The objective of the proposed research is to develop methods that couple an expert user's guidance with automatic image segmentation and registration algorithms. Often, complex processes such as fire, anatomical changes/variations in human bodies, or unpredictable human behavior produce the target images; in these cases, creating a model that precisely describes the process is not feasible. A common solution is to make simplifying assumptions when performing detection, segmentation, or registration tasks automatically. However, when these assumptions are not satisfied, the results are unsatisfactory. Hence, removing these, often times stringent, assumptions at the cost of minimal user input is considered an acceptable trade-off. Three milestones towards reaching this goal have been achieved. First, an interactive image segmentation approach was created in which the user is coupled in a closed-loop control system with a level set segmentation algorithm. The user's expert knowledge is combined with the speed of automatic segmentation. Second, a stochastic point set registration algorithm is presented. The point sets can be derived from simple user input (e.g. a thresholding operation), and time consuming correspondence labeling is not required. Furthermore, common smoothness assumptions on the non-rigid deformation field are removed. Third, a stochastic image registration algorithm is designed to capture large misalignments. For future research, several improvements of the registration are proposed, and an iterative, landmark based segmentation approach, which couples the segmentation and registration, is envisioned.

<p>Digital tomosynthesis (DTS) is a quasi-three-dimensional (3D) imaging technique which reconstructs images from a limited angle of cone-beam projections with shorter acquisition time, lower imaging dose, and less mechanical constraint than full cone-beam CT (CBCT). However, DTS images reconstructed by the conventional filtered back projection method have low plane-to-plane resolution, and they do not provide full volumetric information for target localization due to the limited angle of the DTS acquisition. </p><p>This dissertation presents the optimization and clinical implementation of image guided radiation therapy using limited-angle projections.</p><p>A hybrid multiresolution rigid-body registration technique was developed to automatically register reference DTS images with on-board DTS images to guide patient positioning in radiation therapy. This hybrid registration technique uses a faster but less accurate static method to achieve an initial registration, followed by a slower but more accurate adaptive method to fine tune the registration. A multiresolution scheme is employed in the registration to further improve the registration accuracy, robustness and efficiency. Normalized mutual information is selected as the criterion for the similarity measure, and the downhill simplex method is used as the search engine. This technique was tested using image data both from an anthropomorphic chest phantom and from head-and-neck cancer patients. The effects of the scan angle and the region-of-interest size on the registration accuracy and robustness were investigated. The average capture ranges in single-axis simulations with a 44° scan angle and a large ROI covering the entire DTS volume were between -31 and +34 deg for rotations and between -89 and +78 mm for translations in the phantom study, and between -38 and +38 deg for rotations and between -58 and +65 mm for translations in the patient study.</p><p>Additionally, a novel limited-angle CBCT estimation method using a deformation field map was developed to optimally estimate volumetric information of organ deformation for soft tissue alignment in image guided radiation therapy. The deformation field map is solved by using prior information, a deformation model, and new projection data. Patients' previous CBCT data are used as the prior information, and the new patient volume to be estimated is considered as a deformation of the prior patient volume. The deformation field is solved by minimizing bending energy and maintaining new projection data fidelity using a nonlinear conjugate gradient method. The new patient CBCT volume is then obtained by deforming the prior patient CBCT volume according to the solution to the deformation field. The method was tested for different scan angles in 2D and 3D cases using simulated and real projections of a Shepp-Logan phantom, liver, prostate and head-and-neck patient data. Hardware acceleration and multiresolution scheme are used to accelerate the 3D estimation process. The accuracy of the estimation was evaluated by comparing organ volume, similarity and pixel value differences between limited-angle CBCT and full-rotation CBCT images. Results showed that the respiratory motion in the liver patient, rectum volume change in the prostate patient, and the weight loss and airway volume change in the head-and-neck patient were accurately estimated in the 60° CBCT images. This new estimation method is able to optimally estimate the volumetric information using 60-degree projection images. It is both technically and clinically feasible for image-guidance in radiation therapy.</p> / Dissertation

