Methods for 3D Geometry Processing in the Cultural Heritage Domain

This thesis presents methods for 3D geometry processing under the aspects of cultural heritage applications. After a short overview over the relevant basics in 3D geometry processing, the present thesis investigates the digital acquisition of 3D models. A particular challenge in this context are on the one hand difficult surface or material properties of the model to be captured. On the other hand, the fully automatic reconstruction of models even with suitable surface properties that can be captured with Laser range scanners is not yet completely solved. This thesis presents two approaches to tackle these challenges. One exploits a thorough capture of the object’s appearance and a coarse reconstruction for a concise and realistic object representation even for objects with problematic surface properties like reflectivity and transparency. The other method concentrates on digitisation via Laser-range scanners and exploits 2D colour images that are typically recorded with the range images for a fully automatic registration technique. After reconstruction, the captured models are often still incomplete, exhibit holes and/or regions of insufficient sampling. In addition to that, holes are often deliberately introduced into a registered model to remove some undesired or defective surface part. In order to produce a visually appealing model, for instance for visualisation purposes, for prototype or replica production, these holes have to be detected and filled. Although completion is a well-established research field in 2D image processing and many approaches do exist for image completion, surface completion in 3D is a fairly new field of research. This thesis presents a hierarchical completion approach that employs and extends successful exemplar-based 2D image processing approaches to 3D and fills in detail-equipped surface patches into missing surface regions. In order to identify and construct suitable surface patches, selfsimilarity and coherence properties of the surface context of the hole are exploited. In addition to the reconstruction and repair, the present thesis also investigates methods for a modification of captured models via interactive modelling. In this context, modelling is regarded as a creative process, for instance for animation purposes. On the other hand, it is also demonstrated how this creative process can be used to introduce human expertise into the otherwise automatic completion process. This way, reconstructions are feasible even of objects where already the data source, the object itself, is incomplete due to corrosion, demolition, or decay.Methoden zur 3D-Geometrieverarbeitung im Kulturerbesektor In dieser Arbeit werden Methoden zur Bearbeitung von digitaler 3D-Geometrie unter besonderer Berücksichtigung des Anwendungsbereichs im Kulturerbesektor vorgestellt. Nach einem kurzen Überblick über die relevanten Grundlagen der dreidimensionalen Geometriebehandlung wird zunächst die digitale Akquise von dreidimensionalen Objekten untersucht. Eine besondere Herausforderung stellen bei der Erfassung einerseits ungünstige Oberflächen- oder Materialeigenschaften der Objekte dar (wie z.B. Reflexivität oder Transparenz), andererseits ist auch die vollautomatische Rekonstruktion von solchen Modellen, die sich verhältnismäßig problemlos mit Laser-Range Scannern erfassen lassen, immer noch nicht vollständig gelöst. Daher bilden zwei neuartige Verfahren, die diesen Herausforderungen begegnen, den Anfang. Auch nach der Registrierung sind die erfassten Datensätze in vielen Fällen unvollständig, weisen Löcher oder nicht ausreichend abgetastete Regionen auf. Darüber hinaus werden in vielen Anwendungen auch, z.B. durch Entfernen unerwünschter Oberflächenregionen, Löcher gewollt hinzugefügt. Für eine optisch ansprechende Rekonstruktion, vor allem zu Visualisierungszwecken, im Bildungs- oder Unterhaltungssektor oder zur Prototyp- und Replik-Erzeugung müssen diese Löcher zunächst automatisch detektiert und anschließend geschlossen werden. Obwohl dies im zweidimensionalen Fall der Bildbearbeitung bereits ein gut untersuchtes Forschungsfeld darstellt und vielfältige Ansätze zur automatischen Bildvervollständigung existieren, ist die Lage im dreidimensionalen Fall anders, und die Übertragung von zweidimensionalen Ansätzen in den 3D stellt vielfach eine große Herausforderung dar, die bislang keine zufriedenstellenden Lösungen erlaubt hat. Nichtsdestoweniger wird in dieser Arbeit ein hierarchisches Verfahren vorgestellt, das beispielbasierte Konzepte aus dem 2D aufgreift und Löcher in Oberflächen im 3D unter Ausnutzung von Selbstähnlichkeiten und Kohärenzeigenschaften des Oberflächenkontextes schließt. Um plausible Oberflächen zu erzeugen werden die Löcher dabei nicht nur glatt gefüllt, sondern auch feinere Details aus dem Kontext rekonstruiert. Abschließend untersucht die vorliegende Arbeit noch die Modifikation der vervollständigten Objekte durch Freiformmodellierung. Dies wird dabei zum einen als kreativer Prozess z.B. zu Animationszwecken betrachtet. Zum anderen wird aber auch untersucht, wie dieser kreative Prozess benutzt werden kann, um etwaig vorhandenes Expertenwissen in die ansonsten automatische Vervollständigung mit einfließen zu lassen. Auf diese Weise werden auch Rekonstruktionen ermöglicht von Objekten, bei denen schon die Datenquelle, also das Objekt selbst z.B. durch Korrosion oder mutwillige Zerstörung unvollständig ist

