Contributions of Continuous Max-Flow Theory to Medical Image Processing

Discrete graph cuts and continuous max-flow theory have created a paradigm shift in many areas of medical image processing. As previous methods limited themselves to analytically solvable optimization problems or guaranteed only local optimizability to increasingly complex and non-convex functionals, current methods based now rely on describing an optimization problem in a series of general yet simple functionals with a global, but non-analytic, solution algorithms. This has been increasingly spurred on by the availability of these general-purpose algorithms in an open-source context. Thus, graph-cuts and max-flow have changed every aspect of medical image processing from reconstruction to enhancement to segmentation and registration. To wax philosophical, continuous max-flow theory in particular has the potential to bring a high degree of mathematical elegance to the field, bridging the conceptual gap between the discrete and continuous domains in which we describe different imaging problems, properties and processes. In Chapter 1, we use the notion of infinitely dense and infinitely densely connected graphs to transfer between the discrete and continuous domains, which has a certain sense of mathematical pedantry to it, but the resulting variational energy equations have a sense of elegance and charm. As any application of the principle of duality, the variational equations have an enigmatic side that can only be decoded with time and patience. The goal of this thesis is to show the contributions of max-flow theory through image enhancement and segmentation, increasing incorporation of topological considerations and increasing the role played by user knowledge and interactivity. These methods will be rigorously grounded in calculus of variations, guaranteeing fuzzy optimality and providing multiple solution approaches to addressing each individual problem

Méthodes multi-organes rapides avec a priori de forme pour la localisation et la segmentation en imagerie médicale 3D

With the ubiquity of imaging in medical applications (diagnostic, treatment follow-up, surgery planning. . . ), image processing algorithms have become of primary importance. Algorithms help clinicians extract critical information more quickly and more reliably from increasingly large and complex acquisitions. In this context, anatomy localization and segmentation is a crucial component in modern clinical workflows. Due to particularly high requirements in terms of robustness, accuracy and speed, designing such tools remains a challengingtask.In this work, we propose a complete pipeline for the segmentation of multiple organs in medical images. The method is generic, it can be applied to varying numbers of organs, on different imaging modalities. Our approach consists of three components: (i) an automatic localization algorithm, (ii) an automatic segmentation algorithm, (iii) a framework for interactive corrections. We present these components as a coherent processing chain, although each block could easily be used independently of the others. To fulfill clinical requirements, we focus on robust and efficient solutions. Our anatomy localization method is based on a cascade of Random Regression Forests (Cuingnet et al., 2012). One key originality of our work is the use of shape priors for each organ (thanks to probabilistic atlases). Combined with the evaluation of the trained regression forests, they result in shape-consistent confidence maps for each organ instead of simple bounding boxes. Our segmentation method extends the implicit template deformation framework of Mory et al. (2012) to multiple organs. The proposed formulation builds on the versatility of the original approach and introduces new non-overlapping constraintsand contrast-invariant forces. This makes our approach a fully automatic, robust and efficient method for the coherent segmentation of multiple structures. In the case of imperfect segmentation results, it is crucial to enable clinicians to correct them easily. We show that our automatic segmentation framework can be extended with simple user-driven constraints to allow for intuitive interactive corrections. We believe that this final component is key towards the applicability of our pipeline in actual clinical routine.Each of our algorithmic components has been evaluated on large clinical databases. We illustrate their use on CT, MRI and US data and present a user study gathering the feedback of medical imaging experts. The results demonstrate the interest in our method and its potential for clinical use.Avec l’utilisation de plus en plus répandue de l’imagerie dans la pratique médicale (diagnostic, suivi, planification d’intervention, etc.), le développement d’algorithmes d’analyse d’images est devenu primordial. Ces algorithmes permettent aux cliniciens d’analyser et d’interpréter plus facilement et plus rapidement des données de plus en plus complexes. Dans ce contexte, la localisation et la segmentation de structures anatomiques sont devenues des composants critiques dans les processus cliniques modernes. La conception de tels outils pour répondre aux exigences de robustesse, précision et rapidité demeure cependant un réel défi technique.Ce travail propose une méthode complète pour la segmentation de plusieurs organes dans des images médicales. Cette méthode, générique et pouvant être appliquée à un nombre varié de structures et dans différentes modalités d’imagerie, est constituée de trois composants : (i) un algorithme de localisation automatique, (ii) un algorithme de segmentation, (iii) un outil de correction interactive. Ces différentes parties peuvent s’enchaîner aisément pour former un outil complet et cohérent, mais peuvent aussi bien être utilisées indépendemment. L’accent a été mis sur des méthodes robustes et efficaces afin de répondre aux exigences cliniques. Notre méthode de localisation s’appuie sur une cascade de régression par forêts aléatoires (Cuingnet et al., 2012). Elle introduit l’utilisation d’informations a priori de forme, spécifiques à chaque organe (grâce à des atlas probabilistes) pour des résultats plus cohérents avec la réalité anatomique. Notre méthode de segmentation étend la méthode de segmentation par modèle implicite (Mory et al., 2012) à plusieurs modèles. La formulation proposée permet d’obtenir des déformations cohérentes, notamment en introduisant des contraintes de non recouvrement entre les modèles déformés. En s’appuyant sur des forces images polyvalentes, l’approche proposée se montre robuste et performante pour la segmentation de multiples structures. Toute méthode automatique n’est cependant jamais parfaite. Afin que le clinicien garde la main sur le résultat final, nous proposons d’enrichir la formulation précédente avec des contraintes fournies par l’utilisateur. Une optimisation localisée permet d’obtenir un outil facile à utiliser et au comportement intuitif. Ce dernier composant est crucial pour que notre outil soit réellement utilisable en pratique. Chacun de ces trois composants a été évalué sur plusieurs grandes bases de données cliniques (en tomodensitométrie, imagerie par résonance magnétique et ultrasons). Une étude avec des utilisateurs nous a aussi permis de recueillir des retours positifs de plusieurs experts en imagerie médicale. Les différents résultats présentés dans ce manuscrit montrent l’intérêt de notre méthode et son potentiel pour une utilisation clinique

