2,318 research outputs found
A Novel Diffeomorphic Model for Image Registration and Its Algorithm
In this work, we investigate image registration by mapping one image to another in a variational framework and focus on both model robustness and solver efficiency. We first propose a new variational model with a special regularizer, based on the quasi-conformal theory, which can guarantee that the registration map is diffeomorphic. It is well known that when the deformation is large, many variational models including the popular diffusion model cannot ensure diffeomorphism. One common observation is that the fidelity error appears small while the obtained transform is incorrect by way of mesh folding. However, direct reformulation from the Beltrami framework does not lead to effective models; our new regularizer is constructed based on this framework and added to the diffusion model to get a new model, which can achieve diffeomorphism. However, the idea is applicable to a wide class of models. We then propose an iterative method to solve the resulting nonlinear optimization problem and prove the convergence of the method. Numerical experiments can demonstrate that the new model can not only get a diffeomorphic registration even when the deformation is large, but also possess the accuracy in comparing with the currently best models
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Fast algorithms for biophysically-constrained inverse problems in medical imaging
We present algorithms and software for parameter estimation for forward and inverse tumor growth problems and diffeomorphic image registration. Our methods target the following scenarios: automatic image registration of healthy images to tumor bearing medical images and parameter estimation/calibration of tumor models. This thesis focuses on robust and scalable algorithms for these problems.
Although the proposed framework applies to many problems in oncology, we focus on primary brain tumors and in particular low and high-grade gliomas. For the tumor model, the main quantity of interest is the extent of tumor infiltration into the brain, beyond what is visible in imaging.
The inverse tumor problem assumes that we have patient images at two (or more) well-separated times so that we can observe the tumor growth. Also, the inverse problem requires that the two images are segmented. But in a clinical setting such information is usually not available. In a typical case, we just have multimodal magnetic resonance images with no segmentation. We address this lack of information by solving a coupled inverse registration and tumor problem. The role of image registration is to find a plausible mapping between the patient's
tumor-bearing image and a normal brain (atlas), with known segmentation. Solving this coupled inverse problem has a prohibitive computational cost, especially in 3D. To address this challenge we have developed novel schemes, scaled up to 200K cores.
Our main contributions is the design and implementation of fast solvers for these problems. We also study the performance for the tumor parameter estimation and registration solvers and their algorithmic scalability. In particular, we introduce the following novel algorithms: An adjoint formulation for tumor-growth problems with/without mass-effect; The first parallel 3D Newton-Krylov method for large diffeomorphic image registration; A novel parallel semi-Lagrangian algorithm for solving advection equations in image registration and its parallel implementation on shared and distributed memory architectures; and Accelerated FFT (AccFFT), an open-source parallel FFT library for CPU and GPUs scaled up to 131,000 cores with optimized kernels for computing spectral operators.
The scientific outcomes of this thesis, has appeared in the proceedings of three ACM/IEEE SCxy conferences (two best student paper finalist, and one ACM SRC gold medal), two journal papers, two papers in review, four papers in preparation (coupling, mass effect, segmentation, and multi-species tumor model), and seven conference presentations.Computational Science, Engineering, and Mathematic
Diffeomorphic Metric Mapping of High Angular Resolution Diffusion Imaging based on Riemannian Structure of Orientation Distribution Functions
In this paper, we propose a novel large deformation diffeomorphic
registration algorithm to align high angular resolution diffusion images
(HARDI) characterized by orientation distribution functions (ODFs). Our
proposed algorithm seeks an optimal diffeomorphism of large deformation between
two ODF fields in a spatial volume domain and at the same time, locally
reorients an ODF in a manner such that it remains consistent with the
surrounding anatomical structure. To this end, we first review the Riemannian
manifold of ODFs. We then define the reorientation of an ODF when an affine
transformation is applied and subsequently, define the diffeomorphic group
action to be applied on the ODF based on this reorientation. We incorporate the
Riemannian metric of ODFs for quantifying the similarity of two HARDI images
into a variational problem defined under the large deformation diffeomorphic
metric mapping (LDDMM) framework. We finally derive the gradient of the cost
function in both Riemannian spaces of diffeomorphisms and the ODFs, and present
its numerical implementation. Both synthetic and real brain HARDI data are used
to illustrate the performance of our registration algorithm
A novel variational model for image registration using Gaussian curvature
Image registration is one important task in many image processing
applications. It aims to align two or more images so that useful information
can be extracted through comparison, combination or superposition. This is
achieved by constructing an optimal trans- formation which ensures that the
template image becomes similar to a given reference image. Although many models
exist, designing a model capable of modelling large and smooth deformation
field continues to pose a challenge. This paper proposes a novel variational
model for image registration using the Gaussian curvature as a regulariser. The
model is motivated by the surface restoration work in geometric processing
[Elsey and Esedoglu, Multiscale Model. Simul., (2009), pp. 1549-1573]. An
effective numerical solver is provided for the model using an augmented
Lagrangian method. Numerical experiments can show that the new model
outperforms three competing models based on, respectively, a linear curvature
[Fischer and Modersitzki, J. Math. Imaging Vis., (2003), pp. 81- 85], the mean
curvature [Chumchob, Chen and Brito, Multiscale Model. Simul., (2011), pp.
89-128] and the diffeomorphic demon model [Vercauteren at al., NeuroImage,
(2009), pp. 61-72] in terms of robustness and accuracy.Comment: 23 pages, 5 figures. Key words: Image registration, Non-parametric
image registration, Regularisation, Gaussian curvature, surface mappin
Diffeomorphic density registration
In this book chapter we study the Riemannian Geometry of the density
registration problem: Given two densities (not necessarily probability
densities) defined on a smooth finite dimensional manifold find a
diffeomorphism which transforms one to the other. This problem is motivated by
the medical imaging application of tracking organ motion due to respiration in
Thoracic CT imaging where the fundamental physical property of conservation of
mass naturally leads to modeling CT attenuation as a density. We will study the
intimate link between the Riemannian metrics on the space of diffeomorphisms
and those on the space of densities. We finally develop novel computationally
efficient algorithms and demonstrate there applicability for registering RCCT
thoracic imaging.Comment: 23 pages, 6 Figures, Chapter for a Book on Medical Image Analysi
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