<p>Based on the compressed sensing theorem, we present the integrated software and hardware platform for developing a total-variation based image restoration algorithm by applying prior image information and free-form deformation fields for image guided therapy. The core algorithm we developed solves the image restoration problem for handling missing structures in one image set with prior information, and it enhances the quality of the image and the anatomical information of the volume of the on-board computed tomographic (CT) with limited-angle projections. Through the use of the algorithm, prior anatomical CT scans were used to provide additional information to help reduce radiation doses associated with the improved quality of the image volume produced by on-board Cone-Beam CT, thus reducing the total radiation doses that patients receive and removing distortion artifacts in 3D Digital Tomosynthesis (DTS) and 4D-DTS. The proposed restoration algorithm enables the enhanced resolution of temporal image and provides more anatomical information than conventional reconstructed images.</p><p>The performance of the algorithm was determined and evaluated by two built-in parameters in the algorithm, i.e., B-spline resolution and the regularization factor. These parameters can be adjusted to meet different requirements in different imaging applications. Adjustments also can determine the flexibility and accuracy during the restoration of images. Preliminary results have been generated to evaluate the image similarity and deformation effect for phantoms and real patient's case using shifting deformation window. We incorporated a graphics processing unit (GPU) and visualization interface into the calculation platform, as the acceleration tools for medical image processing and analysis. By combining the imaging algorithm with a GPU implementation, we can make the restoration calculation within a reasonable time to enable real-time on-board visualization, and the platform potentially can be applied to solve complicated, clinical-imaging algorithms.</p> / Dissertation

In this thesis, a novel and efficient numerical method is presented for the computation of the L² optimal mass transport mapping in two and three dimensions. The method uses a direct variational approach. A new projection to the constraint technique has been formulated that can yield a good starting point for the method as well as a second order accurate discretization to the problem. The numerical experiments demonstrate that the algorithm yields accurate results in a relatively small number of iterations that are mesh independent. In the first part of the thesis, the theory and implementation details of the proposed method are presented. These include the reformulation of the Monge-Kantorovich problem using a variational approach and then using a consistent discretization in conjunction with the "discretize-then-optimize" approach to solve the resulting discrete system of differential equations. Advanced numerical methods such as multigrid and adaptive mesh refinement have been employed to solve the linear systems in practical time for even 3D applications. In the second part, the methods efficacy is shown via application to various image processing tasks. These include image registration and morphing. Application of (OMT) to registration is presented in the context of medical imaging and in particular image guided therapy where registration is used to align multiple data sets with each other and with the patient. It is shown that an elastic warping methodology based on the notion of mass transport is quite natural for several medical imaging applications where density can be a key measure of similarity between different data sets e.g. proton density based imagery provided by MR. An application is also presented of the two dimensional optimal mass transport algorithm to compute diffeomorphic correspondence maps between curves for geometric interpolation in an active contour based visual tracking application.

Ventilation imaging using 4D-CT is a convenient and cost effective functional imaging methodology which might be of value in radiotherapy treatment planning to spare functional lung volumes. To calculate ventilation imaging from 4D-CT we must use deformable image registration (DIR). This study validates the DIR methods and investigates the dependence of calculated ventilation on DIR methods and ventilation algorithms. The first hypothesis is if ventilation algorithms are robust then they will be insensitive to the precise DIR used provided the DIR is accurate. The second hypothesis is that the change in Houndsfield Unit (HU) method is less dependent on the DIR used and depends more on the CT image quality due to the inherent noise of HUs in normal CT imaging. DIR of the normal end expiration and inspiration phases of the 4D-CT images was used to correlate the voxels between the two respiratory phases. All DIR algorithms were validated using a 4D pixel-based and point-validated breathing thorax model, consisting of a 4D-CT image data set along with associated landmarks. Three different DIR algorithms, Optical Flow (OF), Diffeomorphic Demons (DD) and Diffeomorphic Morphons (DM), were retrospectively applied to the same group of 10 esophagus and 10 lung cancer cases all of which had associated 4D-CT image sets that encompassed the entire lung volume. Three different ventilation calculation algorithms were compared (Jacobian, ΔV, and HU) using the Dice similarity coefficient comparison. In the validation of the DIR algorithms, the average target registration errors with one standard deviation for the DIR algorithms were 1.6 ± 0.7 mm, maximum 3.1 mm for OF, 1.3 ± 0.6 mm, maximum 3.3 mm for DM, 1.3 ± 0.6 mm, maximum 2.8 mm for DD, indicating registration errors were within 2 voxels. Dependence of ventilation images on the DIR was greater for the ΔV and the Jacobian methods than for the HU method. The Dice similarity coefficient for 20% of low ventilation volume for ΔV was 0.33 ± 0.03 between OF and DM, 0.44 ± 0.05 between OF and DD and 0.51 ± 0.04 between DM and DD. The similarity comparisons for Jacobian was 0.32 ± 0.03, 0.44 ± 0.05 and 0.51 ± 0.04 respectively, and for HU 0.53 ± 0.03, 0.56 ± 0.03 and 0.76 ± 0.04 respectively. Dependence of ventilation images on the ventilation method used showed good agreement between the ΔV and Jacobian methods but differences between these two and the HU method were significantly greater. Dice similarity coefficient for using OF as DIR was 0.86 ± 0.01 between ΔV and Jacobian, 0.28 ± 0.04 between ΔV and HU and 0.28 ± 0.04 between Jacobian and HU respectively. When using DM or DD as DIR, similar values were obtained when comparing the different ventilation calculation methods. The similarity values for 20% of the high ventilation volume were close to those found for the 20% low ventilation volume. Mean target registration error for all three DIR methods was within one voxel suggesting that the registration done by either of the methods is quite accurate. Ventilation calculation from 4D-CT demonstrates some degree of dependency on the DIR algorithm employed. Similarities between ΔV and Jacobian are higher than between ΔV and HU and Jacobian and HU. This shows that ΔV and Jacobian are very similar, but HU is a very different ventilation calculation method.

