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

Deformable Medical Image Registration: A Survey

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: i) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; ii) longitudinal studies, where temporal structural or anatomical changes are investigated; and iii) population modeling and statistical atlases used to study normal anatomical variability. In this technical report, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this technical report is to provide an extensive account of registration techniques in a systematic manner.Le recalage déformable d'images est une des tâches les plus fondamentales dans l'imagerie médicale. Parmi ses applications les plus importantes, on compte: i) la fusion d' information provenant des différents types de modalités a n de faciliter le diagnostic et la planification du traitement; ii) les études longitudinales, oú des changements structurels ou anatomiques sont étudiées en fonction du temps; et iii) la modélisation de la variabilité anatomique normale d'une population et les atlas statistiques. Dans ce rapport de recherche, nous essayons de donner un aperçu des différentes méthodes du recalage déformables, en mettant l'accent sur les avancées les plus récentes du domaine. Nous avons particulièrement insisté sur les techniques appliquées aux images médicales. A n d'étudier les méthodes du recalage d'images, leurs composants principales sont d'abord identifiés puis étudiées de manière indépendante, les techniques les plus récentes étant classifiées en suivant un schéma logique déterminé. La contribution de ce rapport de recherche est de fournir un compte rendu détaillé des techniques de recalage d'une manière systématique

An inexact Newton-Krylov algorithm for constrained diffeomorphic image registration

We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial differential equation (PDE) constrained optimization problem. The PDE constraint consists, in its simplest form, of a hyperbolic transport equation for the evolution of the image intensity. The control variable is the velocity field. Tikhonov regularization on the control ensures well-posedness. We consider standard smoothness regularization based on $H^1$- or $H^2$-seminorms. We augment this regularization scheme with a constraint on the divergence of the velocity field rendering the deformation incompressible and thus ensuring that the determinant of the deformation gradient is equal to one, up to the numerical error. We use a Fourier pseudospectral discretization in space and a Chebyshev pseudospectral discretization in time. We use a preconditioned, globalized, matrix-free, inexact Newton-Krylov method for numerical optimization. A parameter continuation is designed to estimate an optimal regularization parameter. Regularity is ensured by controlling the geometric properties of the deformation field. Overall, we arrive at a black-box solver. We study spectral properties of the Hessian, grid convergence, numerical accuracy, computational efficiency, and deformation regularity of our scheme. We compare the designed Newton-Krylov methods with a globalized preconditioned gradient descent. We study the influence of a varying number of unknowns in time. The reported results demonstrate excellent numerical accuracy, guaranteed local deformation regularity, and computational efficiency with an optional control on local mass conservation. The Newton-Krylov methods clearly outperform the Picard method if high accuracy of the inversion is required.Comment: 32 pages; 10 figures; 9 table

MONOCULAR POSE ESTIMATION AND SHAPE RECONSTRUCTION OF QUASI-ARTICULATED OBJECTS WITH CONSUMER DEPTH CAMERA

Quasi-articulated objects, such as human beings, are among the most commonly seen objects in our daily lives. Extensive research have been dedicated to 3D shape reconstruction and motion analysis for this type of objects for decades. A major motivation is their wide applications, such as in entertainment, surveillance and health care. Most of existing studies relied on one or more regular video cameras. In recent years, commodity depth sensors have become more and more widely available. The geometric measurements delivered by the depth sensors provide significantly valuable information for these tasks. In this dissertation, we propose three algorithms for monocular pose estimation and shape reconstruction of quasi-articulated objects using a single commodity depth sensor. These three algorithms achieve shape reconstruction with increasing levels of granularity and personalization. We then further develop a method for highly detailed shape reconstruction based on our pose estimation techniques. Our first algorithm takes advantage of a motion database acquired with an active marker-based motion capture system. This method combines pose detection through nearest neighbor search with pose refinement via non-rigid point cloud registration. It is capable of accommodating different body sizes and achieves more than twice higher accuracy compared to a previous state of the art on a publicly available dataset. The above algorithm performs frame by frame estimation and therefore is less prone to tracking failure. Nonetheless, it does not guarantee temporal consistent of the both the skeletal structure and the shape and could be problematic for some applications. To address this problem, we develop a real-time model-based approach for quasi-articulated pose and 3D shape estimation based on Iterative Closest Point (ICP) principal with several novel constraints that are critical for monocular scenario. In this algorithm, we further propose a novel method for automatic body size estimation that enables its capability to accommodate different subjects. Due to the local search nature, the ICP-based method could be trapped to local minima in the case of some complex and fast motions. To address this issue, we explore the potential of using statistical model for soft point correspondences association. Towards this end, we propose a unified framework based on Gaussian Mixture Model for joint pose and shape estimation of quasi-articulated objects. This method achieves state-of-the-art performance on various publicly available datasets. Based on our pose estimation techniques, we then develop a novel framework that achieves highly detailed shape reconstruction by only requiring the user to move naturally in front of a single depth sensor. Our experiments demonstrate reconstructed shapes with rich geometric details for various subjects with different apparels. Last but not the least, we explore the applicability of our method on two real-world applications. First of all, we combine our ICP-base method with cloth simulation techniques for Virtual Try-on. Our system delivers the first promising 3D-based virtual clothing system. Secondly, we explore the possibility to extend our pose estimation algorithms to assist physical therapist to identify their patients’ movement dysfunctions that are related to injuries. Our preliminary experiments have demonstrated promising results by comparison with the gold standard active marker-based commercial system. Throughout the dissertation, we develop various state-of-the-art algorithms for pose estimation and shape reconstruction of quasi-articulated objects by leveraging the geometric information from depth sensors. We also demonstrate their great potentials for different real-world applications

