1,053 research outputs found

    Multi-Atlas Segmentation using Partially Annotated Data: Methods and Annotation Strategies

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    Multi-atlas segmentation is a widely used tool in medical image analysis, providing robust and accurate results by learning from annotated atlas datasets. However, the availability of fully annotated atlas images for training is limited due to the time required for the labelling task. Segmentation methods requiring only a proportion of each atlas image to be labelled could therefore reduce the workload on expert raters tasked with annotating atlas images. To address this issue, we first re-examine the labelling problem common in many existing approaches and formulate its solution in terms of a Markov Random Field energy minimisation problem on a graph connecting atlases and the target image. This provides a unifying framework for multi-atlas segmentation. We then show how modifications in the graph configuration of the proposed framework enable the use of partially annotated atlas images and investigate different partial annotation strategies. The proposed method was evaluated on two Magnetic Resonance Imaging (MRI) datasets for hippocampal and cardiac segmentation. Experiments were performed aimed at (1) recreating existing segmentation techniques with the proposed framework and (2) demonstrating the potential of employing sparsely annotated atlas data for multi-atlas segmentation

    Optimisation for image processing

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    The main purpose of optimisation in image processing is to compensate for missing, corrupted image data, or to find good correspondences between input images. We note that image data essentially has infinite dimensionality that needs to be discretised at certain levels of resolution. Most image processing methods find a suboptimal solution, given the characteristics of the problem. While the general optimisation literature is vast, there does not seem to be an accepted universal method for all image problems. In this thesis, we consider three interrelated optimisation approaches to exploit problem structures of various relaxations to three common image processing problems: 1. The first approach to the image registration problem is based on the nonlinear programming model. Image registration is an ill-posed problem and suffers from many undesired local optima. In order to remove these unwanted solutions, certain regularisers or constraints are needed. In this thesis, prior knowledge of rigid structures of the images is included in the problem using linear and bilinear constraints. The aim is to match two images while maintaining the rigid structure of certain parts of the images. A sequential quadratic programming algorithm is used, employing dimensional reduction, to solve the resulting discretised constrained optimisation problem. We show that pre-processing of the constraints can reduce problem dimensionality. Experimental results demonstrate better performance of our proposed algorithm compare to the current methods. 2. The second approach is based on discrete Markov Random Fields (MRF). MRF has been successfully used in machine learning, artificial intelligence, image processing, including the image registration problem. In the discrete MRF model, the domain of the image problem is fixed (relaxed) to a certain range. Therefore, the optimal solution to the relaxed problem could be found in the predefined domain. The original discrete MRF is NP hard and relaxations are needed to obtain a suboptimal solution in polynomial time. One popular approach is the linear programming (LP) relaxation. However, the LP relaxation of MRF (LP-MRF) is excessively high dimensional and contains sophisticated constraints. Therefore, even one iteration of a standard LP solver (e.g. interior-point algorithm), may take too long to terminate. Dual decomposition technique has been used to formulate a convex-nondifferentiable dual LP-MRF that has geometrical advantages. This has led to the development of first order methods that take into account the MRF structure. The methods considered in this thesis for solving the dual LP-MRF are the projected subgradient and mirror descent using nonlinear weighted distance functions. An analysis of the convergence properties of the method is provided, along with improved convergence rate estimates. The experiments on synthetic data and an image segmentation problem show promising results. 3. The third approach employs a hierarchy of problem's models for computing the search directions. The first two approaches are specialised methods for image problems at a certain level of discretisation. As input images are infinite-dimensional, all computational methods require their discretisation at some levels. Clearly, high resolution images carry more information but they lead to very large scale and ill-posed optimisation problems. By contrast, although low level discretisation suffers from the loss of information, it benefits from low computational cost. In addition, a coarser representation of a fine image problem could be treated as a relaxation to the problem, i.e. the coarse problem is less ill-conditioned. Therefore, propagating a solution of a good coarse approximation to the fine problem could potentially improve the fine level. With the aim of utilising low level information within the high level process, we propose a multilevel optimisation method to solve the convex composite optimisation problem. This problem consists of the minimisation of the sum of a smooth convex function and a simple non-smooth convex function. The method iterates between fine and coarse levels of discretisation in the sense that the search direction is computed using information from either the gradient or a solution of the coarse model. We show that the proposed algorithm is a contraction on the optimal solution and demonstrate excellent performance on experiments with image restoration problems.Open Acces

