a function u is introduced and some of its essential properties are proved. Differently from the bounded variation semi-norm, the new concept involves higher order derivatives of u. Numerical examples illustrate the high quality of this functional as a regularization term for mathematical imaging problems...
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  Global Solutions of Variational Models with Convex Regularization paper              
  Thomas Pock, Daniel Cremers, Horst Bischof, Antonin Chambolle       Accepted to SIIMS  
paper We propose an algorithmic framework to compute global solutions of variational models with convex regularity terms that permit quite arbitrary data terms. While the minimization of variational problems with convex data and regularity terms is straight forward (using for example gradient descent), this is no longer trivial for functionals with non-convex data terms...
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  Motion Estimation with Non-Local Total Variation Regularization paper           links  
  Manuel Werlberger, Thomas Pock, Horst Bischof       CVPR 2010, San Francisco, CA  
paper State-of-the-art motion estimation algorithms suffer from three major problems: Poorly textured regions, occlusions and small scale image structures. Based on the Gestalt principles of grouping we propose to incorporate a low level image segmentation process in order to tackle these problems. Our new motion estimation algorithm is based on non-local total variation regularization...
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  FlowGames paper   videos          
  Jakob Santner, Manuel Werlberger, Thomas Mauthner, Wolfgang Paier, Horst Bischof       1st Int. Workshop on Computer Vision for Computer Games (CVCG) in conjunction with IEEE CVPR 2010  
paper Computer vision-based interfaces to games hold the promise of rich natural interaction and thus a more realistic gaming experience. Therefore, the video games industry started to develop and market computer vision-based games recently with great success. Due to limited computational resources, they employ mostly simple algorithms such as background subtraction, instead of sophisticated motion estimation or gesture recognition methods...
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  PROST: Parallel Robust Online Simple Tracking paper           links  
  Jakob Santner, Christian Leistner, Amir Saffari, Thomas Pock, Horst Bischof       CVPR 2010, San Francisco, CA  
paper Tracking-by-detection is increasingly popular in order to tackle the visual tracking problem. Existing adaptive methods suffer from the drifting problem, since they rely on self-updates of an on-line learning method. In contrast to previous work that tackled this problem by employing semi-supervised or multiple-instance learning, we show that augmenting an on-line learning method with complementary tracking approaches can lead to more stable results...
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  An Introduction to Total Variation for Image Analysis paper           links  
  Antonin Chambolle, Vicent Caselles, Matteo Novaga, Daniel Cremers, Thomas Pock       Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery", 2009, Linz, Austria  
paper These are the lecture notes of a course taught in Linz in Sept., 2009, at the school "Theoretical Foundations and Numerical Methods for Sparse Recovery", organized by Massimo Fornasier and Ronny Romlau. They address various theoretical and practical topics...
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  Segmentation of interwoven 3d tubular tree structures utilizing shape priors and graph cuts paper              
  Christian Bauer, Thomas Pock, Erich Sorantin, Horst Bischof, Reinhard Beichel       Medical Image Analysis  
paper We present and evaluate a general approach for robust segmentation of tubular tree structures in 3d medical images.
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  Local, Semi-global, and Global Optimization for Motion Estimation paper              
  Werner Trobin       Phd Thesis 2009  
paper Motion cues are an integral part of our visual experience, and therefore it is not surprising that the recovery of motion information from image sequences is a prominent problem in computer vision...
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  A Variational Approach to Semiautomatic Generation of Digital Terrain Models paper              
  Markus Unger, Thomas Pock, Markus Grabner, Andreas Klaus, Horst Bischof       5th Int. Symp. on Visual Computing, Las Vegas, USA  
paper We present a semiautomatic approach to generate high quality digital terrain models (DTM) from digital surface models (DSM). A DTM is a model of the earths surface, where all man made objects and the vegetation have been removed. In order to achieve this, we use a variational energy minimization approach. The proposed energy functional incorporates Huber regularization to yield piecewise smooth surfaces...
