Medical Image Registration Problem Research Articles

A Hunger Games Search algorithm with opposition-based learning for solving multimodal medical image registration

Multimodal medical image registration involves multiple pieces of medical equipment collecting complementary information on the same content, resulting in information fusion. Beyond its theoretical significance, it has practical applications in areas such as disease diagnosis, patient follow-up, surgical navigation, and radiology. Determining the optimal geometric-space transformation parameters is a major challenge in this field. To address this, we propose the opposition-based Hunger Games Search (OHGS) algorithm, an improved version of the Hunger Games Search (HGS) algorithm. The OHGS algorithm aims to find the optimal translation, scaling, and shearing parameters that result in the highest similarity value between the images being registered. By incorporating opposition-based learning (OBL) and dynamically adjusting mutation criteria, the OHGS algorithm has improved exploration capabilities and the ability to escape local optima. In this study, OHGS was compared with 9 other algorithms developed in recent years on 23 well-known benchmark functions and 10 single-objective optimization functions from IEEE CEC2020. Furthermore, to achieve better registration accuracy and optimal alignment of the geometric space in multimodal medical images, OHGS and 8 other algorithms were tested using RIRE and BraTS datasets, optimizing the two similarity measures of Normalized Mutual Information (NMI) and Structural Similarity Index Measure (SSIM). The results showed that OHGS significantly improved performance on benchmark functions and multimodal medical image registration problems, thereby expanding the application range of the HGS algorithm.

United equilibrium optimizer for solving multimodal image registration

This study presents an optimization algorithm, called united equilibrium optimizer (UEO), which is modified from the equilibrium optimizer (EO). We improved the search structure of the EO and adjusted it using dynamic parameters. These improvements increase the potential of UEO in both exploration and exploitation, which makes UEO perform better in local minima avoidance and fast convergence. In this study, the UEO and other 11 algorithms were benchmarked with 30 unimodal, multimodal, and composition functions, as well as in medical image registration problems. In medical image registration problems, UEO is compared with the other three algorithms that have been successfully applied to medical image registration. The UEO has been tested for benchmark datasets, including three types of different modality images, from up to 16 patients, resulting in 41 multimodal registration scenarios. All the results demonstrated that UEO outperforms other algorithms in most cases, either in optimization tests or in practical problems. The source code of the UEO is publicly available at https://github.com/PengGui-N/United-Equilibrium-Optimizer.

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20× speedup for a two dimensional, real world multi-subject medical image registration problem.

A Tutorial on Combining Nonlinear Optimization with CUDA

Nonlinear optimization is a key component of many image registration algorithms. Improving registration speed is almost always desirable. One way to do this is to accelerate the optimization cost function using a parallel implementation. The purpose of this document is to provide a tutorial on how to combine the CUDA GPU computing framework with standard nonlinear optimization libraries (VNL) using CMake. The provided code can be used as a starting template for programmers looking for a relatively painless introduction to CUDA-accelerated medical image registration and other nonlinear optimization problems.

A Methodology of Three-Dimensional Medical Image Registration Based on Conformal Geometric Invariant

A three-dimensional multimodality medical image registration method using geometric invariant based on conformal geometric algebra (CGA) theory is put forward for responding to challenges resulting from many free degrees and computational burdens with 3D medical image registration problems. The mathematical model and calculation method of dual-vector projection invariant are established using the distribution characteristics of point cloud data and the point-to-plane distance-based measurement in CGA space. The translation operator and geometric rotation operator during registration operation are built in Clifford algebra (CA) space. The conformal geometrical algebra is used to realize the registration of 3D CT/MR-PD medical image data based on the dual vector geometric invariant. The registration experiment results indicate that the methodology proposed in this paper is of stronger commonality, less computation burden, shorter time consumption, and intuitive geometric meaning. Both subjective evaluation and objective indicators show that the methodology proposed here is of high registration accuracy and suitable for 3D medical image registration.

