04172 Abstracts Collection -- Perspectives Workshop: Visualization and Image Processing of Tensor Fields

From 18.04.04 to 23.04.04, the Dagstuhl Seminar 04172 ``Perspectives Workshop: Visualization and Image Processing of Tensor Fields\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Representation Learning: A Review and New Perspectives

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning

Interpretable statistics for complex modelling: quantile and topological learning

As the complexity of our data increased exponentially in the last decades, so has our need for interpretable features. This thesis revolves around two paradigms to approach this quest for insights. In the first part we focus on parametric models, where the problem of interpretability can be seen as a “parametrization selection”. We introduce a quantile-centric parametrization and we show the advantages of our proposal in the context of regression, where it allows to bridge the gap between classical generalized linear (mixed) models and increasingly popular quantile methods. The second part of the thesis, concerned with topological learning, tackles the problem from a non-parametric perspective. As topology can be thought of as a way of characterizing data in terms of their connectivity structure, it allows to represent complex and possibly high dimensional through few features, such as the number of connected components, loops and voids. We illustrate how the emerging branch of statistics devoted to recovering topological structures in the data, Topological Data Analysis, can be exploited both for exploratory and inferential purposes with a special emphasis on kernels that preserve the topological information in the data. Finally, we show with an application how these two approaches can borrow strength from one another in the identification and description of brain activity through fMRI data from the ABIDE project

Novel Image Processing Methods for Improved Fetal Brain MRI

Fetal magnetic resonance imaging (MRI) has been increasingly used as a powerful complement imaging modality to ultrasound imaging (US) for the clinical evaluation of prenatal abnormalities. Specifically, clinical application of fetal MRI has been significantly improved in the nineties by hardware and software advances with the development of ultrafast multi-slice T2-weighted (T2w) acquisition sequences able to freeze the unpredictable fetal motion and provide excellent soft-tissue contrast. Fetal motion is indeed the major challenge in fetal MRI and slice acquisition time should be kept as short as possible. As a result, typical fetal MRI examination involves the acquisition of a set of orthogonally planned scans of thick two-dimensional slices, largely free of intra-slice motion artifacts. The poor resolution in the slice-select dimension as well as possible motion occurring between slices limits further quantitative data analysis, which is the key for a better understanding of the developing brain but also the key for the determination of operator-independent biomarkers that might significantly facilitate fetal diagnosis and prognosis. To this end, several research groups have developed in the past ten years advanced image processing methods, often denoted by motion-robust super-resolution (SR) techniques, to reconstruct from a set of clinical low-resolution (LR) scans, a high-resolution (HR) motion-free volume. SR problem is usually modeled as a linear inverse problem describing the imaging degradation due to acquisition and fetal motion. Typically, such approaches consist in iterating between slice motion estimation that estimates the motion parameters and SR that recovers the HR image given the estimated degradation model. This thesis focuses on the development of novel advanced image processing methods, which have enabled the design of a completely automated reconstruction pipeline for fetal MRI. The proposed techniques help in improving state-of-the-art fetal MRI reconstruction in terms of efficiency, robustness and minimized user-interactions, with the ultimate goal of being translated to the clinical environment. The first part focuses on the development of a more efficient Total Variation (TV)-regularized optimization algorithm for the SR problem. The algorithm uses recent advances in convex optimization with a novel adaptive regularization strategy to offer simultaneously fast, accurate and robust solutions to the fetal image recovery problem. Extensive validations on both simulated fetal and real clinical data show the proposed algorithm is highly robust in front of motion artifacts and that it offers the best trade-off between speed and accuracy for fetal MRI recovery as in comparison with state-of-the art methods. The second part focuses on the development of a novel automatic brain localization and extraction approach based on template-to-slice block matching and deformable slice-totemplate registration. Asmost fetal brain MRI reconstruction algorithms rely only on brain tissue-relevant voxels of low-resolution (LR) images to enhance the quality of inter-slice motion correction and image reconstruction, the fetal brain needs to be localized and extracted as a first step. These tasks generally necessitate user interaction, manually or semi-automatically done. Our methods have enabled the design of completely automated reconstruction pipeline that involves intensity normalization, inter-slice motion estimation, and super-resolution. Quantitative evaluation on clinical MRI scans shows that our approach produces brain masks that are very close to manually drawn brain masks, and ratings performed by two expert observers show that the proposed pipeline achieves similar reconstruction quality to reference reconstruction based on manual slice-by-slice brain extraction without any further effort. The third part investigates the possibility of automatic cortical folding quantification, one of the best biomarkers of brain maturation, by combining our automatic reconstruction pipeline with a state-of-the-art fetal brain tissue segmentation method and existing automated tools provided for adult brain’s cortical folding quantification. Results indicate that our reconstruction pipeline can provide HR MR images with sufficient quality that enable the use of surface tessellation and active surface algorithms similar to those developed for adults to extract meaningful information about fetal brain maturation. Finally, the last part presents new methodological improvements of the reconstruction pipeline aiming at improving the quality of the image for quantitative data analysis, whose accuracy is highly dependent on the quality and resolution of the reconstructed image. In particular, it presents a more consistent and global magnetic bias field correction method which takes advantage of the super-resolution framework to provide a final reconstructed image quasi free of the smooth bias field. Then, it presents a new TV SR algorithm that uses the Huber norm in the data fidelity term to be more robust to non-Gaussian outliers. It also presents the design of a novel joint reconstruction-segmentation framework and the development of a novel TV SR algorithm driven by segmentation to produce images with enhanced edge information that could ultimately improve their segmentation. Finally, it preliminary investigates the capability of increasing the resolution in the in-plane dimensions using SR to ultimately reduce the partial volume effect

