On Invariance, Equivariance, Correlation and Convolution of Spherical Harmonic Representations for Scalar and Vectorial Data

The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation and practical implementation of SH representations, summarizing works on rotation invariant and equivariant features, as well as convolutions and exact correlations of signals on spheres. In extension, these methods are then generalized from scalar SH representations to Vectorial Harmonics (VH), providing the same capabilities for 3d vector fields on spheresComment: 106 pages, tech repor

Variational methods for shape and image registrations.

Estimating and analysis of deformation, either rigid or non-rigid, is an active area of research in various medical imaging and computer vision applications. Its importance stems from the inherent inter- and intra-variability in biological and biomedical object shapes and from the dynamic nature of the scenes usually dealt with in computer vision research. For instance, quantifying the growth of a tumor, recognizing a person\u27s face, tracking a facial expression, or retrieving an object inside a data base require the estimation of some sort of motion or deformation undergone by the object of interest. To solve these problems, and other similar problems, registration comes into play. This is the process of bringing into correspondences two or more data sets. Depending on the application at hand, these data sets can be for instance gray scale/color images or objects\u27 outlines. In the latter case, one talks about shape registration while in the former case, one talks about image/volume registration. In some situations, the combinations of different types of data can be used complementarily to establish point correspondences. One of most important image analysis tools that greatly benefits from the process of registration, and which will be addressed in this dissertation, is the image segmentation. This process consists of localizing objects in images. Several challenges are encountered in image segmentation, including noise, gray scale inhomogeneities, and occlusions. To cope with such issues, the shape information is often incorporated as a statistical model into the segmentation process. Building such statistical models requires a good and accurate shape alignment approach. In addition, segmenting anatomical structures can be accurately solved through the registration of the input data set with a predefined anatomical atlas. Variational approaches for shape/image registration and segmentation have received huge interest in the past few years. Unlike traditional discrete approaches, the variational methods are based on continuous modelling of the input data through the use of Partial Differential Equations (PDE). This brings into benefit the extensive literature on theory and numerical methods proposed to solve PDEs. This dissertation addresses the registration problem from a variational point of view, with more focus on shape registration. First, a novel variational framework for global-to-local shape registration is proposed. The input shapes are implicitly represented through their signed distance maps. A new Sumof- Squared-Differences (SSD) criterion which measures the disparity between the implicit representations of the input shapes, is introduced to recover the global alignment parameters. This new criteria has the advantages over some existing ones in accurately handling scale variations. In addition, the proposed alignment model is less expensive computationally. Complementary to the global registration field, the local deformation field is explicitly established between the two globally aligned shapes, by minimizing a new energy functional. This functional incrementally and simultaneously updates the displacement field while keeping the corresponding implicit representation of the globally warped source shape as close to a signed distance function as possible. This is done under some regularization constraints that enforce the smoothness of the recovered deformations. The overall process leads to a set of coupled set of equations that are simultaneously solved through a gradient descent scheme. Several applications, where the developed tools play a major role, are addressed throughout this dissertation. For instance, some insight is given as to how one can solve the challenging problem of three dimensional face recognition in the presence of facial expressions. Statistical modelling of shapes will be presented as a way of benefiting from the proposed shape registration framework. Second, this dissertation will visit th

Variable illumination and invariant features for detecting and classifying varnish defects

This work presents a method to detect and classify varnish defects on wood surfaces. Since these defects are only partially visible under certain illumination directions, one image doesn\u27t provide enough information for a recognition task. A classification requires inspecting the surface under different illumination directions, which results in image series. The information is distributed along this series and can be extracted by merging the knowledge about the defect shape and light direction

Shape/image registration for medical imaging : novel algorithms and applications.

This dissertation looks at two different categories of the registration approaches: Shape registration, and Image registration. It also considers the applications of these approaches into the medical imaging field. Shape registration is an important problem in computer vision, computer graphics and medical imaging. It has been handled in different manners in many applications like shapebased segmentation, shape recognition, and tracking. Image registration is the process of overlaying two or more images of the same scene taken at different times, from different viewpoints, and/or by different sensors. Many image processing applications like remote sensing, fusion of medical images, and computer-aided surgery need image registration. This study deals with two different applications in the field of medical image analysis. The first one is related to shape-based segmentation of the human vertebral bodies (VBs). The vertebra consists of the VB, spinous, and other anatomical regions. Spinous pedicles, and ribs should not be included in the bone mineral density (BMD) measurements. The VB segmentation is not an easy task since the ribs have similar gray level information. This dissertation investigates two different segmentation approaches. Both of them are obeying the variational shape-based segmentation frameworks. The first approach deals with two dimensional (2D) case. This segmentation approach starts with obtaining the initial segmentation using the intensity/spatial interaction models. Then, shape model is registered to the image domain. Finally, the optimal segmentation is obtained using the optimization of an energy functional which integrating the shape model with the intensity information. The second one is a 3D simultaneous segmentation and registration approach. The information of the intensity is handled by embedding a Willmore flow into the level set segmentation framework. Then the shape variations are estimated using a new distance probabilistic model. The experimental results show that the segmentation accuracy of the framework are much higher than other alternatives. Applications on BMD measurements of vertebral body are given to illustrate the accuracy of the proposed segmentation approach. The second application is related to the field of computer-aided surgery, specifically on ankle fusion surgery. The long-term goal of this work is to apply this technique to ankle fusion surgery to determine the proper size and orientation of the screws that are used for fusing the bones together. In addition, we try to localize the best bone region to fix these screws. To achieve these goals, the 2D-3D registration is introduced. The role of 2D-3D registration is to enhance the quality of the surgical procedure in terms of time and accuracy, and would greatly reduce the need for repeated surgeries; thus, saving the patients time, expense, and trauma

