396 research outputs found
Recommended from our members
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
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
Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models
Segmentation is a fundamental task for extracting semantically meaningful
regions from an image. The goal of segmentation algorithms is to accurately
assign object labels to each image location. However, image-noise, shortcomings
of algorithms, and image ambiguities cause uncertainty in label assignment.
Estimating the uncertainty in label assignment is important in multiple
application domains, such as segmenting tumors from medical images for
radiation treatment planning. One way to estimate these uncertainties is
through the computation of posteriors of Bayesian models, which is
computationally prohibitive for many practical applications. On the other hand,
most computationally efficient methods fail to estimate label uncertainty. We
therefore propose in this paper the Active Mean Fields (AMF) approach, a
technique based on Bayesian modeling that uses a mean-field approximation to
efficiently compute a segmentation and its corresponding uncertainty. Based on
a variational formulation, the resulting convex model combines any
label-likelihood measure with a prior on the length of the segmentation
boundary. A specific implementation of that model is the Chan-Vese segmentation
model (CV), in which the binary segmentation task is defined by a Gaussian
likelihood and a prior regularizing the length of the segmentation boundary.
Furthermore, the Euler-Lagrange equations derived from the AMF model are
equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image
denoising. Solutions to the AMF model can thus be implemented by directly
utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We
qualitatively assess the approach on synthetic data as well as on real natural
and medical images. For a quantitative evaluation, we apply our approach to the
icgbench dataset
Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling
In this thesis, we focus on the image labeling problem which is the task of performing unique
pixel-wise label decisions to simplify the image while reducing its redundant information. We
build upon a recently introduced geometric approach for data labeling by assignment flows
[
APSS17
] that comprises a smooth dynamical system for data processing on weighted graphs.
Hereby we pursue two lines of research that give new application and theoretically-oriented
insights on the underlying segmentation task.
We demonstrate using the example of Optical Coherence Tomography (OCT), which is the
mostly used non-invasive acquisition method of large volumetric scans of human retinal tis-
sues, how incorporation of constraints on the geometry of statistical manifold results in a novel
purely data driven
geometric
approach for order-constrained segmentation of volumetric data
in any metric space. In particular, making diagnostic analysis for human eye diseases requires
decisive information in form of exact measurement of retinal layer thicknesses that has be done
for each patient separately resulting in an demanding and time consuming task. To ease the
clinical diagnosis we will introduce a fully automated segmentation algorithm that comes up
with a high segmentation accuracy and a high level of built-in-parallelism. As opposed to many
established retinal layer segmentation methods, we use only local information as input without
incorporation of additional global shape priors. Instead, we achieve physiological order of reti-
nal cell layers and membranes including a new formulation of ordered pair of distributions in an
smoothed energy term. This systematically avoids bias pertaining to global shape and is hence
suited for the detection of anatomical changes of retinal tissue structure. To access the perfor-
mance of our approach we compare two different choices of features on a data set of manually
annotated
3
D OCT volumes of healthy human retina and evaluate our method against state of
the art in automatic retinal layer segmentation as well as to manually annotated ground truth
data using different metrics.
We generalize the recent work [
SS21
] on a variational perspective on assignment flows and
introduce a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs.
The G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was
introduced in
J. Math. Imaging & Vision
58(2), 2017. Due to this parameterization, solving the
G-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with re-
spect to a nonconvex potential. We devise an entropy-regularized difference-of-convex-functions
(DC) decomposition of this potential and show that the basic geometric Euler scheme for inte-
grating the assignment flow is equivalent to solving the G-PDE by an established DC program-
ming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit
higher-order information of the vector field that drives the assignment flow, in order to devise a
novel accelerated DC programming scheme. A detailed convergence analysis of both numerical
schemes is provided and illustrated by numerical experiments
Globally Optimal Surfaces By Continuous Maximal Flows
In this paper we consider the problem of computing globally minimal continuous curves and surfaces for image segmentation and 3D reconstruction. This is solved using a maximal flow approach expressed as a PDE model. Previously proposed techniques yield either grid-biased solutions (graph based approaches) or sub-optimal solutions (active contours and surfaces). The proposed algorithm simulates the flow of an ideal fluid with a spatially varying velocity constraint derived from image data. A proof is given that the algorithm gives the globally maximal flow at convergence, along with an implementation scheme. The globally minimal surface may be obtained trivially from its output. The new algorithm is applied to segmentation in 2D and 3D medical images and to 3D reconstruction from a stereo image pair. The results in 2D agree remarkably well with an existing planar minimal contour algorithm and the results in 3D segmentation and reconstruction demonstrate that the new algorithm is free from grid bias
- …