A generic approach to the filtering of matrix fields with singular PDEs

There is an increasing demand to develop image processing tools for the filtering and analysis of matrix-valued data, so-called matrix fields. In the case of scalar-valued images parabolic partial differential equations (PDEs) are widely used to perform filtering and denoising processes. Especially interesting from a theoretical as well as from a practical point of view are PDEs with singular diffusivities describing processes like total variation (TV-) diffusion, mean curvature motion and its generalisation, the so-called self-snakes. In this contribution we propose a generic framework that allows us to find the matrix-valued counterparts of the equations mentioned above. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our matrix-valued, singular diffusion filters

A generic approach to diffusion filtering of matrix-fields

Diffusion tensor magnetic resonance imaging (DT-MRI), is a image acquisition method, that provides matrix-valued data, so-called matrix fields. Hence image processing tools for the filtering and analysis of these data types are in demand. In this artricle we propose a generic framework that allows us to find the matrix-valued counterparts of the Perona-Malik PDEs with various diffusivity functions. To this end we extend the notion of derivatives and associated differential operators to matrix fields of symmetric matrices by adopting an operator-algebraic point of view. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our novel matrix-valued Perona-Malik diffusion filters

Homogeneity based segmentation and enhancement of Diffusion Tensor Images : a white matter processing framework

In diffusion magnetic resonance imaging (DMRI) the Brownian motion of the water molecules, within biological tissue, is measured through a series of images. In diffusion tensor imaging (DTI) this diffusion is represented using tensors. DTI describes, in a non-invasive way, the local anisotropy pattern enabling the reconstruction of the nervous fibers - dubbed tractography. DMRI constitutes a powerful tool to analyse the structure of the white matter within a voxel, but also to investigate the anatomy of the brain and its connectivity. DMRI has been proved useful to characterize brain disorders, to analyse the differences on white matter and consequences in brain function. These procedures usually involve the virtual dissection of white matters tracts of interest. The manual isolation of these bundles requires a great deal of neuroanatomical knowledge and can take up to several hours of work. This thesis focuses on the development of techniques able to automatically perform the identification of white matter structures. To segment such structures in a tensor field, the similarity of diffusion tensors must be assessed for partitioning data into regions, which are homogeneous in terms of tensor characteristics. This concept of tensor homogeneity is explored in order to achieve new methods for segmenting, filtering and enhancing diffusion images. First, this thesis presents a novel approach to semi-automatically define the similarity measures that better suit the data. Following, a multi-resolution watershed framework is presented, where the tensor field’s homogeneity is used to automatically achieve a hierarchical representation of white matter structures in the brain, allowing the simultaneous segmentation of different structures with different sizes. The stochastic process of water diffusion within tissues can be modeled, inferring the homogeneity characteristics of the diffusion field. This thesis presents an accelerated convolution method of diffusion images, where these models enable the contextual processing of diffusion images for noise reduction, regularization and enhancement of structures. These new methods are analysed and compared on the basis of their accuracy, robustness, speed and usability - key points for their application in a clinical setting. The described methods enrich the visualization and exploration of white matter structures, fostering the understanding of the human brain

The VHP-F Computational Phantom and its Applications for Electromagnetic Simulations

Modeling of the electromagnetic, structural, thermal, or acoustic response of the human body to various external and internal stimuli is limited by the availability of anatomically accurate and numerically efficient computational models. The models currently approved for use are generally of proprietary or fixed format, preventing new model construction or customization. 1. This dissertation develops a new Visible Human Project - Female (VHP-F) computational phantom, constructed via segmentation of anatomical cryosection images taken in the axial plane of the human body. Its unique property is superior resolution on human head. In its current form, the VHP-F model contains 33 separate objects describing a variety of human tissues within the head and torso. Each obejct is a non-intersecting 2-manifold model composed of contiguous surface triangular elements making the VHP-F model compatible with major commercial and academic numerical simulators employing the Finite Element Method (FEM), Boundary Element Method (BEM), Finite Volume Method (FVM), and Finite-Difference Time-Domain (FDTD) Method. 2. This dissertation develops a new workflow used to construct the VHP-F model that may be utilized to build accessible custom models from any medical image data source. The workflow is customizable and flexible, enabling the creation of standard and parametrically varying models facilitating research on impacts associated with fluctuation of body characteristics (for example, skin thickness) and dynamic processes such as fluid pulsation. 3. This dissertation identifies, enables, and quantifies three new specific computational bioelectromagnetic problems, each of which is solved with the help of the developed VHP-F model: I. Transcranial Direct Current Stimulation (tDCS) of human brain motor cortex with extracephalic versus cephalic electrodes; II. RF channel characterization within cerebral cortex with novel small on-body directional antennas; III. Body Area Network (BAN) characterization and RF localization within the human body using the FDTD method and small antenna models with coincident phase centers. Each of those problems has been (or will be) the subject of a separate dedicated MS thesis

A hitchhiker's guide to diffusion tensor imaging

Diffusion Tensor Imaging (DTI) studies are increasingly popular among clinicians and researchers as they provide unique insights into brain network connectivity. However, in order to optimize the use of DTI, several technical and methodological aspects must be factored in. These include decisions on: acquisition protocol, artifact handling, data quality control, reconstruction algorithm, and visualization approaches, and quantitative analysis methodology. Furthermore, the researcher and/or clinician also needs to take into account and decide on the most suited software tool(s) for each stage of the DTI analysis pipeline. Herein, we provide a straightforward hitchhiker's guide, covering all of the workflow's major stages. Ultimately, this guide will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI.The work was supported by SwitchBox-FP7-HEALTH-2010-grant 259772-2. The authors acknowledge Nadine Santos for her help in editing the manuscript