Non-rigid image registration of brain magnetic resonance images using graph-cuts

We present a graph-cuts based method for non-rigid medical image registration on brain magnetic resonance images. In this paper, the non-rigid medical image registration problem is reformulated as a discrete labeling problem. Based on a voxel-to-voxel intensity similarity measure, each voxel in the source image is assigned a displacement label, which represents a displacement vector indicating which position in the floating image it is spatially corresponding to. In the proposed method, a smoothness constraint based on the first derivative is used to penalize sharp changes in the adjacent displacement labels across voxels. The image registration problem is therefore modeled by two energy terms based on intensity similarity and smoothness of the displacement field. These energy terms are submodular and can be optimized by using the graph-cuts method via α‐expansions, which is a powerful combinatorial optimization tool and capable of yielding either a global minimum or a local minimum in a strong sense. Using the realistic brain phantoms obtained from the Simulated Brain Database, we compare the registration results of the proposed method with two state-of-the-art medical image registration approaches: free-form deformation based method and demons method. In addition, the registration results are also compared with that of the linear programming based image registration method. It is found that the proposed method is more robust against different challenging non-rigid registration cases with consistently higher registration accuracy than those three methods, and gives realistic recovered deformation fields.

GRASP and path relinking hybridizations for the point matching-based image registration problem

In the last decade, image registration has proven to be a very active research area when tackling computer vision problems, especially in medical applications. In general, image registration methods aim to find a transformation between two images taken under different conditions. Point matching is an image registration approach based on searching for the right pairing of points between the two images, which involves a combinatorial optimization problem. From this matching, the registration transformation can be inferred by means of numerical methods. In this paper, we tackle the medical image registration problem by means of a recent hybrid metaheuristic composed of two well-known optimization methods: GRASP and path relinking. Several designs based on this new hybrid approach have been tested. Our experimentation with real-world problems shows the combination of GRASP and evolutionary path relinking performs well when compared to previous state-of-the-art image registration approaches adopting both the point matching and transformation parameter approaches.

Use of Information Discrepancy Measure to Register Medical Images

Function of Degree of Disagreement (FDOD), a new measure of information discrepancy, quantifies the discrepancy of multiple sequences. This function has some peculiar mathematical properties, such as symmetry, boundedness and monotonicity. In this contribution, we first introduce the FDOD function to solve the three-dimensional (3-D) medical image registration problem. Numerical experiments illustrate that the new registration method based on the FDOD function can obtain subvoxel registration accuracy, and it is a competitive method with the mutual information based method.

Intensity inhomogeneity compensation and segmentation of MR brain images using hybrid c-means clustering models

Medical image segmentation and registration problems based on magnetic resonance imaging are frequently disturbed by the intensity inhomogeneity or intensity non-uniformity (INU) of the observed images. Most compensation techniques have serious difficulties at high amplitudes of INU. This study proposes a multiple stage hybrid c-means clustering approach to the estimation and compensation of INU, by modeling it as a slowly varying additive or multiplicative noise. The slowly varying behavior of the estimated inhomogeneity field is assured by a context sensitive smoothing filter based on a morphological criterion. The qualitative and quantitative evaluation using 2-D synthetic phantoms and real T1-weighted MR images place the proposed methodology among the most accurate segmentation techniques in the presence of high-magnitude inhomogeneity.

Elastix: A Toolbox for Intensity-Based Medical Image Registration

Medical image registration is an important task in medical image processing. It refers to the process of aligning data sets, possibly from different modalities (e.g., magnetic resonance and computed tomography), different time points (e.g., follow-up scans), and/or different subjects (in case of population studies). A large number of methods for image registration are described in the literature. Unfortunately, there is not one method that works for all applications. We have therefore developed elastix, a publicly available computer program for intensity-based medical image registration. The software consists of a collection of algorithms that are commonly used to solve medical image registration problems. The modular design of elastix allows the user to quickly configure, test, and compare different registration methods for a specific application. The command-line interface enables automated processing of large numbers of data sets, by means of scripting. The usage of elastix for comparing different registration methods is illustrated with three example experiments, in which individual components of the registration method are varied.