The work covered in this thesis deals with the problem of automatically registering 3D images acquired from different medical imaging modalities. The approach taken is to develop generic measures of image registration derived from the co-occurence of values in the two images. The development of statistical alignment measures is reviewed. The registration problem is then expressed in terms of entropy and developed using tools from information theory. The problem of the optimization of the registration process in the different types of algorithms is identified as important and the power of Genetic Algorithms is applied. The application of image registration techniques, implemented during this thesis, in complex situations is evaluated. The cases of patients with brain ischemia and brain tumour residual disease are elaborated. This is accomplished with the formation of Groupwares where the tacit knowledge, owned by the individual specialists that take part in the collaboration, is exposed and made explicit in the process of the evaluation of the findings, provided by the fused images. This is performed in a high performance computer network that has been developed between the Department of Medicine and the University Hospital. / Η παρούσα εργασία ασχολείται με το πρόβλημα της αυτοματοποιημένης προσαρμογής και σύντηξης τρισδιάστατων απεικονίσεων από διαφορετικές ιατρικές απεικονιστικές μεθοδολογίες.

Deformable image registration (DIR) is a type of registration that calculates a deformable vector field (DVF) between two image data sets and permits contour and dose propagation. However the calculation of a DVF is considered an ill-posed problem, as there is no exact solution to a deformation problem, therefore all DVFs calculated contain errors. As a result it is important to evaluate and assess the accuracy and limitations of any DIR algorithm intended for clinical use. The influence of image quality on the DIR algorithms performance was also evaluated. The hybrid DIR algorithm in RayStation 4.0.1.4 was assessed using a number of evaluation methods and data. The evaluation methods were point of interest (POI) propagation, contour propagation and dose measurements. The data types used were phantom and patient data. A number of metrics were used for quantitative analysis and visual inspection was used for qualitative analysis. The quantitative and qualitative results indicated that all DVFs calculated by the DIR algorithm contained errors which translated into errors in the propagated contours and propagated dose. The results showed that the errors were largest for small contour volumes (<20cm3) and for large anatomical volume changes between the image sets, which pushes the algorithms ability to deform, a significant decrease in accuracy was observed for anatomical volume changes of greater than 10%. When the propagated contours in the head and neck were used for planning the errors in the DVF were found to cause under dosing to the target tumour by up to 32% and over dosing to the organs at risk (OAR) by up to 12% which is clinically significant. The results also indicated that the image quality does not have a significant effect on the DIR algorithms calculations. Dose measurements indicated errors in the DVF calculations that could potentially be clinically significant. The results indicate that contour propagation and dose propagation must be used with caution if clinical use is intended. For clinical use contour propagation requires evaluation of every propagated contour by an expert user and dose propagation requires thorough evaluation of the DVF.

