Variational image registration by a total fractional-order variation model

In this paper, a new framework of nonlocal deformation in non-rigid image registration is presented. It is well known that many non-rigid image registration techniques may lead to unsteady deformation (e.g. not one to one) if the dissimilarity between the reference and template images is too large. We present a novel variational framework of the total fractional-order variation to derive the underlying fractional Euler-Lagrange equations and a numerical implementation combining the semi-implicit update and conjugate gradients (CG) solution to solve the nonlinear systems. Numerical experiments show that the new registration not only produces accurate and smooth solutions but also allows for a large rigid alignment, the evaluations of the new model demonstrate substantial improvements in accuracy and robustness over the conventional image registration approaches

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

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

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

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

Efficient Variational Approach to Multimodal Registration of Anatomical and Functional Intra-Patient Tumorous Brain Data

This paper addresses the functional localization of intra-patient images of the brain. Functional images of the brain (fMRI and PET) provide information about brain function and metabolism whereas anatomical images (MRI and CT) supply the localization of structures with high spatial resolution. The goal is to find the geometric correspondence between functional and anatomical images in order to complement and fuse the information provided by each imaging modality. The proposed approach is based on a variational formulation of the image registration problem in the frequency domain. It has been implemented as a C/C++ library which is invoked from a GUI. This interface is routinely used in the clinical setting by physicians for research purposes (Inscanner, Alicante, Spain), and may be used as well for diagnosis and surgical planning. The registration of anatomic and functional intra-patient images of the brain makes it possible to obtain a geometric correspondence which allows for the localization of the functional processes that occur in the brain. Through 18 clinical experiments, it has been demonstrated how the proposed approach outperforms popular state-of-the-art registration methods in terms of efficiency, information theory-based measures (such as mutual information) and actual registration error (distance in space of corresponding landmarks)Legaz-Aparicio, A.; Verdú-Monedero, R.; Larrey-Ruiz, J.; Morales-Sánchez, J.; López-Mir, F.; Naranjo Ornedo, V.; Bernabéu, Á. (2017). Efficient Variational Approach to Multimodal Registration of Anatomical and Functional Intra-Patient Tumorous Brain Data. International Journal of Neural Systems. 27(6):1750014-1-1750014-11. doi:10.1142/S0129065717500149S1750014-11750014-1127

Interactive Medical Image Registration With Multigrid Methods and Bounded Biharmonic Functions

Interactive image registration is important in some medical applications since automatic image registration is often slow and sometimes error-prone. We consider interactive registration methods that incorporate user-specified local transforms around control handles. The deformation between handles is interpolated by some smooth functions, minimizing some variational energies. Besides smoothness, we expect the impact of a control handle to be local. Therefore we choose bounded biharmonic weight functions to blend local transforms, a cutting-edge technique in computer graphics. However, medical images are usually huge, and this technique takes a lot of time that makes itself impracticable for interactive image registration. To expedite this process, we use a multigrid active set method to solve bounded biharmonic functions (BBF). The multigrid approach is for two scenarios, refining the active set from coarse to fine resolutions, and solving the linear systems constrained by working active sets. We\u27ve implemented both weighted Jacobi method and successive over-relaxation (SOR) in the multigrid solver. Since the problem has box constraints, we cannot directly use regular updates in Jacobi and SOR methods. Instead, we choose a descent step size and clamp the update to satisfy the box constraints. We explore the ways to choose step sizes and discuss their relation to the spectral radii of the iteration matrices. The relaxation factors, which are closely related to step sizes, are estimated by analyzing the eigenvalues of the bilaplacian matrices. We give a proof about the termination of our algorithm and provide some theoretical error bounds. Another minor problem we address is to register big images on GPU with limited memory. We\u27ve implemented an image registration algorithm with virtual image slices on GPU. An image slice is treated similarly to a page in virtual memory. We execute a wavefront of subtasks together to reduce the number of data transfers. Our main contribution is a fast multigrid method for interactive medical image registration that uses bounded biharmonic functions to blend local transforms. We report a novel multigrid approach to refine active set quickly and use clamped updates based on weighted Jacobi and SOR. This multigrid method can be used to efficiently solve other quadratic programs that have active sets distributed over continuous regions

Variational Image Segmentation with Constraints

The research of Huizhu Pan addresses the problem of image segmentation with constraints though designing and solving various variational models. A novel constraint term is designed for the use of landmarks in image segmentation. Two region-based segmentation models were proposed where the segmentation contour passes through landmark points. A more stable and memory efficient solution to the self-repelling snakes model, a variational model with the topology preservation constraint, was also designed