Feature based estimation of myocardial motion from tagged MR images

In the past few years we witnessed an increase in mortality due to cancer relative to mortality due to cardiovascular diseases. In 2008, the Netherlands Statistics Agency reports that 33.900 people died of cancer against 33.100 deaths due to cardiovascular diseases, making cancer the number one cause of death in the Netherlands [33]. Even if the rate of people affected by heart diseases is continually rising, they "simply don’t die of it", according to the research director Prof. Mat Daemen of research institute CARIM of the University of Maastricht [50]. The reason for this is the early diagnosis, and the treatment of people with identified risk factors for diseases like ischemic heart disease, hypertrophic cardiomyopathy, thoracic aortic disease, pericardial (sac around the heart) disease, cardiac tumors, pulmonary artery disease, valvular disease, and congenital heart disease before and after surgical repair. Cardiac imaging plays a crucial role in the early diagnosis, since it allows the accurate investigation of a large amount of imaging data in a small amount of time. Moreover, cardiac imaging reduces costs of inpatient care, as has been shown in recent studies [77]. With this in mind, in this work we have provided several tools with the aim to help the investigation of the cardiac motion. In chapters 2 and 3 we have explored a novel variational optic flow methodology based on multi-scale feature points to extract cardiac motion from tagged MR images. Compared to constant brightness methods, this new approach exhibits several advantages. Although the intensity of critical points is also influenced by fading, critical points do retain their characteristic even in the presence of intensity changes, such as in MR imaging. In an experiment in section 5.4 we have applied this optic flow approach directly on tagged MR images. A visual inspection confirmed that the extracted motion fields realistically depicted the cardiac wall motion. The method exploits also the advantages from the multiscale framework. Because sparse velocity formulas 2.9, 3.7, 6.21, and 7.5 provide a number of equations equal to the number of unknowns, the method does not suffer from the aperture problem in retrieving velocities associated to the critical points. In chapters 2 and 3 we have moreover introduced a smoothness component of the optic flow equation described by means of covariant derivatives. This is a novelty in the optic flow literature. Many variational optic flow methods present a smoothness component that penalizes for changes from global assumptions such as isotropic or anisotropic smoothness. In the smoothness term proposed deviations from a predefined motion model are penalized. Moreover, the proposed optic flow equation has been decomposed in rotation-free and divergence-free components. This decomposition allows independent tuning of the two components during the vector field reconstruction. The experiments and the Table of errors provided in 3.8 showed that the combination of the smoothness term, influenced by a predefined motion model, and the Helmholtz decomposition in the optic flow equation reduces the average angular error substantially (20%-25%) with respect to a similar technique that employs only standard derivatives in the smoothness term. In section 5.3 we extracted the motion field of a phantom of which we know the ground truth of and compared the performance of this optic flow method with the performance of other optic flow methods well known in the literature, such as the Horn and Schunck [76] approach, the Lucas and Kanade [111] technique and the tuple image multi-scale optic flow constraint equation of Van Assen et al. [163]. Tests showed that the proposed optic flow methodology provides the smallest average angular error (AAE = 3.84 degrees) and L2 norm = 0.1. In this work we employed the Helmholtz decomposition also to study the cardiac behavior, since the vector field decomposition allows to investigate cardiac contraction and cardiac rotation independently. In chapter 4 we carried out an analysis of cardiac motion of ten volunteers and one patient where we estimated the kinetic energy for the different components. This decomposition is useful since it allows to visualize and quantify the contributions of each single vector field component to the heart beat. Local measurements of the kinetic energy have also been used to detect areas of the cardiac walls with little movement. Experiments on a patient and a comparison between a late enhancement cardiac image and an illustration of the cardiac kinetic energy on a bull’s eye plot illustrated that a correspondence between an infarcted area and an area with very small kinetic energy exists. With the aim to extend in the future the proposed optic flow equation to a 3D approach, in chapter 6 we investigated the 3D winding number approach as a tool to locate critical points in volume images. We simplified the mathematics involved with respect to a previous work [150] and we provided several examples and applications such as cardiac motion estimation from 3-dimensional tagged images, follicle and neuronal cell counting. Finally in chapter 7 we continued our investigation on volume tagged MR images, by retrieving the cardiac motion field using a 3-dimensional and simple version of the proposed optic flow equation based on standard derivatives. We showed that the retrieved motion fields display the contracting and rotating behavior of the cardiac muscle. We moreover extracted the through-plane component, which provides a realistic illustration of the vector field and is missed by 2-dimensional approaches

Bridging Brain and Cognition: A Multilayer Network Analysis of Brain Structural Covariance and General Intelligence in a Developmental Sample of Struggling Learners.

Network analytic methods that are ubiquitous in other areas, such as systems neuroscience, have recently been used to test network theories in psychology, including intelligence research. The network or mutualism theory of intelligence proposes that the statistical associations among cognitive abilities (e.g., specific abilities such as vocabulary or memory) stem from causal relations among them throughout development. In this study, we used network models (specifically LASSO) of cognitive abilities and brain structural covariance (grey and white matter) to simultaneously model brain-behavior relationships essential for general intelligence in a large (behavioral, N = 805; cortical volume, N = 246; fractional anisotropy, N = 165) developmental (ages 5-18) cohort of struggling learners (CALM). We found that mostly positive, small partial correlations pervade our cognitive, neural, and multilayer networks. Moreover, using community detection (Walktrap algorithm) and calculating node centrality (absolute strength and bridge strength), we found convergent evidence that subsets of both cognitive and neural nodes play an intermediary role 'between' brain and behavior. We discuss implications and possible avenues for future studies

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