    Multi-Modal Learning For Adaptive Scene Understanding

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    Modern robotics systems typically possess sensors of different modalities. Segmenting scenes observed by the robot into a discrete set of classes is a central requirement for autonomy. Equally, when a robot navigates through an unknown environment, it is often necessary to adjust the parameters of the scene segmentation model to maintain the same level of accuracy in changing situations. This thesis explores efficient means of adaptive semantic scene segmentation in an online setting with the use of multiple sensor modalities. First, we devise a novel conditional random field(CRF) inference method for scene segmentation that incorporates global constraints, enforcing particular sets of nodes to be assigned the same class label. To do this efficiently, the CRF is formulated as a relaxed quadratic program whose maximum a posteriori(MAP) solution is found using a gradient-based optimization approach. These global constraints are useful, since they can encode "a priori" information about the final labeling. This new formulation also reduces the dimensionality of the original image-labeling problem. The proposed model is employed in an urban street scene understanding task. Camera data is used for the CRF based semantic segmentation while global constraints are derived from 3D laser point clouds. Second, an approach to learn CRF parameters without the need for manually labeled training data is proposed. The model parameters are estimated by optimizing a novel loss function using self supervised reference labels, obtained based on the information from camera and laser with minimum amount of human supervision. Third, an approach that can conduct the parameter optimization while increasing the model robustness to non-stationary data distributions in the long trajectories is proposed. We adopted stochastic gradient descent to achieve this goal by using a learning rate that can appropriately grow or diminish to gain adaptability to changes in the data distribution

    Half-integrality, LP-branching and FPT Algorithms

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    A recent trend in parameterized algorithms is the application of polytope tools (specifically, LP-branching) to FPT algorithms (e.g., Cygan et al., 2011; Narayanaswamy et al., 2012). However, although interesting results have been achieved, the methods require the underlying polytope to have very restrictive properties (half-integrality and persistence), which are known only for few problems (essentially Vertex Cover (Nemhauser and Trotter, 1975) and Node Multiway Cut (Garg et al., 1994)). Taking a slightly different approach, we view half-integrality as a \emph{discrete} relaxation of a problem, e.g., a relaxation of the search space from {0,1}V\{0,1\}^V to {0,1/2,1}V\{0,1/2,1\}^V such that the new problem admits a polynomial-time exact solution. Using tools from CSP (in particular Thapper and \v{Z}ivn\'y, 2012) to study the existence of such relaxations, we provide a much broader class of half-integral polytopes with the required properties, unifying and extending previously known cases. In addition to the insight into problems with half-integral relaxations, our results yield a range of new and improved FPT algorithms, including an O(Σ2k)O^*(|\Sigma|^{2k})-time algorithm for node-deletion Unique Label Cover with label set Σ\Sigma and an O(4k)O^*(4^k)-time algorithm for Group Feedback Vertex Set, including the setting where the group is only given by oracle access. All these significantly improve on previous results. The latter result also implies the first single-exponential time FPT algorithm for Subset Feedback Vertex Set, answering an open question of Cygan et al. (2012). Additionally, we propose a network flow-based approach to solve some cases of the relaxation problem. This gives the first linear-time FPT algorithm to edge-deletion Unique Label Cover.Comment: Added results on linear-time FPT algorithms (not present in SODA paper

    Flow pattern analysis for magnetic resonance velocity imaging

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    Blood flow in the heart is highly complex. Although blood flow patterns have been investigated by both computational modelling and invasive/non-invasive imaging techniques, their evolution and intrinsic connection with cardiovascular disease has yet to be explored. Magnetic resonance (MR) velocity imaging provides a comprehensive distribution of multi-directional in vivo flow distribution so that detailed quantitative analysis of flow patterns is now possible. However, direct visualisation or quantification of vector fields is of little clinical use, especially for inter-subject or serial comparison of changes in flow patterns due to the progression of the disease or in response to therapeutic measures. In order to achieve a comprehensive and integrated description of flow in health and disease, it is necessary to characterise and model both normal and abnormal flows and their effects. To accommodate the diversity of flow patterns in relation to morphological and functional changes, we have described in this thesis an approach of detecting salient topological features prior to analytical assessment of dynamical indices of the flow patterns. To improve the accuracy of quantitative analysis of the evolution of topological flow features, it is essential to restore the original flow fields so that critical points associated with salient flow features can be more reliably detected. We propose a novel framework for the restoration, abstraction, extraction and tracking of flow features such that their dynamic indices can be accurately tracked and quantified. The restoration method is formulated as a constrained optimisation problem to remove the effects of noise and to improve the consistency of the MR velocity data. A computational scheme is derived from the First Order Lagrangian Method for solving the optimisation problem. After restoration, flow abstraction is applied to partition the entire flow field into clusters, each of which is represented by a local linear expansion of its velocity components. This process not only greatly reduces the amount of data required to encode the velocity distribution but also permits an analytical representation of the flow field from which critical points associated with salient flow features can be accurately extracted. After the critical points are extracted, phase portrait theory can be applied to separate them into attracting/repelling focuses, attracting/repelling nodes, planar vortex, or saddle. In this thesis, we have focused on vortical flow features formed in diastole. To track the movement of the vortices within a cardiac cycle, a tracking algorithm based on relaxation labelling is employed. The constraints and parameters used in the tracking algorithm are designed using the characteristics of the vortices. The proposed framework is validated with both simulated and in vivo data acquired from patients with sequential MR examination following myocardial infarction. The main contribution of the thesis is in the new vector field restoration and flow feature abstraction method proposed. They allow the accurate tracking and quantification of dynamic indices associated with salient features so that inter- and intra-subject comparisons can be more easily made. This provides further insight into the evolution of blood flow patterns and permits the establishment of links between blood flow patterns and localised genesis and progression of cardiovascular disease.Open acces