Reconstruction Methods for Free-Breathing Dynamic Contrast-Enhanced MRI

Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) is a valuable diagnostic tool due to the combination of anatomical and physiological information it provides. However, the sequential sampling of MRI presents an inherent tradeoff between spatial and temporal resolution. Compressed Sensing (CS) methods have been applied to undersampled MRI to reconstruct full-resolution images at sub-Nyquist sampling rates. In exchange for shorter data acquisition times, CS-MRI requires more computationally intensive iterative reconstruction methods. We present several model-based image reconstruction (MBIR) methods to improve the spatial and temporal resolution of MR images and/or the computational time for multi-coil MRI reconstruction. We propose efficient variable splitting (VS) methods for support-constrained MRI reconstruction, image reconstruction and denoising with non-circulant boundary conditions, and improved temporal regularization for breast DCE-MRI. These proposed VS algorithms decouple the system model and sparsity terms of the convex optimization problem. By leveraging matrix structures in the system model and sparsifying operator, we perform alternating minimization over a list of auxiliary variables, each of which can be performed efficiently. We demonstrate the computational benefits of our proposed VS algorithms compared to similar proposed methods. We also demonstrate convergence guarantees for two proposed methods, ADMM-tridiag and ADMM-FP-tridiag. With simulation experiments, we demonstrate lower error in spatial and temporal dimensions for these VS methods compared to other object models. We also propose a method for indirect motion compensation in 5D liver DCE-MRI. 5D MRI separates temporal changes due to contrast from anatomical changes due to respiratory motion into two distinct dimensions. This work applies a pre-computed motion model to perform motion-compensated regularization across the respiratory dimension and improve the conditioning of this highly sparse 5D reconstruction problem. We demonstrate a proof of concept using a digital phantom with contrast and respiratory changes, and we show preliminary results for motion model-informed regularization on in vivo patient data.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138498/1/mtle_1.pd

