Incompressible image registration using divergence-conforming B-splines

Anatomically plausible image registration often requires volumetric preservation. Previous approaches to incompressible image registration have exploited relaxed constraints, ad hoc optimisation methods or practically intractable computational schemes. Divergence-free velocity fields have been used to achieve incompressibility in the continuous domain, although, after discretisation, no guarantees have been provided. In this paper, we introduce stationary velocity fields (SVFs) parameterised by divergence-conforming B-splines in the context of image registration. We demonstrate that sparse linear constraints on the parameters of such divergence-conforming B-Splines SVFs lead to being exactly divergence-free at any point of the continuous spatial domain. In contrast to previous approaches, our framework can easily take advantage of modern solvers for constrained optimisation, symmetric registration approaches, arbitrary image similarity and additional regularisation terms. We study the numerical incompressibility error for the transformation in the case of an Euler integration, which gives theoretical insights on the improved accuracy error over previous methods. We evaluate the proposed framework using synthetically deformed multimodal brain images, and the STACOM11 myocardial tracking challenge. Accuracy measurements demonstrate that our method compares favourably with state-of-the-art methods whilst achieving volume preservation.Comment: Accepted at MICCAI 201

Mid-space-independent deformable image registration

Aligning images in a mid-space is a common approach to ensuring that deformable image registration is symmetric – that it does not depend on the arbitrary ordering of the input images. The results are, however, generally dependent on the mathematical definition of the mid-space. In particular, the set of possible solutions is typically restricted by the constraints that are enforced on the transformations to prevent the mid-space from drifting too far from the native image spaces. The use of an implicit atlas has been proposed as an approach to mid-space image registration. In this work, we show that when the atlas is aligned to each image in the native image space, the data term of implicit-atlas-based deformable registration is inherently independent of the mid-space. In addition, we show that the regularization term can be reformulated independently of the mid-space as well. We derive a new symmetric cost function that only depends on the transformation morphing the images to each other, rather than to the atlas. This eliminates the need for anti-drift constraints, thereby expanding the space of allowable deformations. We provide an implementation scheme for the proposed framework, and validate it through diffeomorphic registration experiments on brain magnetic resonance images

Constrained camera motion estimation and 3D reconstruction

The creation of virtual content from visual data is a tedious task which requires a high amount of skill and expertise. Although the majority of consumers is in possession of multiple imaging devices that would enable them to perform this task in principle, the processing techniques and tools are still intended for the use by trained experts. As more and more capable hardware becomes available, there is a growing need among consumers and professionals alike for new flexible and reliable tools that reduce the amount of time and effort required to create high-quality content. This thesis describes advances of the state of the art in three areas of computer vision: camera motion estimation, probabilistic 3D reconstruction, and template fitting. First, a new camera model geared towards stereoscopic input data is introduced, which is subsequently developed into a generalized framework for constrained camera motion estimation. A probabilistic reconstruction method for 3D line segments is then described, which takes global connectivity constraints into account. Finally, a new framework for symmetry-aware template fitting is presented, which allows the creation of high-quality models from low-quality input 3D scans. Evaluations with a broad range of challenging synthetic and real-world data sets demonstrate that the new constrained camera motion estimation methods provide improved accuracy and flexibility, and that the new constrained 3D reconstruction methods improve the current state of the art.Die Erzeugung virtueller Inhalte aus visuellem Datenmaterial ist langwierig und erfordert viel Geschick und Sachkenntnis. Obwohl der Großteil der Konsumenten mehrere Bildgebungsgeräte besitzt, die es ihm im Prinzip erlauben würden, dies durchzuführen, sind die Techniken und Werkzeuge noch immer für den Einsatz durch ausgebildete Fachleute gedacht. Da immer leistungsfähigere Hardware zur Verfügung steht, gibt es sowohl bei Konsumenten als auch bei Fachleuten eine wachsende Nachfrage nach neuen flexiblen und verlässlichen Werkzeugen, die die Erzeugung von qualitativ hochwertigen Inhalten vereinfachen. In der vorliegenden Arbeit werden Erweiterungen des Stands der Technik in den folgenden drei Bereichen der Bildverarbeitung beschrieben: Kamerabewegungsschätzung, wahrscheinlichkeitstheoretische 3D-Rekonstruktion und Template-Fitting. Zuerst wird ein neues Kameramodell vorgestellt, das für die Verarbeitung von stereoskopischen Eingabedaten ausgelegt ist. Dieses Modell wird in der Folge in eine generalisierte Methode zur Kamerabewegungsschätzung unter Nebenbedingungen erweitert. Anschließend wird ein wahrscheinlichkeitstheoretisches Verfahren zur Rekonstruktion von 3D-Liniensegmenten beschrieben, das globale Verbindungen als Nebenbedingungen berücksichtigt. Schließlich wird eine neue Methode zum Fitting eines Template-Modells präsentiert, bei der die Berücksichtigung der Symmetriestruktur des Templates die Erzeugung von Modellen hoher Qualität aus 3D-Eingabedaten niedriger Qualität erlaubt. Evaluierungen mit einem breiten Spektrum an anspruchsvollen synthetischen und realen Datensätzen zeigen, dass die neuen Methoden zur Kamerabewegungsschätzung unter Nebenbedingungen höhere Genauigkeit und mehr Flexibilität ermöglichen, und dass die neuen Methoden zur 3D-Rekonstruktion unter Nebenbedingungen den Stand der Technik erweitern