A Statistical Model for Point-Based Target Registration Error With Anisotropic Fiducial Localizer Error

Error models associated with point-based medical image registration problems were first introduced in the late 1990s. The concepts of fiducial localizer error, fiducial registration error, and target registration error are commonly used in the literature. The model for estimating the target registration error at a position r in a coordinate frame defined by a set of fiducial markers rigidly fixed relative to one another is ubiquitous in the medical imaging literature. The model has also been extended to simulate the target registration error at the point of interest in optically tracked tools. However, the model is limited to describing the error in situations where the fiducial localizer error is assumed to have an isotropic normal distribution in R3. In this work, the model is generalized to include a fiducial localizer error that has an anisotropic normal distribution. Similar to the previous models, the root mean square statistic rms tre is provided along with an extension that provides the covariance Sigma tre. The new model is verified using a Monte Carlo simulation and a set of statistical hypothesis tests. Finally, the differences between the two assumptions, isotropic and anisotropic, are discussed within the context of their use in 1) optical tool tracking simulation and 2) image registration.

A New Derivative-Free Algorithm for the Medical Image Registration Problem

The medical image registration problem can be formulated as a nonlinear programming problem. To identify appropriate algorithms to solve it, it is critical to analyze the properties of the problem. In this paper, we consider the image registration problem based on maximization of mutual information when the partial volume (PV) interpolation is used to update the joint histogram. We identify pathological cases which may happen in practice, and which may lead to discontinuous instances of the objective function. We show that the objective function is not differentiable and that the set of nondifferentiability is of null measure. Then, we propose a derivative-free algorithm specially designed for this application. Derivative-free optimization involves all the methods used to minimize an objective function when its derivatives are not available and when the function is expensive. We present here, a trust-region algorithm based on radial basis functions instead of the classical second-order polynomials. Actually, our surrogate of the objective function is a mixed radial and polynomial model. On the instances of the medical image registration problem, our method surpasses all the tested state-of-the-art derivative-free algorithms.

A NEW DERIVATIVE-FREE ALGORITHM FOR THE MEDICAL IMAGE REGISTRATION PROBLEM

The medical image registration problem can be formulated as a nonlinear programming problem. To identify appropriate algorithms to solve it, it is critical to analyze the properties of the problem. In this paper, we consider the image registration problem based on maximization of mutual information when the partial volume (PV) interpolation is used to update the joint histogram. We identify pathological cases which may happen in practice, and which may lead to discontinuous instances of the objective function. We show that the objective function is not differentiable and that the set of non-differentiability is of null measure. Then, we propose a derivative-free algorithm specially designed for this application. Derivative-free optimization involves all the methods used to minimize an objective function when its derivatives are not available and when the function is expensive. We present here, a trust-region algorithm based on radial basis functions instead of the classical second-order polynomials. Actually, our surrogate of the objective function is a mixed radial and polynomial model. On the instances of the medical image registration problem, our method surpasses all the tested state-of-the-art derivative-free algorithms.

Multiscale Image Registration

A multiscale image registration technique is presented for the registration of medical images that contain significant levels of noise. An overview of the medical image registration problem is presented, and various registration techniques are discussed. Experiments using mean squares, normalized correlation, and mutual information optimal linear registration are presented that determine the noise levels at which registration using these techniques fails. Further experiments in which classical denoising algorithms are applied prior to registration are presented, and it is shown that registration fails in this case for significantly high levels of noise, as well. The hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese [20] is presented, and accurate registration of noisy images is achieved by obtaining a hierarchical multiscale decomposition of the images and registering the resulting components. This approach enables successful registration of images that contain noise levels well beyond the level at which ordinary optimal linear registration fails. Image registration experiments demonstrate the accuracy and efficiency of the multiscale registration technique, and for all noise levels, the multiscale technique is as accurate as or more accurate than ordinary registration techniques.