Graph ambiguity

In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved

Automated Morphometric Characterization of the Cerebral Cortex for the Developing and Ageing Brain

Morphometric characterisation of the cerebral cortex can provide information about patterns of brain development and ageing and may be relevant for diagnosis and estimation of the progression of diseases such as Alzheimer's, Huntington's, and schizophrenia. Therefore, understanding and describing the differences between populations in terms of structural volume, shape and thickness is of critical importance. Methodologically, due to data quality, presence of noise, PV effects, limited resolution and pathological variability, the automated, robust and time-consistent estimation of morphometric features is still an unsolved problem. This thesis focuses on the development of tools for robust cross-sectional and longitudinal morphometric characterisation of the human cerebral cortex. It describes techniques for tissue segmentation, structural and morphometric characterisation, cross-sectional and longitudinally cortical thickness estimation from serial MRI images in both adults and neonates. Two new probabilistic brain tissue segmentation techniques are introduced in order to accurately and robustly segment the brain of elderly and neonatal subjects, even in the presence of marked pathology. Two other algorithms based on the concept of multi-atlas segmentation propagation and fusion are also introduced in order to parcelate the brain into its multiple composing structures with the highest possible segmentation accuracy. Finally, we explore the use of the Khalimsky cubic complex framework for the extraction of topologically correct thickness measurements from probabilistic segmentations without explicit parametrisation of the edge. A longitudinal extension of this method is also proposed. The work presented in this thesis has been extensively validated on elderly and neonatal data from several scanners, sequences and protocols. The proposed algorithms have also been successfully applied to breast and heart MRI, neck and colon CT and also to small animal imaging. All the algorithms presented in this thesis are available as part of the open-source package NiftySeg

Generative embeddings based on Rician mixtures:Application to kernel-based discriminative classification of magnetic resonance images

Most approaches to classifier learning for structured objects (such as images or sequences) are based on probabilistic generative models. On the other hand, state-of-the-art classifiers for vectorial data are learned discrim-inatively. In recent years, these two dual paradigms have been combined via the use of generative embeddings (of which the Fisher kernel is arguably the best known example); these embeddings are mappings from the object space into a fixed dimensional score space, induced by a generative model learned from data, on which a (maybe kernel-based) discriminative approach can then be used. This paper proposes a new semi-parametric approach to build generative embeddings for classification of magnetic resonance images (MRI). Based on the fact that MRI data is well described by Rice distributions, we propose to use Rician mixtures as the underlying generative model, based on which several different generative embeddings are built. These embeddings yield vectorial representations on which kernel-based support vector machines (SVM) can be trained for classification. Concerning the choice of kernel, we adopt the recently proposed nonextensive information theoretic kernels. The methodology proposed was tested on a challenging classification task, which consists in classifying MRI images as belonging to schizophrenic or non-schizophrenic human subjects. The classification is based on a set of regions of interest (ROIs) in each image, with the classifiers corresponding to each ROI being combined via boosting. The experimental results show that the proposed methodology outperforms the previous state-of-the-art methods on the same dataset

Generative embeddings based on Rician mixtures for kernel-based classification of magnetic resonance images

Classical approaches to classifier learning for structured objects (such as images or sequences) are based on probabilistic generative models. On the other hand, state-of-the-art classifiers for vectorial data are learned discriminatively. In recent years, these two dual paradigms have been combined via the use of generative embeddings (of which the Fisher kernel is arguably the best known example); these embeddings are mappings from the object space into a fixed dimensional score space, induced by a generative model learned from data, on which a (maybe kernel-based) discriminative approach can then be used.This paper proposes a new semi-parametric approach to build generative embeddings for classification of magnetic resonance images (MRI). Based on the fact that MRI data is well described by Rice distributions, we propose to use Rician mixtures as the underlying generative model, based on which several different generative embeddings are built. These embeddings yield vectorial representations on which kernel-based support vector machines (SVM) can be trained for classification. Concerning the choice of kernel, we adopt the recently proposed nonextensive information theoretic kernels.The methodology proposed was tested on a challenging classification task, which consists in classifying MRI images as belonging to schizophrenic or non-schizophrenic human subjects. The classification is based on a set of regions of interest (ROIs) in each image, with the classifiers corresponding to each ROI being combined via AdaBoost. The experimental results show that the proposed methodology outperforms the previous state-of-the-art methods on the same dataset