Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach

Cardiac motion estimation is an important diagnostic tool to detect heart diseases and it has been explored with modalities such as MRI and conventional ultrasound (US) sequences. US cardiac motion estimation still presents challenges because of the complex motion patterns and the presence of noise. In this work, we propose a novel approach to estimate the cardiac motion using ultrafast ultrasound data. -- Our solution is based on a variational formulation characterized by the L2-regularized class. The displacement is represented by a lattice of b-splines and we ensure robustness by applying a maximum likelihood type estimator. While this is an important part of our solution, the main highlight of this paper is to combine a low-rank data representation with topology preservation. Low-rank data representation (achieved by finding the k-dominant singular values of a Casorati Matrix arranged from the data sequence) speeds up the global solution and achieves noise reduction. On the other hand, topology preservation (achieved by monitoring the Jacobian determinant) allows to radically rule out distortions while carefully controlling the size of allowed expansions and contractions. Our variational approach is carried out on a realistic dataset as well as on a simulated one. We demonstrate how our proposed variational solution deals with complex deformations through careful numerical experiments. While maintaining the accuracy of the solution, the low-rank preprocessing is shown to speed up the convergence of the variational problem. Beyond cardiac motion estimation, our approach is promising for the analysis of other organs that experience motion.Comment: 15 pages, 10 figures, Physics in Medicine and Biology, 201

Deformable meshes for shape recovery: models and applications

With the advance of scanning and imaging technology, more and more 3D objects become available. Among them, deformable objects have gained increasing interests. They include medical instances such as organs, a sequence of objects in motion, and objects of similar shapes where a meaningful correspondence can be established between each other. Thus, it requires tools to store, compare, and retrieve them. Many of these operations depend on successful shape recovery. Shape recovery is the task to retrieve an object from the environment where its geometry is hidden or implicitly known. As a simple and versatile tool, mesh is widely used in computer graphics for modelling and visualization. In particular, deformable meshes are meshes which can take the deformation of deformable objects. They extend the modelling ability of meshes. This dissertation focuses on using deformable meshes to approach the 3D shape recovery problem. Several models are presented to solve the challenges for shape recovery under different circumstances. When the object is hidden in an image, a PDE deformable model is designed to extract its surface shape. The algorithm uses a mesh representation so that it can model any non-smooth surface with an arbitrary precision compared to a parametric model. It is more computational efficient than a level-set approach. When the explicit geometry of the object is known but is hidden in a bank of shapes, we simplify the deformation of the model to a graph matching procedure through a hierarchical surface abstraction approach. The framework is used for shape matching and retrieval. This idea is further extended to retain the explicit geometry during the abstraction. A novel motion abstraction framework for deformable meshes is devised based on clustering of local transformations and is successfully applied to 3D motion compression

Dynamic Multivariate Simplex Splines For Volume Representation And Modeling

Volume representation and modeling of heterogeneous objects acquired from real world are very challenging research tasks and playing fundamental roles in many potential applications, e.g., volume reconstruction, volume simulation and volume registration. In order to accurately and efficiently represent and model the real-world objects, this dissertation proposes an integrated computational framework based on dynamic multivariate simplex splines (DMSS) that can greatly improve the accuracy and efficacy of modeling and simulation of heterogenous objects. The framework can not only reconstruct with high accuracy geometric, material, and other quantities associated with heterogeneous real-world models, but also simulate the complicated dynamics precisely by tightly coupling these physical properties into simulation. The integration of geometric modeling and material modeling is the key to the success of representation and modeling of real-world objects. The proposed framework has been successfully applied to multiple research areas, such as volume reconstruction and visualization, nonrigid volume registration, and physically based modeling and simulation

Joint Image Reconstruction and Nonrigid Motion Estimation with a Simple Penalty That Encourages Local Invertibility

Motion artifacts are a significant issue in medical image reconstruction. There are many methods for incorporating motion information into image reconstruction. However, there are fewer studies that focus on deformation regularization in motioncompensated image reconstruction. The usual choice for deformation regularization has been penalty functions based on the assumption that tissues are elastic. In the image registration field, there have been some methods proposed that impose deformation invertibility using constraints or regularization, assuming that organ motions are invertible transformations. However, most of these methods require very high memory or computation complexity, making them poorly suited for dealing with multiple images simultaneously in motion-compensated image reconstruction. Recently we proposed an image registration method that uses a simple penalty function based on a sufficient condition for the local invertibility of deformations.1 That approach encourages local invertibility in a fast and memory-efficient way. This paper investigates the use of that regularization method for the more challenging problem of joint image reconstruction and nonrigid motion estimation. A 2D PET simulation (based on realistic motion from real patient CT data) demonstrates the benefits of such motion regularization for joint image reconstruction/registration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85929/1/Fessler237.pd

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