Variational models and numerical algorithms for selective image segmentation

This thesis deals with the numerical solution of nonlinear partial differential equations and their application in image processing. The differential equations we deal with here arise from the minimization of variational models for image restoration techniques (such as denoising) and recognition of objects techniques (such as segmentation). Image denoising is a technique aimed at restoring a digital image that has been contaminated by noise while segmentation is a fundamental task in image analysis responsible for partitioning an image as sub-regions or representing the image into something that is more meaningful and easier to analyze such as extracting one or more specific objects of interest in images based on relevant information or a desired feature. Although there has been a lot of research in the restoration of images, the performance of such methods is still poor, especially when the images have a high level of noise or when the algorithms are slow. Task of the segmentation is even more challenging problem due to the difficulty of delineating, even manually, the contours of the objects of interest. The problems are often due to low contrast, fuzzy contours, similar intensities with adjacent objects, or the objects to be extracted having no real contours. The first objective of this work is to develop fast image restoration and segmentation methods which provide better denoising and fast and robust performance for image segmentation. The contribution presented here is the development of a restarted homotopy analysis method which has been designed to be easily adaptable to various types of image processing problems. As a second research objective we propose a framework for image selective segmentation which partitions an image based on the information known in advance of the object/objects to be extracted (for example the left kidney is the target to be extracted in a CT image and the prior knowledge is a few markers in this object of interest). This kind of segmentation appears especially in medical applications. Medical experts usually estimate and manually draw the boundaries of the organ/organs based on their experience. Our aim is to introduce automatic segmentation of the object of interest as a contribution not only to the way doctors and surgeons diagnose and operate but to other fields as well. The proposed methods showed success in segmenting different objects and perform well in different types of images not only in two-dimensional but in three-dimensional images as well

Contributions à la segmentation d'image : phase locale et modèles statistiques

Ce document presente une synthèse de mes travaux apres these, principalement sur la problematique de la segmentation d’images

Entropy in Image Analysis III

Image analysis can be applied to rich and assorted scenarios; therefore, the aim of this recent research field is not only to mimic the human vision system. Image analysis is the main methods that computers are using today, and there is body of knowledge that they will be able to manage in a totally unsupervised manner in future, thanks to their artificial intelligence. The articles published in the book clearly show such a future

A magnetic study of the west Iberia and conjugate rifted continental margins: constraints on rift-to-/drift processes

The analysis and modelling of magnetic anomalies at the conjugate rifted continental margins of the southern Iberia Abyssal Plain (TAP) and Newfoundland Basin have revealed that the sources of magnetic anomalies are distinctly different across both each margin and between the two margins. Analyses of synthetic anomalies and gridded sea surface magnetic anomaly charts west of Iberia and east of Newfoundland were accomplished by the methods of Euler deconvolution, forward and inverse modelling of the power spectrum, reduction-to-the-pole, and forward and inverse indirect methods. In addition, three near-bottom magnetometer profiles were analysed by the same methods in addition to the application of componental magnetometry. The results have revealed that oceanic crust, transitional basement and thinned continental crust are defined by magnetic sources with different characteristics. Over oceanic crust, magnetic sources are present as lava-flow-like bodies whose depths coincide with the top of acoustic basement seen on MCS profiles. Top-basement source depths are consistent with those determined in two other regions of oceanic crust. In the southern IAP, oceanic crust, ~4 km thick with magnetizations up to +1.5 A/m, generated by organized seafloor spreading was first accreted -126 Ma at the position of a N-S oriented segmented basement peridotite ridge. To the west, seafloor spreading anomalies can be modelled at spreading rates of 10 mm/yr or more. Immediately to the east, in a zone -10-20 km in width, I identify seafloor spreading anomahes which can only be modelled assuming variable spreading rates. In the OCT, sources of magnetic anomalies are present at the top of basement and up to -6 km beneath. I interpret the uppermost source as serpentinized peridotite, and the lowermost source as intruded gabbroic bodies which were impeded, whilst rising upwards, by the lower density serpentinized peridotites. Intrusion was accompanied by tectonism and a gradual change in conditions from rifting to seafloor spreading as the North Atlantic rift propagated northwards in Early Cretaceous times. Within thinned continental crust, sources are poorly lineated, and distributed in depth. Scaling relationships of susceptibility are consistent with the sources of magnetic anomalies within continental crust. OCT-type intrusions may be present in the mantle beneath continental crust. At the conjugate Newfoundland margin, seafloor spreading anomalies can be modelled at rates of 8 and 10 mm/yr suggesting an onset age consistent with that of the IAP. In the OCT there, I propose that magnetic anomalies are sourced in near top-basement serpentinized peridotites. An absence of magmatic material and the differences in basement character (with the IAP) suggest that conjugate margin evolution may have been asymmetric

Seismological forward and inverse modelling for upper mantle seismic anisotropy studies