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy

Development of novel magnetic resonance methods for advanced parametric mapping of the right ventricle

The detection of diffuse fibrosis is of particular interest in congenital heart disease patients, including repaired Tetralogy of Fallot (rTOF), as clinical outcome is linked to the accurate identification of diffuse fibrosis. In the Left Ventricular (LV) myocardium native T1 mapping and Diffusion Tensor Cardiac Magnetic Resonance (DT-CMR) are promising approaches for detection of diffuse fibrosis. In the Right Ventricle (RV) current techniques are limited due to the thinner, mobile and complex shaped compact myocardium. This thesis describes technical development of RV tissue characterisation methods. An interleaved variable density spiral DT-CMR method was implemented on a clinical 3T scanner allowing both ex and in vivo imaging. A range of artefact corrections were implemented and tested (gradient timing delays, off-resonance and T2* corrections). The off- resonance and T2* corrections were evaluated using computational simulation demonstrating that for in vivo acquisitions, off-resonance correction is essential. For the first-time high-resolution Stimulated Echo Acquisition Mode (STEAM) DT-CMR data was acquired in both healthy and rTOF ex-vivo hearts using an interleaved spiral trajectory and was shown to outperform single-shot EPI methods. In vivo the first DT-CMR data was shown from the RV using both an EPI and an interleaved spiral sequence. Both sequences provided were reproducible in healthy volunteers. Results suggest that the RV conformation of cardiomyocytes differs from the known structure in the LV. A novel STEAM-SAturation-recovery Single-sHot Acquisition (SASHA) sequence allowed the acquisition of native T1 data in the RV. The excellent blood and fat suppression provided by STEAM is leveraged to eliminate partial fat and blood signal more effectively than Modified Look-Locker Imaging (MOLLI) sequences. STEAM-SASHA T1 was validated in a phantom showing more accurate results in the native myocardial T1 range than MOLLI. STEAM-SASHA demonstrated good reproducibility in healthy volunteers and initial promising results in a single rTOF patient.Open Acces

Generalizable deep learning based medical image segmentation

Deep learning is revolutionizing medical image analysis and interpretation. However, its real-world deployment is often hindered by the poor generalization to unseen domains (new imaging modalities and protocols). This lack of generalization ability is further exacerbated by the scarcity of labeled datasets for training: Data collection and annotation can be prohibitively expensive in terms of labor and costs because label quality heavily dependents on the expertise of radiologists. Additionally, unreliable predictions caused by poor model generalization pose safety risks to clinical downstream applications. To mitigate labeling requirements, we investigate and develop a series of techniques to strengthen the generalization ability and the data efficiency of deep medical image computing models. We further improve model accountability and identify unreliable predictions made on out-of-domain data, by designing probability calibration techniques. In the first and the second part of thesis, we discuss two types of problems for handling unexpected domains: unsupervised domain adaptation and single-source domain generalization. For domain adaptation we present a data-efficient technique that adapts a segmentation model trained on a labeled source domain (e.g., MRI) to an unlabeled target domain (e.g., CT), using a small number of unlabeled training images from the target domain. For domain generalization, we focus on both image reconstruction and segmentation. For image reconstruction, we design a simple and effective domain generalization technique for cross-domain MRI reconstruction, by reusing image representations learned from natural image datasets. For image segmentation, we perform causal analysis of the challenging cross-domain image segmentation problem. Guided by this causal analysis we propose an effective data-augmentation-based generalization technique for single-source domains. The proposed method outperforms existing approaches on a large variety of cross-domain image segmentation scenarios. In the third part of the thesis, we present a novel self-supervised method for learning generic image representations that can be used to analyze unexpected objects of interest. The proposed method is designed together with a novel few-shot image segmentation framework that can segment unseen objects of interest by taking only a few labeled examples as references. Superior flexibility over conventional fully-supervised models is demonstrated by our few-shot framework: it does not require any fine-tuning on novel objects of interest. We further build a publicly available comprehensive evaluation environment for few-shot medical image segmentation. In the fourth part of the thesis, we present a novel probability calibration model. To ensure safety in clinical settings, a deep model is expected to be able to alert human radiologists if it has low confidence, especially when confronted with out-of-domain data. To this end we present a plug-and-play model to calibrate prediction probabilities on out-of-domain data. It aligns the prediction probability in line with the actual accuracy on the test data. We evaluate our method on both artifact-corrupted images and images from an unforeseen MRI scanning protocol. Our method demonstrates improved calibration accuracy compared with the state-of-the-art method. Finally, we summarize the major contributions and limitations of our works. We also suggest future research directions that will benefit from the works in this thesis.Open Acces

Advancements and Breakthroughs in Ultrasound Imaging

Ultrasonic imaging is a powerful diagnostic tool available to medical practitioners, engineers and researchers today. Due to the relative safety, and the non-invasive nature, ultrasonic imaging has become one of the most rapidly advancing technologies. These rapid advances are directly related to the parallel advancements in electronics, computing, and transducer technology together with sophisticated signal processing techniques. This book focuses on state of the art developments in ultrasonic imaging applications and underlying technologies presented by leading practitioners and researchers from many parts of the world