435 research outputs found
A robust multigrid approach for variational image registration models
AbstractVariational registration models are non-rigid and deformable imaging techniques for accurate registration of two images. As with other models for inverse problems using the Tikhonov regularization, they must have a suitably chosen regularization term as well as a data fitting term. One distinct feature of registration models is that their fitting term is always highly nonlinear and this nonlinearity restricts the class of numerical methods that are applicable. This paper first reviews the current state-of-the-art numerical methods for such models and observes that the nonlinear fitting term is mostly ‘avoided’ in developing fast multigrid methods. It then proposes a unified approach for designing fixed point type smoothers for multigrid methods. The diffusion registration model (second-order equations) and a curvature model (fourth-order equations) are used to illustrate our robust methodology. Analysis of the proposed smoothers and comparisons to other methods are given. As expected of a multigrid method, being many orders of magnitude faster than the unilevel gradient descent approach, the proposed numerical approach delivers fast and accurate results for a range of synthetic and real test images
Prostate Biopsy Assistance System with Gland Deformation Estimation for Enhanced Precision
Computer-assisted prostate biopsies became a very active research area during
the last years. Prostate tracking makes it possi- ble to overcome several
drawbacks of the current standard transrectal ultrasound (TRUS) biopsy
procedure, namely the insufficient targeting accuracy which may lead to a
biopsy distribution of poor quality, the very approximate knowledge about the
actual location of the sampled tissues which makes it difficult to implement
focal therapy strategies based on biopsy results, and finally the difficulty to
precisely reach non-ultrasound (US) targets stemming from different modalities,
statistical atlases or previous biopsy series. The prostate tracking systems
presented so far are limited to rigid transformation tracking. However, the
gland can get considerably deformed during the intervention because of US probe
pres- sure and patient movements. We propose to use 3D US combined with
image-based elastic registration to estimate these deformations. A fast elastic
registration algorithm that copes with the frequently occurring US shadows is
presented. A patient cohort study was performed, which yielded a statistically
significant in-vivo accuracy of 0.83+-0.54mm.Comment: This version of the paper integrates a correction concerning the
local similarity measure w.r.t. the proceedings (this typing error could not
be corrected before editing the proceedings
A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution
To overcome the weakness of a total variation based model for image
restoration, various high order (typically second order) regularization models
have been proposed and studied recently. In this paper we analyze and test a
fractional-order derivative based total -order variation model, which
can outperform the currently popular high order regularization models. There
exist several previous works using total -order variations for image
restoration; however first no analysis is done yet and second all tested
formulations, differing from each other, utilize the zero Dirichlet boundary
conditions which are not realistic (while non-zero boundary conditions violate
definitions of fractional-order derivatives). This paper first reviews some
results of fractional-order derivatives and then analyzes the theoretical
properties of the proposed total -order variational model rigorously.
It then develops four algorithms for solving the variational problem, one based
on the variational Split-Bregman idea and three based on direct solution of the
discretise-optimization problem. Numerical experiments show that, in terms of
restoration quality and solution efficiency, the proposed model can produce
highly competitive results, for smooth images, to two established high order
models: the mean curvature and the total generalized variation.Comment: 26 page
Aerial video geo-registration using terrain models from dense and coherent stereo matching
In the context of aerial imagery, one of the first steps toward a coherent processing of the information contained
in multiple images is geo-registration, which consists in assigning geographic 3D coordinates to the pixels of the
image. This enables accurate alignment and geo-positioning of multiple images, detection of moving objects
and fusion of data acquired from multiple sensors.
To solve this problem there are different approaches that
require, in addition to a precise characterization of the camera sensor, high resolution referenced images or terrain
elevation models, which are usually not publicly available or out of date. Building upon the idea of developing
technology that does not need a reference terrain elevation model, we propose a geo-registration technique that
applies variational methods to obtain a dense and coherent surface elevation model that is used to replace the
reference model. The surface elevation model is built by interpolation of scattered 3D points, which are obtained
in a two-step process following a classical stereo pipeline: first, coherent disparity maps between image pairs
of a video sequence are estimated and then image point correspondences are back-projected.
The proposed variational method enforces continuity of the disparity map not only along epipolar lines (as done by previous geo-registration techniques) but also across them, in the full 2D image domain. In the experiments, aerial images from synthetic video sequences have been used to validate the proposed technique
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
Line search multilevel optimization as computational methods for dense optical flow
We evaluate the performance of different optimization techniques developed in the context of optical flowcomputation with different variational models. In particular, based on truncated Newton methods (TN) that have been an effective approach for large-scale unconstrained optimization, we develop the use of efficient multilevel schemes for computing the optical flow. More precisely, we evaluate the performance of a standard unidirectional multilevel algorithm - called multiresolution optimization (MR/OPT), to a bidrectional multilevel algorithm - called full multigrid optimization (FMG/OPT). The FMG/OPT algorithm treats the coarse grid correction as an optimization search direction and eventually scales it using a line search. Experimental results on different image sequences using four models of optical flow computation show that the FMG/OPT algorithm outperforms both the TN and MR/OPT algorithms in terms of the computational work and the quality of the optical flow estimation
Variational optic flow computation in real-time
Variational methods for optic flow computation have the reputation of producing good results at the expense of being too slow for realtime applications. We show that real-time variational computation of optic flow fields is possible when appropriate methods are combined with modern numerical techniques. We consider the CLG method, a recent variational technique that combines the quality of the dense flow fields of the Horn and Schunck approach with the noise robustness of the Lucas-Kanade method. For the linear system of equations resulting from the discretised Euler-Lagrange equations, we present different multigrid schemes in detail. We show that under realistic accuracy requirements they are up to 247 times more efficient than the widely used Gauß-Seidel algorithm. On a 3.06 GHz PC, we have computed 40 dense flow fields of size 200 x 200 pixels within a single second
An Efficient Numerical Method for Mean Curvature-Based Image Registration Model
Mean curvature-based image registration model firstly proposed by Chumchob-Chen-Brito (2011) offered a better regularizer technique for both smooth and nonsmooth deformation fields. However, it is extremely challenging to solve efficiently this model and the existing methods are slow or become efficient only with strong assumptions on the smoothing parameter β. In this paper, we take a different solution approach. Firstly, we discretize the joint energy functional, following an idea of relaxed fixed point is implemented and combine with Gauss-Newton scheme with Armijo's Linear Search for solving the discretized mean curvature model and further to combine with a multilevel method to achieve fast convergence. Numerical experiments not only confirm that our proposed method is efficient and stable, but also it can give more satisfying registration results according to image quality
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