Image processing for plastic surgery planning

This thesis presents some image processing tools for plastic surgery planning. In particular, it presents a novel method that combines local and global context in a probabilistic relaxation framework to identify cephalometric landmarks used in Maxillofacial plastic surgery. It also uses a method that utilises global and local symmetry to identify abnormalities in CT frontal images of the human body. The proposed methodologies are evaluated with the help of several clinical data supplied by collaborating plastic surgeons

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Local Geometry Processing for Deformations of Non-Rigid 3D Shapes

Geometry processing and in particular spectral geometry processing deal with many different deformations that complicate shape analysis problems for non-rigid 3D objects. Furthermore, pointwise description of surfaces has increased relevance for several applications such as shape correspondences and matching, shape representation, shape modelling and many others. In this thesis we propose four local approaches to face the problems generated by the deformations of real objects and improving the pointwise characterization of surfaces. Differently from global approaches that work simultaneously on the entire shape we focus on the properties of each point and its local neighborhood. Global analysis of shapes is not negative in itself. However, having to deal with local variations, distortions and deformations, it is often challenging to relate two real objects globally. For this reason, in the last decades, several instruments have been introduced for the local analysis of images, graphs, shapes and surfaces. Starting from this idea of localized analysis, we propose both theoretical insights and application tools within the local geometry processing domain. In more detail, we extend the windowed Fourier transform from the standard Euclidean signal processing to different versions specifically designed for spectral geometry processing. Moreover, from the spectral geometry processing perspective, we define a new family of localized basis for the functional space defined on surfaces that improve the spatial localization for standard applications in this field. Finally, we introduce the discrete time evolution process as a framework that characterizes a point through its pairwise relationship with the other points on the surface in an increasing scale of locality. The main contribute of this thesis is a set of tools for local geometry processing and local spectral geometry processing that could be used in standard useful applications. The overall observation of our analysis is that localization around points could factually improve the geometry processing in many different applications

Subspace Clustering and Active Learning with Constraints

Data representations can often be high-dimensional, whether it is due to the large number of collected / recorded features or due to how the data sources (e.g. images, texts) are processed. It is often the case that the main structure of the data can be summarised well in a lower dimensional subspace or multiple lower dimensional subspaces. Subspace clustering addresses the problem of simultaneously uncovering multiple subspace structures in the data and grouping the data according to their underlying subspace structures. The first contribution of this thesis is the development of a Subspace Clustering with Active Learning (SCAL) framework that is designed for Subspace Clustering. This framework allows clustering performance to improve in an effective and efficient manner over time, with the need to query only a small amount of labelling information. It also has the potential to be applied to more general subspace clustering methods, which has been further explored and developed in our next methodological contribution. The second contribution of this thesis is a unified active learning and constrained clustering framework for spectral-based subspace clustering methods. In this work, we propose a spectral-based subspace clustering methodology named Weighted Sparse Simplex Representation (WSSR). It has been demonstrated to have favourable performance against state-of-the-art spectral-based subspace clustering methods on both synthetic and real data. We also propose a flexible weighting scheme that can incorporate external information into the problem formulation, which leads to a constrained clustering extension of WSSR. We show that it can be applied in conjunction with our previously proposed SCAL strategy when labelling information can be queried sequentially. The third contribution of this thesis is the development of an algebraic subspace clustering methodology – Minimum Angle Clustering (MAC). It is motivated by the application of clustering Amazon products based on their titles when represented using the TF-IDF matrix, which is both sparse and high-dimensional. The proposed methodology is composed of two stages. In the first stage, it identifies a large number of subspaces in the data through the Reduced Row Echelon Form technique. In the second stage, we propose a new subspace proximity measure to construct an affinity matrix for the formed subspaces before spectral clustering is applied to obtain the final cluster labels. The proposed methodology has been shown to enjoy competitive performance against a number of well-established subspace clustering and document clustering techniques on the application of clustering Amazon product names

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available