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  Advanced Data Terms for Variational Optic Flow Estimation paper              
  Frank Steinbruecker, Thomas Pock, Daniel Cremers       Vision, Modeling, and Visualization Workshop, Braunschweig (GER)  
paper In this paper, we present optic flow algorithms which are based on a variety of increasingly sophisticated data terms. Such data terms allow to better identify correspondences between points in either image than the traditional intensity difference since they characterize the local image structure more uniquely. We present an algorithmic framework which allows to directly incorporate arbitrary data terms...
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  Tracking as Segmentation of Spatial-Temporal Volumes by Anisotropic Weighted TV paper              
  Markus Unger, Thomas Mauthner, Thomas Pock, Horst Bischof       EMMCVPR 2009  
paper Tracking is usually interpreted as finding an object in single consecutive frames. Regularization is done by enforcing temporal smoothness of appearance, shape and motion. We propose a tracker, by interpreting the task of tracking as segmentation of a volume in 3D...
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  Anisotropic Huber-L1 Optical Flow paper           links  
  Manuel Werlberger, Werner Trobin, Thomas Pock, Andreas Wedel, Daniel Cremers, Horst Bischof       British Machine Vision Conference 2009  
paper The presented work is motivated by the problem of restoring severely degraded historic video material via an optical flow-based interpolation. In order to increase the robustness as well as the accuracy of discontinuity preserving variational optical flow models, we propose two extensions...
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  Flowball 2009 - An Interactive Game based on Optical Flow paper              
  Wolfgang Paier       Bachelor Thesis  
paper This document roughly covers the steps which are needed to provide a user interface solely based on optical flow. We used two di fferent digital cameras: A simple webcam or an expensive AVT-Marlin industrial camera. We also used two different algorithms to calculate the optical flow...
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  Video Super Resolution using Duality Based TV-L1 Optical Flow paper              
  Dennis Mitzel, Thomas Pock, Thomas Schoenemann, Daniel Cremers       DAGM 2009  
paper In this paper, we propose a variational framework for computing a superresolved image of a scene from an arbitrary input video. To this end, we employ a recently proposed quadratic relaxation scheme for high accuracy optic flow estimation. Subsequently we estimate a high resolution image using a variational approach...
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  Large Displacement Optical Flow Computation without Warping paper              
  Frank Steinbruecker, Thomas Pock, Daniel Cremers       International Conference on Computer Vision 2009  
paper We propose an algorithm for large displacement optical flow estimation which does not require the commonly used coarse-to-fine warping strategy. It is based on a quadratic relaxation of the optical flow functional which decouples data term and regularizer...
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  Structure- and Motion-adaptive Regularization for High Accuracy Optic Flow paper              
  Andreas Wedel, Daniel Cremers, Thomas Pock, Horst Bischof       International Conference on Computer Vision 2009  
paper The accurate estimation of motion in image sequences is of central importance to numerous computer vision applications. Most competitive algorithms compute flow fields by minimizing an energy made of a data and a regularity term. To date, the best performing methods rely on rather simple purely geometric regularizers...
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  Interactive Texture Segmentation using Random Forests and Total Variation paper              
  Jakob Santner, Markus Unger, Thomas Pock, Christian Leistner, Amir Saffari, Horst Bischof       British Machine Vision Conference 2009  
paper Common methods for interactive texture segmentation rely on probability maps based on low dimensional features such as e.g. intensity or color, that are usually modeled using basic learning algorithms such as histograms or Gaussian Mixture Models. The use of low level features allows for fast generation of these hypotheses but limits applicability to a small class of images. We address this problem by learning complex descriptors with Random Forests...
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  An Algorithm for Minimizing the Mumford-Shah Functional paper              
  Thomas Pock, Daniel Cremers, Horst Bischof, Antonin Chambolle       International Conference on Computer Vision 2009  
paper In this work we revisit the Mumford-Shah functional, one of the most studied variational approaches to image segmentation. The contribution of this paper is to propose an algorithm which allows to minimize a convex relaxation of the Mumford-Shah functional obtained by functional lifting. The algorithm is an efficient primal-dual projection algorithm for which we prove convergence.