Bayesian generative learning of brain and spinal cord templates from neuroimaging datasets

In the field of neuroimaging, Bayesian modelling techniques have been largely adopted and recognised as powerful tools for the purpose of extracting quantitative anatomical and functional information from medical scans. Nevertheless the potential of Bayesian inference has not yet been fully exploited, as many available tools rely on point estimation techniques, such as maximum likelihood estimation, rather than on full Bayesian inference. The aim of this thesis is to explore the value of approximate learning schemes, for instance variational Bayes, to perform inference from brain and spinal cord MRI data. The applications that will be explored in this work mainly concern image segmentation and atlas construction, with a particular emphasis on the problem of shape and intensity prior learning, from large training data sets of structural MR scans. The resulting computational tools are intended to enable integrated brain and spinal cord morphometric analyses, as opposed to the approach that is most commonly adopted in neuroimaging, which consists in optimising separate tools for brain and spine morphometrics

Registration of pre-operative lung cancer PET/CT scans with post-operative histopathology images

Non-invasive imaging modalities used in the diagnosis of lung cancer, such as Positron Emission Tomography (PET) or Computed Tomography (CT), currently provide insuffcient information about the cellular make-up of the lesion microenvironment, unless they are compared against the gold standard of histopathology.The aim of this retrospective study was to build a robust imaging framework for registering in vivo and post-operative scans from lung cancer patients, in order to have a global, pathology-validated multimodality map of the tumour and its surroundings.;Initial experiments were performed on tissue-mimicking phantoms, to test different shape reconstruction methods. The choice of interpolator and slice thickness were found to affect the algorithm's output, in terms of overall volume and local feature recovery. In the second phase of the study, nine lung cancer patients referred for radical lobectomy were recruited. Resected specimens were inflated with agar, sliced at 5 mm intervals, and each cross-section was photographed. The tumour area was delineated on the block-face pathology images and on the preoperative PET/CT scans.;Airway segments were also added to the reconstructed models, to act as anatomical fiducials. Binary shapes were pre-registered by aligning their minimal bounding box axes, and subsequently transformed using rigid registration. In addition, histopathology slides were matched to the block-face photographs using moving least squares algorithm.;A two-step validation process was used to evaluate the performance of the proposed method against manual registration carried out by experienced consultants. In two out of three cases, experts rated the results generated by the algorithm as the best output, suggesting that the developed framework outperforms the current standard practice.Non-invasive imaging modalities used in the diagnosis of lung cancer, such as Positron Emission Tomography (PET) or Computed Tomography (CT), currently provide insuffcient information about the cellular make-up of the lesion microenvironment, unless they are compared against the gold standard of histopathology.The aim of this retrospective study was to build a robust imaging framework for registering in vivo and post-operative scans from lung cancer patients, in order to have a global, pathology-validated multimodality map of the tumour and its surroundings.;Initial experiments were performed on tissue-mimicking phantoms, to test different shape reconstruction methods. The choice of interpolator and slice thickness were found to affect the algorithm's output, in terms of overall volume and local feature recovery. In the second phase of the study, nine lung cancer patients referred for radical lobectomy were recruited. Resected specimens were inflated with agar, sliced at 5 mm intervals, and each cross-section was photographed. The tumour area was delineated on the block-face pathology images and on the preoperative PET/CT scans.;Airway segments were also added to the reconstructed models, to act as anatomical fiducials. Binary shapes were pre-registered by aligning their minimal bounding box axes, and subsequently transformed using rigid registration. In addition, histopathology slides were matched to the block-face photographs using moving least squares algorithm.;A two-step validation process was used to evaluate the performance of the proposed method against manual registration carried out by experienced consultants. In two out of three cases, experts rated the results generated by the algorithm as the best output, suggesting that the developed framework outperforms the current standard practice

Toward adaptive radiotherapy

Intensity Modulated Radiotherapy (IMRT) and proton therapy are the state-of-art external radiotherapy modalities. To make the most of such precise delivery, accurate knowledge of the patient anatomy and biology during treatment is necessary, as unaccounted variations can compromise the outcome of the treatment. Treatment modification to account for deviations from the planning stage is a framework known as adaptive radiotherapy (ART). To fully utilise the information extracted from different modalities and/or at different time-points it is required to accurately align the imaging data. In this work the feasibility of cone-beam computed tomography (CBCT) and deformable image registration (DIR) for ART was evaluated in the context of head and neck (HN) and lung malignancies, and for IMRT and proton therapy applications. This included the geometric validation of deformations for multiple DIR algorithms, estimating the uncertainty in dose recalculation of a CBCT-based deformed CT (dCT), and the uncertainty in dose summation resulting from the properties of the underlying deformations. The dCT method was shown to be a good interim solution to repeat CT and a superior alternative to simpler direct usage of CBCT for dose calculation; proton therapy treatments were more sensitive to registration errors than IMRT. The ability to co-register multimodal and multitemporal data of the HN was also explored; the results found were promising and the limitations of current algorithms and data acquisition protocols were identified. The use of novel artificial cancer masses as a novel platform for the study of imaging during radiotherapy was explored in this study. The artificial cancer mass model was extended to generate magnetic resonance imaging (MRI)-friendly samples. The tumoroids were imageable in standard T1 and T2 MRI acquisitions, and the relaxometric properties were measured. The main limitation of the current tumour model was the poor reproducibility and controllability of the properties of the samples