Learning and comparing functional connectomes across subjects

Functional connectomes capture brain interactions via synchronized fluctuations in the functional magnetic resonance imaging signal. If measured during rest, they map the intrinsic functional architecture of the brain. With task-driven experiments they represent integration mechanisms between specialized brain areas. Analyzing their variability across subjects and conditions can reveal markers of brain pathologies and mechanisms underlying cognition. Methods of estimating functional connectomes from the imaging signal have undergone rapid developments and the literature is full of diverse strategies for comparing them. This review aims to clarify links across functional-connectivity methods as well as to expose different steps to perform a group study of functional connectomes

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Cerebral white matter analysis using diffusion imaging

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2006.Includes bibliographical references (p. 183-198).In this thesis we address the whole-brain tractography segmentation problem. Diffusion magnetic resonance imaging can be used to create a representation of white matter tracts in the brain via a process called tractography. Whole brain tractography outputs thousands of trajectories that each approximate a white matter fiber pathway. Our method performs automatic organization, or segmention, of these trajectories into anatomical regions and gives automatic region correspondence across subjects. Our method enables both the automatic group comparison of white matter anatomy and of its regional diffusion properties, and the creation of consistent white matter visualizations across subjects. We learn a model of common white matter structures by analyzing many registered tractography datasets simultaneously. Each trajectory is represented as a point in a high-dimensional spectral embedding space, and common structures are found by clustering in this space. By annotating the clusters with anatomical labels, we create a model that we call a high-dimensional white matter atlas.(cont.) Our atlas creation method discovers structures corresponding to expected white matter anatomy, such as the corpus callosum, uncinate fasciculus, cingulum bundles, arcuate fasciculus, etc. We show how to extend the spectral clustering solution, stored in the atlas, using the Nystrom method to perform automatic segmentation of tractography from novel subjects. This automatic tractography segmentation gives an automatic region correspondence across subjects when all subjects are labeled using the atlas. We show the resulting automatic region correspondences, demonstrate that our clustering method is reproducible, and show that the automatically segmented regions can be used for robust measurement of fractional anisotropy.by Lauren Jean O'Donnell.Ph.D

Segmentation of brain MRI structures with deep machine learning

Several studies on brain Magnetic Resonance Images (MRI) show relations between neuroanatomical abnormalities of brain structures and neurological disorders, such as Attention De fficit Hyperactivity Disorder (ADHD) and Alzheimer. These abnormalities seem to be correlated with the size and shape of these structures, and there is an active fi eld of research trying to find accurate methods for automatic MRI segmentation. In this project, we study the automatic segmentation of structures from the Basal Ganglia and we propose a new methodology based on Stacked Sparse Autoencoders (SSAE). SSAE is a strategy that belongs to the family of Deep Machine Learning and consists on a supervised learning method based on an unsupervisely pretrained Feed-forward Neural Network. Moreover, we present two approaches based on 2D and 3D features of the images. We compare the results obtained on the di fferent regions of interest with those achieved by other machine learning techniques such as Neural Networks and Support Vector Machines. We observed that in most cases SSAE improves those other methods. We demonstrate that the 3D features do not report better results than the 2D ones as could be thought. Furthermore, we show that SSAE provides state-of-the-art Dice Coe fficient results (left, right): Caudate (90.6+-3 1.4, 90.31 +-1.7), Putamen (91.03 +-1.4, 90.82+- 1.4), Pallidus (85.11+-1.8, 83.47 +-2.2), Accumbens (74.26+- 4.4, 74.46 +-4.6)

Enabling Scalable Neurocartography: Images to Graphs for Discovery

In recent years, advances in technology have enabled researchers to ask new questions predicated on the collection and analysis of big datasets that were previously too large to study. More specifically, many fundamental questions in neuroscience require studying brain tissue at a large scale to discover emergent properties of neural computation, consciousness, and etiologies of brain disorders. A major challenge is to construct larger, more detailed maps (e.g., structural wiring diagrams) of the brain, known as connectomes. Although raw data exist, obstacles remain in both algorithm development and scalable image analysis to enable access to the knowledge within these data volumes. This dissertation develops, combines and tests state-of-the-art algorithms to estimate graphs and glean other knowledge across six orders of magnitude, from millimeter-scale magnetic resonance imaging to nanometer-scale electron microscopy. This work enables scientific discovery across the community and contributes to the tools and services offered by NeuroData and the Open Connectome Project. Contributions include creating, optimizing and evaluating the first known fully-automated brain graphs in electron microscopy data and magnetic resonance imaging data; pioneering approaches to generate knowledge from X-Ray tomography imaging; and identifying and solving a variety of image analysis challenges associated with building graphs suitable for discovery. These methods were applied across diverse datasets to answer questions at scales not previously explored