Convex Variational Approaches to Image Motion Estimation, Denoising and Segmentation

Energy minimization and variational methods are widely used in image processing and computer vision, where most energy functions and related constraints can be expressed as, or at least relaxed to, a convex formulation. In this regard, the central role is played by convexity, which not only provides an elegant analytical tool in mathematics but also facilitates the derivation of fast and tractable numerical solvers. In this thesis, four challenging topics of computer vision and image processing are studied by means of modern convex optimization techniques: non-rigid motion decomposition and estimation, TV-L1 image approximation, image segmentation, and multi-class image partition. Some of them are originally modelled in a convex formulation and can be directly solved by convex optimization methods, such as non-rigid flow estimation and non-smooth flow decomposition. The others are first stated as a non-convex model, then studied and solved in a convex relaxation manner, for which their dual models are employed to derive both novel analytical results and fast numerical solvers

Interactive Segmentation of 3D Medical Images with Implicit Surfaces

To cope with a variety of clinical applications, research in medical image processing has led to a large spectrum of segmentation techniques that extract anatomical structures from volumetric data acquired with 3D imaging modalities. Despite continuing advances in mathematical models for automatic segmentation, many medical practitioners still rely on 2D manual delineation, due to the lack of intuitive semi-automatic tools in 3D. In this thesis, we propose a methodology and associated numerical schemes enabling the development of 3D image segmentation tools that are reliable, fast and interactive. These properties are key factors for clinical acceptance. Our approach derives from the framework of variational methods: segmentation is obtained by solving an optimization problem that translates the expected properties of target objects in mathematical terms. Such variational methods involve three essential components that constitute our main research axes: an objective criterion, a shape representation and an optional set of constraints. As objective criterion, we propose a unified formulation that extends existing homogeneity measures in order to model the spatial variations of statistical properties that are frequently encountered in medical images, without compromising efficiency. Within this formulation, we explore several shape representations based on implicit surfaces with the objective to cover a broad range of typical anatomical structures. Firstly, to model tubular shapes in vascular imaging, we introduce convolution surfaces in the variational context of image segmentation. Secondly, compact shapes such as lesions are described with a new representation that generalizes Radial Basis Functions with non-Euclidean distances, which enables the design of basis functions that naturally align with salient image features. Finally, we estimate geometric non-rigid deformations of prior templates to recover structures that have a predictable shape such as whole organs. Interactivity is ensured by restricting admissible solutions with additional constraints. Translating user input into constraints on the sign of the implicit representation at prescribed points in the image leads us to consider inequality-constrained optimization

Segmentation, tracking, and kinematics of lung parenchyma and lung tumors from 4D CT with application to radiation treatment planning.