Dynamical models and machine learning for supervised segmentation

This thesis is concerned with the problem of how to outline regions of interest in medical images, when the boundaries are weak or ambiguous and the region shapes are irregular. The focus on machine learning and interactivity leads to a common theme of the need to balance conflicting requirements. First, any machine learning method must strike a balance between how much it can learn and how well it generalises. Second, interactive methods must balance minimal user demand with maximal user control. To address the problem of weak boundaries,methods of supervised texture classification are investigated that do not use explicit texture features. These methods enable prior knowledge about the image to benefit any segmentation framework. A chosen dynamic contour model, based on probabilistic boundary tracking, combines these image priors with efficient modes of interaction. We show the benefits of the texture classifiers over intensity and gradient-based image models, in both classification and boundary extraction. To address the problem of irregular region shape, we devise a new type of statistical shape model (SSM) that does not use explicit boundary features or assume high-level similarity between region shapes. First, the models are used for shape discrimination, to constrain any segmentation framework by way of regularisation. Second, the SSMs are used for shape generation, allowing probabilistic segmentation frameworks to draw shapes from a prior distribution. The generative models also include novel methods to constrain shape generation according to information from both the image and user interactions. The shape models are first evaluated in terms of discrimination capability, and shown to out-perform other shape descriptors. Experiments also show that the shape models can benefit a standard type of segmentation algorithm by providing shape regularisers. We finally show how to exploit the shape models in supervised segmentation frameworks, and evaluate their benefits in user trials

Automating the multimodal analysis of musculoskeletal imaging in the presence of hip implants

In patients treated with hip arthroplasty, the muscular condition and presence of inflammatory reactions are assessed using magnetic resonance imaging (MRI). As MRI lacks contrast for bony structures, computed tomography (CT) is preferred for clinical evaluation of bone tissue and orthopaedic surgical planning. Combining the complementary information of MRI and CT could improve current clinical practice for diagnosis, monitoring and treatment planning. In particular, the different contrast of these modalities could help better quantify the presence of fatty infiltration to characterise muscular condition after hip replacement. In this thesis, I developed automated processing tools for the joint analysis of CT and MR images of patients with hip implants. In order to combine the multimodal information, a novel nonlinear registration algorithm was introduced, which imposes rigidity constraints on bony structures to ensure realistic deformation. I implemented and thoroughly validated a fully automated framework for the multimodal segmentation of healthy and pathological musculoskeletal structures, as well as implants. This framework combines the proposed registration algorithm with tailored image quality enhancement techniques and a multi-atlas-based segmentation approach, providing robustness against the large population anatomical variability and the presence of noise and artefacts in the images. The automation of muscle segmentation enabled the derivation of a measure of fatty infiltration, the Intramuscular Fat Fraction, useful to characterise the presence of muscle atrophy. The proposed imaging biomarker was shown to strongly correlate with the atrophy radiological score currently used in clinical practice. Finally, a preliminary work on multimodal metal artefact reduction, using an unsupervised deep learning strategy, showed promise for improving the postprocessing of CT and MR images heavily corrupted by metal artefact. This work represents a step forward towards the automation of image analysis in hip arthroplasty, supporting and quantitatively informing the decision-making process about patient’s management

Cumulative Distribution Functions As The Foundation For Probabilistic Models

This thesis discusses applications of probabilistic and connectionist models for constructing and training cumulative distribution functions (CDFs). First, it is shown how existing tools from the copula literature can be combined to build probabilistic models. It is found that this simple construction leads to numerical and scalability issues that make training and inference challenging. Next, several innovative ideas, combining neural networks, automatic differentiation and copula functions, introduce how to assemble black-box probabilistic models. The basic building block is a cumulative distribution function that is straightforward to construct, composed of arithmetic operations and nonlinear functions. There is no need to assume any specific parametric probability density function (PDF), making the model flexible and normalisation unnecessary. The only requirement is to design a computational graph that parameterises monotonically non-decreasing functions with a constrained range. Training can be then performed using standard tools from any neural network software library. Finally, factorial hidden Markov models (FHMMs) for sequential data are presented. It is shown how to leverage cumulative distribution functions in the form of the Gaussian copula and amortised stochastic variational method to encode hidden Markov chains coherently. This approach enables efficient learning and inference to model long sequences of high-dimensional data with long-range dependencies. Tackling such complex problems was impossible with the established FHMM approximate inference algorithm. It is empirically verified on several problems that some of the estimators introduced in this work can perform comparably or better than the currently popular models. Especially for tasks requiring tail-area or marginal probabilities that can be read directly from a cumulative distribution function