Multireference Alignment using Semidefinite Programming

The multireference alignment problem consists of estimating a signal from multiple noisy shifted observations. Inspired by existing Unique-Games approximation algorithms, we provide a semidefinite program (SDP) based relaxation which approximates the maximum likelihood estimator (MLE) for the multireference alignment problem. Although we show that the MLE problem is Unique-Games hard to approximate within any constant, we observe that our poly-time approximation algorithm for the MLE appears to perform quite well in typical instances, outperforming existing methods. In an attempt to explain this behavior we provide stability guarantees for our SDP under a random noise model on the observations. This case is more challenging to analyze than traditional semi-random instances of Unique-Games: the noise model is on vertices of a graph and translates into dependent noise on the edges. Interestingly, we show that if certain positivity constraints in the SDP are dropped, its solution becomes equivalent to performing phase correlation, a popular method used for pairwise alignment in imaging applications. Finally, we show how symmetry reduction techniques from matrix representation theory can simplify the analysis and computation of the SDP, greatly decreasing its computational cost

Non-rigid medical image registration with extended free form deformations: modelling general tissue transitions

Image registration seeks pointwise correspondences between the same or analogous objects in different images. Conventional registration methods generally impose continuity and smoothness throughout the image. However, there are cases in which the deformations may involve discontinuities. In general, the discontinuities can be of different types, depending on the physical properties of the tissue transitions involved and boundary conditions. For instance, in the respiratory motion the lungs slide along the thoracic cage following the tangential direction of their interface. In the normal direction, however, the lungs and the thoracic cage are constrained to be always in contact but they have different material properties producing different compression or expansion rates. In the literature, there is no generic method, which handles different types of discontinuities and considers their directional dependence. The aim of this thesis is to develop a general registration framework that is able to correctly model different types of tissue transitions with a general formalism. This has led to the development of the eXtended Free Form Deformation (XFFD) registration method. XFFD borrows the concept of the interpolation method from the eXtended Finite Element method (XFEM) to incorporate discontinuities by enriching B-spline basis functions, coupled with extra degrees of freedom. XFFD can handle different types of discontinuities and encodes their directional-dependence without any additional constraints. XFFD has been evaluated on digital phantoms, publicly available 3D liver and lung CT images. The experiments show that XFFD improves on previous methods and that it is important to employ the correct model that corresponds to the discontinuity type involved at the tissue transition. The effect of using incorrect models is more evident in the strain, which measures mechanical properties of the tissues

A Geometric Approach for Deciphering Protein Structure from Cryo-EM Volumes

Electron Cryo-Microscopy or cryo-EM is an area that has received much attention in the recent past. Compared to the traditional methods of X-Ray Crystallography and NMR Spectroscopy, cryo-EM can be used to image much larger complexes, in many different conformations, and under a wide range of biochemical conditions. This is because it does not require the complex to be crystallisable. However, cryo-EM reconstructions are limited to intermediate resolutions, with the state-of-the-art being 3.6A, where secondary structure elements can be visually identified but not individual amino acid residues. This lack of atomic level resolution creates new computational challenges for protein structure identification. In this dissertation, we present a suite of geometric algorithms to address several aspects of protein modeling using cryo-EM density maps. Specifically, we develop novel methods to capture the shape of density volumes as geometric skeletons. We then use these skeletons to find secondary structure elements: SSEs) of a given protein, to identify the correspondence between these SSEs and those predicted from the primary sequence, and to register high-resolution protein structures onto the density volume. In addition, we designed and developed Gorgon, an interactive molecular modeling system, that integrates the above methods with other interactive routines to generate reliable and accurate protein backbone models

Dense Vision in Image-guided Surgery

Image-guided surgery needs an efficient and effective camera tracking system in order to perform augmented reality for overlaying preoperative models or label cancerous tissues on the 2D video images of the surgical scene. Tracking in endoscopic/laparoscopic scenes however is an extremely difficult task primarily due to tissue deformation, instrument invasion into the surgical scene and the presence of specular highlights. State of the art feature-based SLAM systems such as PTAM fail in tracking such scenes since the number of good features to track is very limited. When the scene is smoky and when there are instrument motions, it will cause feature-based tracking to fail immediately. The work of this thesis provides a systematic approach to this problem using dense vision. We initially attempted to register a 3D preoperative model with multiple 2D endoscopic/laparoscopic images using a dense method but this approach did not perform well. We subsequently proposed stereo reconstruction to directly obtain the 3D structure of the scene. By using the dense reconstructed model together with robust estimation, we demonstrate that dense stereo tracking can be incredibly robust even within extremely challenging endoscopic/laparoscopic scenes. Several validation experiments have been conducted in this thesis. The proposed stereo reconstruction algorithm has turned out to be the state of the art method for several publicly available ground truth datasets. Furthermore, the proposed robust dense stereo tracking algorithm has been proved highly accurate in synthetic environment (< 0.1 mm RMSE) and qualitatively extremely robust when being applied to real scenes in RALP prostatectomy surgery. This is an important step toward achieving accurate image-guided laparoscopic surgery.Open Acces