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  A Variational Model for Interactive Shape Prior Segmentation and Real-Time Tracking paper              
  Manuel Werlberger, Thomas Pock, Markus Unger, Horst Bischof       SSVM 2009, Voss, Norway  
paper In this paper, we introduce a semi-automated segmentation method based on minimizing the Geodesic Active Contour energy incorporating a shape prior. We increase the robustness of the segmentation result using the additional shape information that represents the desired structure. Furthermore the user has the possibility to take corrective actions during the segmentation...
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  Semi Automatic Segmentation of Articular Cartilage using Variational Methods paper              
  Christian Reinbacher       Master's Thesis  
paper In this Master's Thesis we propose an interactive segmentation framework for the semi automatic segmentation of articular cartilage. Until today, no automatic segmentation method is able achieve the accuracy, necessary for a trustworthy diagnosis. Also, physicians in general prefer to be able to control and modify the segmentation result, which is usually complicated using automatic methods...
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  A Convex Relaxation Approach for Computing Minimal Partitions paper              
  Thomas Pock, Antonin Chambolle, Daniel Cremers, Horst Bischof       CVPR 2009, Miami, FL  
paper In this work we propose a convex relaxation approach for computing minimal partitions. Our approach is based on rewriting the minimal partition problem (also known as Potts model) in terms of a primal dual Total Variation functional. We show that the Potts prior can be incorporated by means of convex constraints on the dual variables. For minimization we propose an efficient primal dual projected gradient algorithm...
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  A convex approach for computing minimal partitions paper              
  Antonin Chambolle, Daniel Cremers, Thomas Pock       Technical Report  
paper We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically, we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct...
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  Duality TV-L1 Flow with Fundamental Matrix Prior paper              
  Andreas Wedel, Thomas Pock, Juergen Braun, Uwe Franke, Daniel Cremers       Image and Vision Computing, Auckland (NZ), 2008  
paper Variational techniques yield the most accurate results for dense optical flow fields between two images. They have the nice property of inherent smoothness to cope with untextured image regions: the filling-in of such regions is driven by neighbouring pixels. Such filling-in is not always the best choice...
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  Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware paper              
  Florian Knoll, Markus Unger, Franz Ebner, Rudolf Stollberger       20th Annual Int. Conference on Magnetic Resonance Angiography  
paper Undersampled imaging strategies with state of the art reconstruction methods like compressed sensing, which reformulate image reconstruction as a constrained optimization problem, have the potential to deliver CE MRA images with high spatial and temporal resolution. The drawback...
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  Continuous Energy Minimization via Repeated Binary Fusion paper              
  Werner Trobin, Thomas Pock, Daniel Cremers, Horst Bischof       European Conference on Computer Vision 2008  
paper Variational problems, which are commonly used to solve lowlevel vision tasks, are typically minimized via a local, iterative optimization strategy, e.g. gradient descent. Since every iteration is restricted to a small, local improvement, the overall convergence can be slow...
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  A Convex Formulation of Continuous Multi-Label Problems paper              
  Thomas Pock, Thomas Schoenemann, Gottfried Graber, Horst Bischof, Daniel Cremers       European Conference on Computer Vision 2008  
paper We propose a spatially continuous formulation of Ishikawa's discrete multi-label problem.We show that the resulting non-convex variational problem can be reformulated as a convex variational problem via embedding in a higher dimensional space.
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paper Flowball is an interactive game presented at our Institute's annualy Open Lab Night in October 2008. Using dense optical flow computed in realtime on a Geforce GTX 280, flowball is a demonstration of current capabilities of GPGPU for the interested public.
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  TVSeg - Interactive Total Variation Based Image Segmentation paper              
  Markus Unger, Thomas Pock, Werner Trobin, Daniel Cremers, Horst Bischof       British Machine Vision Conference 2008  
paper Interactive object extraction is an important part in any image editing software. We present a two step segmentation algorithm that first obtains a binary segmentation and then applies matting on the border regions to obtain a smooth alpha channel...