This thesis is concerned with development of techniques for efficient computerized analysis of 4-D CT data. The goal is to have a highly automated approach to segmentation of the lung boundary and lung nodules inside the lung. The determination of exact lung tumor location over space and time by image segmentation is an essential step to track thoracic malignancies. Accurate image segmentation helps clinical experts examine the anatomy and structure and determine the disease progress. Since 4-D CT provides structural and anatomical information during tidal breathing, we use the same data to also measure mechanical properties related to deformation of the lung tissue including Jacobian and strain at high resolutions and as a function of time. Radiation Treatment of patients with lung cancer can benefit from knowledge of these measures of regional ventilation. Graph-cuts techniques have been popular for image segmentation since they are able to treat highly textured data via robust global optimization, avoiding local minima in graph based optimization. The graph-cuts methods have been used to extract globally optimal boundaries from images by s/t cut, with energy function based on model-specific visual cues, and useful topological constraints. The method makes N-dimensional globally optimal segmentation possible with good computational efficiency. Even though the graph-cuts method can extract objects where there is a clear intensity difference, segmentation of organs or tumors pose a challenge. For organ segmentation, many segmentation methods using a shape prior have been proposed. However, in the case of lung tumors, the shape varies from patient to patient, and with location. In this thesis, we use a shape prior for tumors through a training step and PCA analysis based on the Active Shape Model (ASM). The method has been tested on real patient data from the Brown Cancer Center at the University of Louisville. We performed temporal B-spline deformable registration of the 4-D CT data - this yielded 3-D deformation fields between successive respiratory phases from which measures of regional lung function were determined. During the respiratory cycle, the lung volume changes and five different lobes of the lung (two in the left and three in the right lung) show different deformation yielding different strain and Jacobian maps. In this thesis, we determine the regional lung mechanics in the Lagrangian frame of reference through different respiratory phases, for example, Phase10 to 20, Phase10 to 30, Phase10 to 40, and Phase10 to 50. Single photon emission computed tomography (SPECT) lung imaging using radioactive tracers with SPECT ventilation and SPECT perfusion imaging also provides functional information. As part of an IRB-approved study therefore, we registered the max-inhale CT volume to both VSPECT and QSPECT data sets using the Demon\u27s non-rigid registration algorithm in patient subjects. Subsequently, statistical correlation between CT ventilation images (Jacobian and strain values), with both VSPECT and QSPECT was undertaken. Through statistical analysis with the Spearman\u27s rank correlation coefficient, we found that Jacobian values have the highest correlation with both VSPECT and QSPECT

Rapid Segmentation Techniques for Cardiac and Neuroimage Analysis

Recent technological advances in medical imaging have allowed for the quick acquisition of highly resolved data to aid in diagnosis and characterization of diseases or to guide interventions. In order to to be integrated into a clinical work flow, accurate and robust methods of analysis must be developed which manage this increase in data. Recent improvements in in- expensive commercially available graphics hardware and General-Purpose Programming on Graphics Processing Units (GPGPU) have allowed for many large scale data analysis problems to be addressed in meaningful time and will continue to as parallel computing technology improves. In this thesis we propose methods to tackle two clinically relevant image segmentation problems: a user-guided segmentation of myocardial scar from Late-Enhancement Magnetic Resonance Images (LE-MRI) and a multi-atlas segmentation pipeline to automatically segment and partition brain tissue from multi-channel MRI. Both methods are based on recent advances in computer vision, in particular max-flow optimization that aims at solving the segmentation problem in continuous space. This allows for (approximately) globally optimal solvers to be employed in multi-region segmentation problems, without the particular drawbacks of their discrete counterparts, graph cuts, which typically present with metrication artefacts. Max-flow solvers are generally able to produce robust results, but are known for being computationally expensive, especially with large datasets, such as volume images. Additionally, we propose two new deformable registration methods based on Gauss-Newton optimization and smooth the resulting deformation fields via total-variation regularization to guarantee the problem is mathematically well-posed. We compare the performance of these two methods against four highly ranked and well-known deformable registration methods on four publicly available databases and are able to demonstrate a highly accurate performance with low run times. The best performing variant is subsequently used in a multi-atlas segmentation pipeline for the segmentation of brain tissue and facilitates fast run times for this computationally expensive approach. All proposed methods are implemented using GPGPU for a substantial increase in computational performance and so facilitate deployment into clinical work flows. We evaluate all proposed algorithms in terms of run times, accuracy, repeatability and errors arising from user interactions and we demonstrate that these methods are able to outperform established methods. The presented approaches demonstrate high performance in comparison with established methods in terms of accuracy and repeatability while largely reducing run times due to the employment of GPU hardware

Data-driven patient-specific breast modeling: a simple, automatized, and robust computational pipeline

