A robust similarity measure for volumetric image registration with outliers

Image registration under challenging realistic conditions is a very important area of research. In this paper, we focus on algorithms that seek to densely align two volumetric images according to a global similarity measure. Despite intensive research in this area, there is still a need for similarity measures that are robust to outliers common to many different types of images. For example, medical image data is often corrupted by intensity inhomogeneities and may contain outliers in the form of pathologies. In this paper we propose a global similarity measure that is robust to both intensity inhomogeneities and outliers without requiring prior knowledge of the type of outliers. We combine the normalised gradients of images with the cosine function and show that it is theoretically robust against a very general class of outliers. Experimentally, we verify the robustness of our measures within two distinct algorithms. Firstly, we embed our similarity measures within a proof-of-concept extension of the Lucas–Kanade algorithm for volumetric data. Finally, we embed our measures within a popular non-rigid alignment framework based on free-form deformations and show it to be robust against both simulated tumours and intensity inhomogeneities

Investigation of Intensity Correction in the Context of Image Registration

An image registration algorithm with intensity correction was developed. A particular goal was to apply intensity correction instead of using multimodal similarity measures. The algorithm utilises common Levenberg-Marquardt optimisation. The author has chosen two dimensional affine and one dimensional B-Spline model as spatial transformation, as well as intensity correction models specific to CT images. They are global non-linear mapping and smooth local affine correction. The algorithm was tested experimentally using a wide class of simulated images and a limited class of medical images. Affine registration works properly even for deformations which exceed typical deformation encountered in medical practice. B-Spline registration works properly for small deformations and requires further development to increase capture range. The idea of separating intensity correction mapping from similarity measure is shown to have advantages. Choosing intensity correction model can make the registration algorithm specific to the image class of interest

A Hybrid Similarity Measure Framework for Multimodal Medical Image Registration

Medical imaging is widely used today to facilitate both disease diagnosis and treatment planning practice, with a key prerequisite being the systematic process of medical image registration (MIR) to align either mono or multimodal images of different anatomical parts of the human body. MIR utilises a similarity measure (SM) to quantify the level of spatial alignment and is particularly demanding due to the presence of inherent modality characteristics like intensity non-uniformities (INU) in magnetic resonance images and large homogeneous non-vascular regions in retinal images. While various intensity and feature-based SMs exist for MIR, mutual information (MI) has become established because of its computational efficiency and ability to register multimodal images. It is however, very sensitive to interpolation artefacts in the presence of INU with noise and can be compromised when overlapping areas are small. Recently MI-based hybrid variants which combine regional features with intensity have emerged, though these incur high dimensionality and large computational overheads. To address these challenges and secure accurate, efficient and robust registration of images containing high INU, noise and large homogeneous regions, this thesis presents a new hybrid SM framework for 2D multimodal rigid MIR. The framework consistently provides superior quantitative and qualitative performance, while offering a uniquely flexible design trade-off between registration accuracy and computational time. It makes three significant technical contributions to the field: i) An expectation maximisation-based principal component analysis with mutual information (EMPCA-MI) framework incorporating neighbourhood feature information; ii) Two innovative enhancements to reduce information redundancy and improve MI computational efficiency; and iii) an adaptive algorithm to select the most significant principal components for feature selection. The thesis findings conclusively confirm the hybrid SM framework offers an accurate and robust 2D registration solution for challenging multimodal medical imaging datasets, while its inherent flexibility means it can also be extended to the 3D registration domain

Non-rigid medical image registration with extended free form deformations: modelling general tissue transitions

Image registration seeks pointwise correspondences between the same or analogous objects in different images. Conventional registration methods generally impose continuity and smoothness throughout the image. However, there are cases in which the deformations may involve discontinuities. In general, the discontinuities can be of different types, depending on the physical properties of the tissue transitions involved and boundary conditions. For instance, in the respiratory motion the lungs slide along the thoracic cage following the tangential direction of their interface. In the normal direction, however, the lungs and the thoracic cage are constrained to be always in contact but they have different material properties producing different compression or expansion rates. In the literature, there is no generic method, which handles different types of discontinuities and considers their directional dependence. The aim of this thesis is to develop a general registration framework that is able to correctly model different types of tissue transitions with a general formalism. This has led to the development of the eXtended Free Form Deformation (XFFD) registration method. XFFD borrows the concept of the interpolation method from the eXtended Finite Element method (XFEM) to incorporate discontinuities by enriching B-spline basis functions, coupled with extra degrees of freedom. XFFD can handle different types of discontinuities and encodes their directional-dependence without any additional constraints. XFFD has been evaluated on digital phantoms, publicly available 3D liver and lung CT images. The experiments show that XFFD improves on previous methods and that it is important to employ the correct model that corresponds to the discontinuity type involved at the tissue transition. The effect of using incorrect models is more evident in the strain, which measures mechanical properties of the tissues