Seismic anisotropy is the dependence of seismic wave velocity on the propagation direction and it is mainly generated by strain-induced lattice preferred orientation (LPO) of intrinsically anisotropic minerals. Despite previous studies have demonstrated that neglecting anisotropy introduces notable imaging artifacts, most tomographic methods rely on the assumption of isotropy, interpreting fast and slow velocity anomalies as related to seismically isotropic sources (e.g., temperature anomalies, presence of a liquid phase, etc). In this Thesis we carried out numerical simulations aiming at improving strain-induced fabric estimates and predicting realistic elastic properties in 2-D and 3-D synthetic domains. We generated synthetic datasets with forward waveform modelling and explored different inverse methodologies (e.g., P- and S-wave travel time tomography, automatic partitioned waveform inversion of surface waves) both with real and synthetic data. Among the results, we present ani-NEWTON21, the first 3D anisotropic teleseismic P-wave tomography revealing upper mantle structures and dynamics beneath the Central Mediterranean. By performing synthetic seismic data inversions we tested how ray density, data quality and regularization (i.e., damping and smoothing factors) influence the tomographic image. Finally, from the comparison of purely isotropic and anisotropic tests, we observed that the first-order effect of including anisotropy in the inversion is to reduce the magnitude of isotropic anomalies, more significantly for low-velocity zones relative to high-velocity zones. The research activities described in this Thesis altogether provide important insights for predicting and isolating seismic anisotropy, and for obtaining more reliable and physically consistent imaging of the Earth’s internal structure.Seismic anisotropy is the dependence of seismic wave velocity on the propagation direction and it is mainly generated by strain-induced lattice preferred orientation (LPO) of intrinsically anisotropic minerals. Despite previous studies have demonstrated that neglecting anisotropy introduces notable imaging artifacts, most tomographic methods rely on the assumption of isotropy, interpreting fast and slow velocity anomalies as related to seismically isotropic sources (e.g., temperature anomalies, presence of a liquid phase, etc). In this Thesis we carried out numerical simulations aiming at improving strain-induced fabric estimates and predicting realistic elastic properties in 2-D and 3-D synthetic domains. We generated synthetic datasets with forward waveform modelling and explored different inverse methodologies (e.g., P- and S-wave travel time tomography, automatic partitioned waveform inversion of surface waves) both with real and synthetic data. Among the results, we present ani-NEWTON21, the first 3D anisotropic teleseismic P-wave tomography revealing upper mantle structures and dynamics beneath the Central Mediterranean. By performing synthetic seismic data inversions we tested how ray density, data quality and regularization (i.e., damping and smoothing factors) influence the tomographic image. Finally, from the comparison of purely isotropic and anisotropic tests, we observed that the first-order effect of including anisotropy in the inversion is to reduce the magnitude of isotropic anomalies, more significantly for low-velocity zones relative to high-velocity zones. The research activities described in this Thesis altogether provide important insights for predicting and isolating seismic anisotropy, and for obtaining more reliable and physically consistent imaging of the Earth’s internal structure

Topics in environmental and physical geodesy

A compilation of mathematical techniques and physical basic knowledge in order to prepare the post graduate students of the subjects of physical geodesy, environmental physics and the visiting students of Erasmus-Socrates projects of the Mediterranean Institute of Oceanography of Toulon and the Campus Universitari de la Mediterrania in Vilanova i la Geltru, Barcelona.Postprint (published version

Fractal analyses of some natural systems

Fractal dimensions are estimated by the box-counting method for real world data sets and for mathematical models of three natural systems. 1 he natural systems are nearshore sea wave profiles, the topography of Shei-pa National Park in Taiwan, and the normalised difference vegetation index (NDV1) image of a fresh fern. I he mathematical models which represent the natural systems utilise multi-frequency sinusoids for the sea waves, a synthetic digital elevation model constructed by the mid-point displacement method for the topography and the Iterated Function System (IFS) codes for the fern leaf. The results show that similar fractal dimensions are obtained for discrete sub-sections of the real and synthetic one-dimensional wave data, whilst different fractal dimensions are obtained for discrete sections of the real and synthetic topographical and fern data. The similarities and differences are interpreted in the context of system evolution which was introduced by Mandelbrot (1977). Finally, the results for the fern images show that use of fractal dimensions can successfully separate void and filled elements of the two-dimensional series

Mathematical approaches for the clinical translation of hyperpolarised 13C imaging in oncology

Dissolution dynamic nuclear polarisation is an emerging clinical technique which enables the metabolism of hyperpolarised 13C-labelled molecules to be dynamically and non- invasively imaged in tissue. The first molecule to gain clinical approval is [1-13C]pyruvate, the conversion of which to [1-13C]lactate has been shown to detect early treatment re- sponse in cancers and correlate with tumour grade. As the technique has recently been translated into humans, accurate and reliable quantitative methods are required in order to detect, analyse and compare regions of altered metabolism in patients. Furthermore, there is a requirement to understand the biological processes which govern lactate pro- duction in tumours in order to draw reliable conclusions from this data. This work begins with a comprehensive analysis of the quantitative methods which have previously been applied to hyperpolarised 13C data and compares these to some novel approaches. The most appropriate kinetic model to apply to hyperpolarised data is determined and some simple, robust quantitative metrics are identified which are suitable for clinical use. A means of automatically segmenting 5D hyperpolarised imaging data using a fuzzy Markov random field approach is presented in order to reliably identify regions of abnormal metabolic activity. The utility of the algorithm is demonstrated on both in silico and animal data. To gain insight into the processes driving lactate metabolism, a mathematical model is developed which is capable of simulating tumour growth and treatment response under a range of metabolic and tissue conditions, focusing on the interaction between tumour and stroma. Finally, hyperpolarised 13C-pyruvate imaging data from the first human subjects to be imaged in Cambridge is analysed. The ability to detect and quantify lactate production in patients is demonstrated through application of the methods derived in earlier chapters. The mathematical approaches presented in this work have the potential to inform both the analysis and interpretation of clinical hyperpolarised 13C imaging data and to aid in the clinical translation of this technique.Joint funded by GlaxoSmithKline and the Cambridge Biomedical Research Centre