Background: Breast-conserving surgery is the most acceptable option for breast cancer removal from an invasive and psychological point of view. During the surgical procedure, the imaging acquisition using Magnetic Image Resonance is performed in the prone configuration, while the surgery is achieved in the supine stance. Thus, a considerable movement of the breast between the two poses drives the tumor to move, complicating the surgeon's task. Therefore, to keep track of the lesion, the surgeon employs ultrasound imaging to mark the tumor with a metallic harpoon or radioactive tags. This procedure, in addition to an invasive characteristic, is a supplemental source of uncertainty. Consequently, developing a numerical method to predict the tumor movement between the imaging and intra-operative configuration is of significant interest. Methods: In this work, a simulation pipeline allowing the prediction of patient-specific breast tumor movement was put forward, including personalized preoperative surgical drawings. Through image segmentation, a subject-specific finite element biomechanical model is obtained. By first computing an undeformed state of the breast (equivalent to a nullified gravity), the estimated intra-operative configuration is then evaluated using our developed registration methods. Finally, the model is calibrated using a surface acquisition in the intra-operative stance to minimize the prediction error. Findings: The capabilities of our breast biomechanical model to reproduce real breast deformations were evaluated. To this extent, the estimated geometry of the supine breast configuration was computed using a corotational elastic material model formulation. The subject-specific mechanical properties of the breast and skin were assessed, to get the best estimates of the prone configuration. The final results are a Mean Absolute Error of 4.00 mm for the mechanical parameters E_breast = 0.32 kPa and E_skin = 22.72 kPa. The optimized mechanical parameters are congruent with the recent state-of-the-art. The simulation (including finding the undeformed and prone configuration) takes less than 20 s. The Covariance Matrix Adaptation Evolution Strategy optimizer converges on average between 15 to 100 iterations depending on the initial parameters for a total time comprised between 5 to 30 min. To our knowledge, our model offers one of the best compromises between accuracy and speed. The model could be effortlessly enriched through our recent work to facilitate the use of complex material models by only describing the strain density energy function of the material. In a second study, we developed a second breast model aiming at mapping a generic model embedding breast-conserving surgical drawing to any patient. We demonstrated the clinical applications of such a model in a real-case scenario, offering a relevant education tool for an inexperienced surgeon

Variational Methods in Shape Space

This dissertation deals with the application of variational methods in spaces of geometric shapes. In particular, the treated topics include shape averaging, principal component analysis in shape space, computation of geodesic paths in shape space, as well as shape optimisation. Chapter 1 provides a brief overview over the employed models of shape space. Geometric shapes are identified with two- or three-dimensional, deformable objects. Deformations will be described via physical models; in particular, the objects will be interpreted as consisting of either a hyperelastic solid or a viscous liquid material. Furthermore, the description of shapes via phase fields or level sets is briefly introduced. Chapter 2 reviews different and related approaches to shape space modelling. References to related topics in image segmentation and registration are also provided. Finally, the relevant shape optimisation literature is introduced. Chapter 3 recapitulates the employed concepts from continuum mechanics and phase field modelling and states basic theoretical results needed for the later analysis. Chapter 4 addresses the computation of shape averages, based on a hyperelastic notion of shape dissimilarity: The dissimilarity between two shapes is measured as the minimum deformation energy required to deform the first into the second shape. A corresponding phase-field model is introduced, analysed, and finally implemented numerically via finite elements. A principal component analysis of shapes, which is consistent with the previously introduced average, is considered in Chapter 5. Elastic boundary stresses on the average shape are used as representatives of the input shapes in a linear vector space. On these linear representatives, a standard principal component analysis can be performed, where the employed covariance metric should be properly chosen to depend on the input shapes. Chapter 6 interprets shapes as belonging to objects made of a viscous liquid and correspondingly defines geodesic paths between shapes. The energy of a path is given as the total physical dissipation during the deformation of an object along the path. A rigid body motion invariant time discretisation is achieved by approximating the dissipation along a path segment by the deformation energy of a small solid deformation. The numerical implementation is based on level sets. Chapter 7 is concerned with the optimisation of the geometry and topology of solid structures that are subject to a mechanical load. Given the load configuration, the structure rigidity, its volume, and its surface area shall be optimally balanced. A phase field model is devised and analysed for this purpose. In this context, the use of nonlinear elasticity allows to detect buckling phenomena which would be ignored in linearised elasticity