Efficient dense non-rigid registration using the free-form deformation framework

Medical image registration consists of finding spatial correspondences between two images or more. It is a powerful tool which is commonly used in various medical image processing tasks. Even though medical image registration has been an active topic of research for the last two decades, significant challenges in the field remain to be solved. This thesis addresses some of these challenges through extensions to the Free-Form Deformation (FFD) registration framework, which is one of the most widely used and well-established non-rigid registration algorithm. Medical image registration is a computationally expensive task because of the high degrees of freedom of the non-rigid transformations. In this work, the FFD algorithm has been re-factored to enable fast processing, while maintaining the accuracy of the results. In addition, parallel computing paradigms have been employed to provide near real-time image registration capabilities. Further modifications have been performed to improve the registration robustness to artifacts such as tissues non-uniformity. The plausibility of the generated deformation field has been improved through the use of bio-mechanical models based regularization. Additionally, diffeomorphic extensions to the algorithm were also developed. The work presented in this thesis has been extensively validated using brain magnetic resonance imaging of patients diagnosed with dementia or patients undergoing brain resection. It has also been applied to lung X-ray computed tomography and imaging of small animals. Alongside with this thesis an open-source package, NiftyReg, has been developed to release the presented work to the medical imaging community

Adaptive stochastic gradient descent optimisation for image registration.

Abstract We present a stochastic gradient descent optimisation method for image registration with adaptive step size prediction. The method is based on the theoretical work by Plakhov and Cruz (J. Math. Sci. 120(1): [964][965][966][967][968][969][970][971][972][973] 2004). Our main methodological contribution is the derivation of an image-driven mechanism to select proper values for the most important free parameters of the method. The selection mechanism employs general characteristics of the cost functions that commonly occur in intensity-based image registration. Also, the theoretical convergence conditions of the optimisation method are taken into account. The proposed adaptive stochastic gradient descent (ASGD) method is compared to a standard, non-adaptive RobbinsMonro (RM) algorithm. Both ASGD and RM employ a stochastic subsampling technique to accelerate the optimisation process. Registration experiments were performed on 3D CT and MR data of the head, lungs, and prostate, using various similarity measures and transformation models. The results indicate that ASGD is robust to these variations in the registration framework and is less sensitive to the settings of the user-defined parameters than RM. The main disadvantage of RM is the need for a predetermined step size function. The ASGD method provides a solution for that issue

On the usefulness of gradient information in multi-objective deformable image registration using a B-spline-based dual-dynamic transformation model: comparison of three optimization algorithms

The use of gradient information is well-known to be highly useful in single-objective optimization-based image registration methods. However, its usefulness has not yet been investigated for deformable image registration from a multi-objective optimization perspective. To this end, within a previously introduced multi-objective optimization framework, we use a smooth B-spline-based dual-dynamic transformation model that allows us to derive gradient information analytically, while still being able to account for large deformations. Within the multi-objective framework, we previously employed a powerful evolutionary algorithm (EA) that computes and advances multiple outcomes at once, resulting in a set of solutions (a so-called Pareto front) that represents efficient trade-offs between the objectives. With the addition of the B-spline-based transformation model, we studied the usefulness of gradient information in multiobjective deformable image registration using three different optimization algorithms: the (gradient-less) EA, a gradientonly algorithm, and a hybridization of these two. We evaluated the algorithms to register highly deformed images: 2D MRI slices of the breast in prone and supine positions. Results demonstrate that gradient-based multi-objective optimization significantly speeds up optimization in the initial stages of optimization. However, allowing sufficient computational resources, better results could still be obtained with the EA. Ultimately, the hybrid EA found the best overall approximation of the optimal Pareto front, further indicating that adding gradient-based optimization for multiobjective optimization-based deformable image registration can indeed be beneficial

An Augmented Lagrangian Method for Solving a New Variational Model based on Gradients Similarity Measures and High Order Regularization for Multimodality Registration

In this work we propose a variational model for multi-modal image registration. It minimizes a new functional based on using reformulated normalized gradients of the images as the fidelity term and higher-order derivatives as the regularizer. We first present a theoretical analysis of the proposed model. Then, to solve the model numerically, we use an augmented Lagrangian method (ALM) to reformulate it to a few more amenable subproblems (each giving rise to an Euler-Lagrange equation that is discretized by finite difference methods) and solve iteratively the main linear systems by the fast Fourier transform; a multilevel technique is employed to speed up the initialisation and avoid likely local minima of the underlying functional. Finally we show the convergence of the ALM solver and give numerical results of the new approach. Comparisons with some existing methods are presented to illustrate its effectiveness and advantages