    Global optimisation techniques for image segmentation with higher order models

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    Energy minimisation methods are one of the most successful approaches to image segmentation. Typically used energy functions are limited to pairwise interactions due to the increased complexity when working with higher-order functions. However, some important assumptions about objects are not translatable to pairwise interactions. The goal of this thesis is to explore higher order models for segmentation that are applicable to a wide range of objects. We consider: (1) a connectivity constraint, (2) a joint model over the segmentation and the appearance, and (3) a model for segmenting the same object in multiple images. We start by investigating a connectivity prior, which is a natural assumption about objects. We show how this prior can be formulated in the energy minimisation framework and explore the complexity of the underlying optimisation problem, introducing two different algorithms for optimisation. This connectivity prior is useful to overcome the “shrinking bias” of the pairwise model, in particular in interactive segmentation systems. Secondly, we consider an existing model that treats the appearance of the image segments as variables. We show how to globally optimise this model using a Dual Decomposition technique and show that this optimisation method outperforms existing ones. Finally, we explore the current limits of the energy minimisation framework. We consider the cosegmentation task and show that a preference for object-like segmentations is an important addition to cosegmentation. This preference is, however, not easily encoded in the energy minimisation framework. Instead, we use a practical proposal generation approach that allows not only the inclusion of a preference for object-like segmentations, but also to learn the similarity measure needed to define the cosegmentation task. We conclude that higher order models are useful for different object segmentation tasks. We show how some of these models can be formulated in the energy minimisation framework. Furthermore, we introduce global optimisation methods for these energies and make extensive use of the Dual Decomposition optimisation approach that proves to be suitable for this type of models

    3D shape matching and registration : a probabilistic perspective

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    Dense correspondence is a key area in computer vision and medical image analysis. It has applications in registration and shape analysis. In this thesis, we develop a technique to recover dense correspondences between the surfaces of neuroanatomical objects over heterogeneous populations of individuals. We recover dense correspondences based on 3D shape matching. In this thesis, the 3D shape matching problem is formulated under the framework of Markov Random Fields (MRFs). We represent the surfaces of neuroanatomical objects as genus zero voxel-based meshes. The surface meshes are projected into a Markov random field space. The projection carries both geometric and topological information in terms of Gaussian curvature and mesh neighbourhood from the original space to the random field space. Gaussian curvature is projected to the nodes of the MRF, and the mesh neighbourhood structure is projected to the edges. 3D shape matching between two surface meshes is then performed by solving an energy function minimisation problem formulated with MRFs. The outcome of the 3D shape matching is dense point-to-point correspondences. However, the minimisation of the energy function is NP hard. In this thesis, we use belief propagation to perform the probabilistic inference for 3D shape matching. A sparse update loopy belief propagation algorithm adapted to the 3D shape matching is proposed to obtain an approximate global solution for the 3D shape matching problem. The sparse update loopy belief propagation algorithm demonstrates significant efficiency gain compared to standard belief propagation. The computational complexity and convergence property analysis for the sparse update loopy belief propagation algorithm are also conducted in the thesis. We also investigate randomised algorithms to minimise the energy function. In order to enhance the shape matching rate and increase the inlier support set, we propose a novel clamping technique. The clamping technique is realized by combining the loopy belief propagation message updating rule with the feedback from 3D rigid body registration. By using this clamping technique, the correct shape matching rate is increased significantly. Finally, we investigate 3D shape registration techniques based on the 3D shape matching result. Based on the point-to-point dense correspondences obtained from the 3D shape matching, a three-point based transformation estimation technique is combined with the RANdom SAmple Consensus (RANSAC) algorithm to obtain the inlier support set. The global registration approach is purely dependent on point-wise correspondences between two meshed surfaces. It has the advantage that the need for orientation initialisation is eliminated and that all shapes of spherical topology. The comparison of our MRF based 3D registration approach with a state-of-the-art registration algorithm, the first order ellipsoid template, is conducted in the experiments. These show dense correspondence for pairs of hippocampi from two different data sets, each of around 20 60+ year old healthy individuals