Advances in Probabilistic Meta-Learning and the Neural Process Family

A natural progression in machine learning research is to automate and learn from data increasingly many components of our learning agents.Meta-learning is a paradigm that fully embraces this perspective, and can be intuitively described as embodying the idea of learning to learn. A goal of meta-learning research is the development of models to assist users in navigating the intricate space of design choices associated with specifying machine learning solutions. This space is particularly formidable when considering deep learning approaches, which involve myriad design choices interacting in complex fashions to affect the performance of the resulting agents. Despite the impressive successes of deep learning in recent years, this challenge remains a significant bottleneck in deploying neural network based solutions in several important application domains. But how can we reason about and design solutions to this daunting task? This thesis is concerned with a particular perspective for meta-learning in supervised settings. We view supervised learning algorithms as mappings that take data sets to predictive models, and consider meta-learning as learning to approximate functions of this form. In particular, we are interested in meta-learners that (i) employ neural networks to approximate these functions in an end-to-end manner, and (ii) provide predictive distributions rather than single predictors. The former is motivated by the success of neural networks as function approximators, and the latter by our interest in the few-shot learning scenario. The introductory chapters of this thesis formalise this notion, and use it to provide a tutorial introducing the Neural Process Family (NPF), a class of models introduced by Garnelo et al (2018) satisfying the above-mentioned modelling desiderata. We then present our own technical contributions to the NPF. First, we focus on fundamental properties of the model-class, such as expressivity and limiting behaviours of the associated training procedures. Next, we study the role of translation equivariance in the NPF. Considering the intimate relationship between the NPF and the representation of functions operating on sets, we extend the underlying theory of DeepSets to include translation equivariance. We then develop novel members of the NPF endowed with this important inductive bias. Through extensive empirical evaluation, we demonstrate that, in many settings, they significantly outperform their non-equivariant counterparts. Finally, we turn our attention to the development of Neural Processes for few-shot image-classification. We introduce models that navigate the important tradeoffs associated with this setting, and describe the specification of their central components. We demonstrate that the resulting models---CNAPs---achieve state-of-the-art performance on a challenging benchmark called Meta-Dataset, while adapting faster and with less computational overhead than their best-performing competitors

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Enhancing automatic level generation for platform videogames

This dissertation addresses the challenge of improving automatic level generation processes for plat-form videogames. As Procedural Content Generation (PCG) techniques evolved from the creation of simple elements to the construction of complete levels and scenarios, the principles behind the generation algorithms became more ambitious and complex, representing features that beforehand were only possible with human design. PCG goes beyond the search for valid geometries that can be used as levels, where multiple challenges are represented in an adequate way. It is also a search for user-centred design content and the creativity sparks of humanly created content. In order to improve the creativity capabilities of such generation algorithms, we conducted part of our research directed to the creation of new techniques using more ambitious design patterns. For this purpose, we have implemented two overall structure generation algorithms and created an addi-tional adaptation algorithm. The later can transform simple branched paths into more compelling game challenges by adding items and other elements in specific places, such as gates and levers for their activation. Such approach is suitable to avoid excessive level linearity and to represent certain design patterns with additional content richness. Moreover, content adaptation was transposed from general design domain to user-centred principles. In this particular case, we analysed success and failure patterns in action videogames and proposed a set of metrics to estimate difficulty, taking into account that each user has a different perception of that concept. This type of information serves the generation algorithms to make them more directed to the creation of personalised experiences. Furthermore, the conducted research also aimed to the integration of different techniques into a common ground. For this purpose, we have developed a general framework to represent content of platform videogames, compatible with several titles within the genre. Our algorithms run over this framework, whereby they are generic and game independent. We defined a modular architecture for the generation process, using this framework to normalise the content that is shared by multiple modules. A level editor tool was also created, which allows human level design and the testing of automatic generation algorithms. An adapted version of the editor was implemented for the semi-automatic creation of levels, in which the designer may simply define the type of content that he/she desires, in the form of quests and missions, and the system creates a corresponding level structure. This materialises our idea of bridging human high-level design patterns with lower level automated generation algorithms. Finally, we integrated the different contributions into a game prototype. This implementation allowed testing the different proposed approaches altogether, reinforcing the validity of the proposed archi-tecture and framework. It also allowed performing a more complete gameplay data retrieval in order to strengthen and validate the proposed metrics regarding difficulty perceptions

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