This thesis presents a technique for face recognition that is based on image registration. The image registration technique is based on finding a set of feature points in the two images and using these feature points for registration. This is done in four steps. In the first, images are filtered with the Mexican hat wavelet to obtain the feature point locations. In the second, the Zernike moments of neighbourhoods around the feature points are calculated and compared in the third step to establish correspondence between feature points in the two images and in the fourth the transformation parameters between images are obtained using an iterative weighted least squares technique. The face recognition technique consists of three parts, a training part, an image registration part and a post-processing part. During training a set of images are chosen as the training images and the Zernike moments for the feature points of the training images are obtained and stored. In the registration part, the transformation parameters to register the training images with the images under consideration are obtained. In the post-processing, these transformation parameters are used to determine whether a valid match is found or not. The performance of the proposed method is evaluated using various face databases and it is compared with the performance of existing techniques. Results indicate that the proposed technique gives excellent results for face recognition in conditions of varying pose, illumination, background and scale. These results are comparable to other well known face recognition techniques.

The first component of this work is a parallel algorithm for constructing non-uniform octree meshes for finite element computations. Prior to octree meshing, the linear octree data structure must be constructed and a constraint known as "2:1 balancing" must be enforced; parallel algorithms for these two subproblems are also presented. The second component of this work is a parallel matrix-free geometric multigrid algorithm for solving elliptic partial differential equations (PDEs) using these octree meshes. The last component of this work is a parallel multiscale Gauss Newton optimization algorithm for solving the elastic image registration problem. The registration problem is discretized using finite elements on octree meshes and the parallel geometric multigrid algorithm is used as a preconditioner in the Conjugate Gradient (CG) algorithm to solve the linear system of equations formed in each Gauss Newton iteration. Several ideas were used to reduce the overhead for constructing the octree meshes. These include (a) a way to lower communication costs by reducing the number of synchronizations and reducing the communication message size, (b) a way to reduce the number of searches required to build element-to-vertex mappings, and (c) a compression scheme to reduce the memory footprint of the entire data structure. To our knowledge, the multigrid algorithm presented in this work is the only matrix-free multiplicative geometric multigrid implementation for solving finite element equations on octree meshes using thousands of processors. The proposed registration algorithm is also unique; it is a combination of many different ideas: adaptivity, parallelism, fast optimization algorithms, and fast linear solvers. All the algorithms were implemented in C++ using the Message Passing Interface (MPI) standard and were built on top of the PETSc library from Argonne National Laboratory. The multigrid implementation has been released as an open source software: Dendro. Several numerical experiments were performed to test the performance of the algorithms. These experiments were performed on a variety of NSF TeraGrid platforms. Our largest run was a highly-nonuniform, 8-billion-unknown, elasticity calculation on 32,000 processors.

Image super-resolution aims to produce a higher resolution representation of a scene from an ensemble of low-resolution images that may be warped, aliased, blurred and degraded by noise. There are a variety of methods for performing super-resolution described in the literature, and in general they consist of three major steps: image registration, fusion and deblurring. This thesis proposes a novel method of performing the first two of these steps. The ultimate aim of image super-resolution is to produce a higher-quality image that is visually clearer, sharper and contains more detail than the individual input images. Machine algorithms can not assess images qualitatively and typically use a quantitative error criterion, often least-squares. This thesis aims to optimise leastsquares directly using a fast method, in particular one that can be implemented using linear filters; hence, a closed-form solution is required. The concepts of optimal interpolation and resampling are derived and demonstrated in practice. Optimal filters optimised on one image are shown to perform nearoptimally on other images, suggesting that common image features, such as stepedges, can be used to optimise a near-optimal filter without requiring the knowledge of the ground-truth output. This leads to the construction of a pulse model, which is used to derive filters for resampling non-uniformly sampled images that result from the fusion of registered input images. An experimental comparison shows that a 10th order pulse model-based filter outperforms a number of methods common in the literature. The use of optimal interpolation for image registration linearises an otherwise nonlinear problem, resulting in a direct solution. Experimental analysis is used to show that optimal interpolation-based registration outperforms a number of existing methods, both iterative and direct, at a range of noise levels and for both heavily aliased images and images with a limited degree of aliasing. The proposed method offers flexibility in terms of the size of the region of support, offering a good trade-off in terms of computational complexity and accuracy of registration. Together, optimal interpolation-based registration and fusion are shown to perform fast, direct and effective super-resolution.