    Low-rate non-intrusive load monitoring approaches via graph signal processing

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    The large-scale roll-out of smart metering worldwide brings many new application possibilities. One promising application is appliance-level energy feedback based on identifying individual loads from aggregate measurements. Driven by high application potentials, the research in this area has intensified. In particular, non-intrusive load monitoring (NILM), that is, estimating appliance load consumption from aggregate readings, using software means only, has attracted a lot of attention, since it does not require any additional hardware to be installed. This thesis first proposes two Graph Signal Processing (GSP)-based approaches for disaggregation of total energy consumption down to individual appliances used. The first approach uses the Graph Laplacian Regularisation (GLR) minimiser results as a starting point, adding further refinement via Simulated Annealing (SA). The second approach applies data segmentation and associates data segments with graph nodes. A Dynamic Time Warping (DTW) distance is applied for evaluating weights between graph nodes. GLR minimiser is again used for clustering. Finally, a generic optimisation based approach is proposed for improving the accuracy of existing NILM by minimising the difference between the measured aggregate load and the sum of estimated individual loads with the difference from original NILM approaches' results as regularisation. For all proposed methods, the competitive performance are demonstrated in terms of both accuracy and effciency compared to state-of-the-art approaches, using the public Personalised Retrofit Decision Support Tools For UK Homes Using Smart Home Technology (REFIT) dataset and Reference Energy Disaggregation Dataset (REDD) electrical load datasets.The large-scale roll-out of smart metering worldwide brings many new application possibilities. One promising application is appliance-level energy feedback based on identifying individual loads from aggregate measurements. Driven by high application potentials, the research in this area has intensified. In particular, non-intrusive load monitoring (NILM), that is, estimating appliance load consumption from aggregate readings, using software means only, has attracted a lot of attention, since it does not require any additional hardware to be installed. This thesis first proposes two Graph Signal Processing (GSP)-based approaches for disaggregation of total energy consumption down to individual appliances used. The first approach uses the Graph Laplacian Regularisation (GLR) minimiser results as a starting point, adding further refinement via Simulated Annealing (SA). The second approach applies data segmentation and associates data segments with graph nodes. A Dynamic Time Warping (DTW) distance is applied for evaluating weights between graph nodes. GLR minimiser is again used for clustering. Finally, a generic optimisation based approach is proposed for improving the accuracy of existing NILM by minimising the difference between the measured aggregate load and the sum of estimated individual loads with the difference from original NILM approaches' results as regularisation. For all proposed methods, the competitive performance are demonstrated in terms of both accuracy and effciency compared to state-of-the-art approaches, using the public Personalised Retrofit Decision Support Tools For UK Homes Using Smart Home Technology (REFIT) dataset and Reference Energy Disaggregation Dataset (REDD) electrical load datasets

    The power of linear programming for general-valued CSPs

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    Let DD, called the domain, be a fixed finite set and let Γ\Gamma, called the valued constraint language, be a fixed set of functions of the form f:DmQ{}f:D^m\to\mathbb{Q}\cup\{\infty\}, where different functions might have different arity mm. We study the valued constraint satisfaction problem parametrised by Γ\Gamma, denoted by VCSP(Γ)(\Gamma). These are minimisation problems given by nn variables and the objective function given by a sum of functions from Γ\Gamma, each depending on a subset of the nn variables. Finite-valued constraint languages contain functions that take on only rational values and not infinite values. Our main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation (BLP). For a valued constraint language Γ\Gamma, BLP is a decision procedure for Γ\Gamma if and only if Γ\Gamma admits a symmetric fractional polymorphism of every arity. For a finite-valued constraint language Γ\Gamma, BLP is a decision procedure if and only if Γ\Gamma admits a symmetric fractional polymorphism of some arity, or equivalently, if Γ\Gamma admits a symmetric fractional polymorphism of arity 2. Using these results, we obtain tractability of several novel classes of problems, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) kk-submodular on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees.Comment: A full version of a FOCS'12 paper by the last two authors (arXiv:1204.1079) and an ICALP'13 paper by the first author (arXiv:1207.7213) to appear in SIAM Journal on Computing (SICOMP
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