48,640 research outputs found
Finite element surface registration incorporating curvature, volume preservation, and statistical model information
We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models
Finite Element Based Tracking of Deforming Surfaces
We present an approach to robustly track the geometry of an object that
deforms over time from a set of input point clouds captured from a single
viewpoint. The deformations we consider are caused by applying forces to known
locations on the object's surface. Our method combines the use of prior
information on the geometry of the object modeled by a smooth template and the
use of a linear finite element method to predict the deformation. This allows
the accurate reconstruction of both the observed and the unobserved sides of
the object. We present tracking results for noisy low-quality point clouds
acquired by either a stereo camera or a depth camera, and simulations with
point clouds corrupted by different error terms. We show that our method is
also applicable to large non-linear deformations.Comment: additional experiment
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 - or
-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
Medical imaging analysis with artificial neural networks
Given that neural networks have been widely reported in the research community of medical imaging, we provide a focused literature survey on recent neural network developments in computer-aided diagnosis, medical image segmentation and edge detection towards visual content analysis, and medical image registration for its pre-processing and post-processing, with the aims of increasing awareness of how neural networks can be applied to these areas and to provide a foundation for further research and practical development. Representative techniques and algorithms are explained in detail to provide inspiring examples illustrating: (i) how a known neural network with fixed structure and training procedure could be applied to resolve a medical imaging problem; (ii) how medical images could be analysed, processed, and characterised by neural networks; and (iii) how neural networks could be expanded further to resolve problems relevant to medical imaging. In the concluding section, a highlight of comparisons among many neural network applications is included to provide a global view on computational intelligence with neural networks in medical imaging
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