After [10, 15, 12, 2, 4] minimum cut/maximum ow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-ow algorithms with dierent polynomial time complexity. Their practical eciency, however, has to date been studied mainly outside the scope of computer vision.

Abstract—In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.

Abstract—An overview is presented of the medical image processing literature on mutual-information-based registration. The aim of the survey is threefold: an introduction for those new to the field, an overview for those working in the field, and a reference for those searching for literature on a specific application. Methods are classified according to the different aspects of mutual-information-based registration. The main division is in aspects of the methodology and of the application. The part on methodology describes choices made on facets such as preprocessing of images, gray value interpolation, optimization, adaptations to the mutual information measure, and different types of geometrical transformations. The part on applications is a reference of the literature available on different modalities, on interpatient registration and on different anatomical objects. Comparison studies including mutual information are also considered. The paper starts with a description of entropy and mutual information and it closes with a discussion on past achievements and some future challenges. Index Terms—Image registration, literature survey, matching, mutual information. I.

Abstract. Previous work [5] has shown how Ising spatial priors [1] can be incorported into fMRI analysis in a principled manner by using Mutual Information as a statistic for protocol-related activity. The activation image with maximum a posteriori (MAP) probability can then be computed exactly in polynomial time by reduction to a Min-Cut/Max-Flow Problem [4]. In this work, we show that an Ising prior can be applied in the same manner using a standard, linear activation model. 1

Existing parallel MRI methods are limited by a fundamental trade-off in that suppressing noise introduces aliasing artifacts. Bayesian methods with an appropriately chosen image prior offer a promising alternative; however, previous methods with spatial priors assume that intensities vary smoothly over the entire image, resulting in blurred edges. Here we introduce an edge-preserving prior (EPP) that instead assumes that intensities are piecewise smooth, and propose a new approach to efficiently compute its Bayesian estimate. The estimation task is formulated as an optimization problem that requires a nonconvex objective function to be minimized in a space with thousands of dimensions. As a result, traditional continuous minimization methods cannot be applied. This optimization task is closely related to some problems in the field of computer vision for which discrete optimization methods have been developed in the last few years. We adapt these algorithms, which are based on graph cuts, to address our optimization problem. The results of several parallel imaging experiments on brain and torso regions performed under challenging conditions with high acceleration factors are shown and compared with the results of conventional sensitivity encoding (SENSE) methods. An empirical analysis indicates that the proposed method visually improves overall quality compared to conventional methods.

Abstract. This paper describes a new segmentation technique for multidimensional dynamic data. One example of such data is a perfusion sequence where a number of 3D MRI volumes shows the dynamics of a contrast agent inside the kidney or heart at end-diastole. We assume that the volumes are registered. If not, we register consecutive volumes via mutual information maximization. The sequence of n registered volumes is regarded as a single volume where each voxel holds an n-dimensional vector of intensities, or intensity curve. Our approach is to segment this volume directly based on voxels intensity curves using a generalization of the graph cut techniques in [7, 2]. These techniques use a spatial Markov model to describe correlations between voxels. Our contribution is in introducing a temporal Markov model to describe the desired dynamic properties of segments. Graph cuts obtain a globally optimal segmentation with the best balance between boundary and regional properties among all segmentations satisfying user placed hard constraints. Flexibility, coherent theoretical formulation, and the possibility of a globally optimal solution are attractive features of our method that gracefully handles even low quality data. We demonstrate results for 3D kidney and 2D heart perfusion sequences. 1

In recent years, graph cuts have emerged as a powerful optimization technique for minimizing energy functions that arise in low-level vision problems. Graph cuts avoid the problems of local minima inherent in other approaches (such as gradient descent). The goal of this thesis is to apply graph cuts to a classical computer vision problem — scene reconstruction from multiple views, i.e. computing the 3-dimensional shape of the scene. This thesis provides a technical result which greatly facilitates the derivation of the scene reconstruction algorithm. Our result should also be useful for devel-oping other energy minimization algorithms based on graph cuts. Previously such algorithms explicitly constructed graphs where a minimum cut also minimizes the appropriate energy. It is natural to ask for what energy functions we can construct such a graph. We answer this question for the class of functions of binary variables that can be written as a sum of terms containing three or fewer variables. We give a simple criterion for functions in this class which is necessary and sufficient, as well as a necessary condition for any function of binary variables. We also give a

Phase contrast magnetic resonance angiography (PC-MRA) is a non-invasive method for 3D vessel delineation, which for each voxel not only provides measurement of speed (conveyed as a speed image), but also gives a three-component estimate of flow direction (in the form of phase images). In this thesis, we present a new approach to reconstructing vessels and aneurysms from PC-MRA, and demonstrate how speed and flow coherence information extracted from a PC-MRA dataset can be combined for detecting and reconstructing normal vessels and aneurysms with relatively low flow rate and low signal-to-noise ratio (SNR). We propose to use a Maxwell-Gaussian mixture density to model the background signal and combine this with a uniform distribution for modelling vascular signal to give a Maxwell-Gaussian-uniform (MGU) mixture model of speed image intensity. The MGU model param-eters are estimated by the Expectation-Maximisation (EM) algorithm. It is shown that the Maxwell-Gaussian mixture distribution models the background signal more accurately than a Maxwell distribution. Although the MGU model works satisfactorily in classifying the back-

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