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  Automatic Differentiation for GPU-Accelerated 2D/3D Registration paper              
  Markus Grabner, Thomas Pock, Tobias Gross, Bernhard Kainz       Proc. 5th International Conference on Automatic Differentiation  
paper We demonstrate the applicability of automatic differentiation (AD) techniques to a class of 2D/3D registration problems which are highly computationally intensive and can therefore greatly benefit from a parallel implementation on recent graphics processing units (GPUs)...
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  Interactive globally optimal image segmentation paper              
  Markus Unger, Thomas Pock, Horst Bischof       Technical Report 08/02  
paper Image segmentation is a challenging task in computer vision. We present a general purpose image segmentation framework, and focus on its application to medical imaging...
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  Fast and Exact Solution of Total Variation Models on the GPU paper              
  Thomas Pock, Markus Unger, Daniel Cremers, Horst Bischof       CVPR 2008, Workshop on Computer Vision on GPUs  
paper This paper discusses fast and accurate methods to solve Total Variation (TV) models on the graphics processing unit (GPU). We review two prominent models incorporating TV regularization and present different algorithms to solve these models...
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  An Unbiased Second-Order Prior for High-Accuracy Motion Estimation paper              
  Werner Trobin, Thomas Pock, Daniel Cremers, Horst Bischof       DAGM 2008  
paper Virtually all variational methods for motion estimation regularize the gradient of the flow field, which introduces a bias towards piecewise constant motions in weakly textured areas. We propose a novel regularization approach...
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  Globally Optimal TV-L1 Shape Prior Segmentation paper              
  Manuel Werlberger       Master Thesis 2008  
paper Interpreting an image is a common and challenging task in computer vision. A human observer does not only use intensity or color information or other basic features when looking for region boundaries but also takes prior knowledge into account...
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  Continuous Globally Optimal Image Segmentation with Local Constraints paper              
  Markus Unger, Thomas Pock, Horst Bischof       Computer Vision Winter Workshop 2008  
paper The Geodesic Active contour model is a very flexible model for variational image segmentation. Unfortunately the Geodesic Active Contour model exhibits local minima making segmentation results strongly dependent on its initialization...
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  Fast Total Variation for Computer Vision paper              
  Thomas Pock       Phd Thesis 2008  
paper Motivated by statistical inference methods, variational methods are among the most successful methods to solve a number of different Computer Vision problems. Variational methods aim to minimize an energy functional...
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  A Globally Optimal Algorithm for Robust TV-L1 Range Image Integration paper              
  Christopher Zach, Thomas Pock, Horst Bischof       International Conference on Computer Vision 2007  
paper Robust integration of range images is an important task for building high-quality 3D models. Since range images may have a substantial amount of outliers, any integration approach aimed at high-quality models needs an increased level of robustness...
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  A Duality Based Approach for Realtime TV-L1 Optical Flow paper              
  Christopher Zach, Thomas Pock, Horst Bischof       DAGM 2007  
paper Energy-based methods are highly successful and accurate approaches to calculate the optical flow between images. If discontinuity preservation and robustness against image noise and local illumination changes are required...
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  Mumford-Shah Meets Stereo: Integration of Weak Depth Hypotheses paper              
  Thomas Pock, Christopher Zach, Horst Bischof       Conference on Computer Vision and Pattern Recognition 2007  
paper Recent results on stereo indicate that an accurate segmentation is crucial for obtaining faithful depth maps. Variational methods have successfully been applied to both image segmentation and computational stereo. In this paper we propose a combination...
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  Real-time Computation of Variational Methods on Graphics Hardware paper              
  Thomas Pock, Markus Grabner, Horst Bischof       Computer Vision Winter Workshop 2007  
paper This paper combines two powerful approaches: variational methods and graphics hardware. Variational methods have demonstrated considerable success in computer vision for such diverse tasks as denoising, segmentation, registration, stereo matching...
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  A Probabilistic Multi-phase Model for Variational Image Segmentation paper              
  Thomas Pock, Horst Bischof       Pattern Recognition (Proc. DAGM) 2006  
paper Recently, the Phase Field Method has shown to be a powerful tool for variational image segmentation. In this paper, we present a novel multi-phase model for probability based image segmentation...
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