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

A Survey on Deep Learning in Medical Image Registration: New Technologies, Uncertainty, Evaluation Metrics, and Beyond

Over the past decade, deep learning technologies have greatly advanced the field of medical image registration. The initial developments, such as ResNet-based and U-Net-based networks, laid the groundwork for deep learning-driven image registration. Subsequent progress has been made in various aspects of deep learning-based registration, including similarity measures, deformation regularizations, and uncertainty estimation. These advancements have not only enriched the field of deformable image registration but have also facilitated its application in a wide range of tasks, including atlas construction, multi-atlas segmentation, motion estimation, and 2D-3D registration. In this paper, we present a comprehensive overview of the most recent advancements in deep learning-based image registration. We begin with a concise introduction to the core concepts of deep learning-based image registration. Then, we delve into innovative network architectures, loss functions specific to registration, and methods for estimating registration uncertainty. Additionally, this paper explores appropriate evaluation metrics for assessing the performance of deep learning models in registration tasks. Finally, we highlight the practical applications of these novel techniques in medical imaging and discuss the future prospects of deep learning-based image registration

Numerical methods for coupled reconstruction and registration in digital breast tomosynthesis.

Digital Breast Tomosynthesis (DBT) provides an insight into the fine details of normal fibroglandular tissues and abnormal lesions by reconstructing a pseudo-3D image of the breast. In this respect, DBT overcomes a major limitation of conventional X-ray mam- mography by reducing the confounding effects caused by the superposition of breast tissue. In a breast cancer screening or diagnostic context, a radiologist is interested in detecting change, which might be indicative of malignant disease. To help automate this task image registration is required to establish spatial correspondence between time points. Typically, images, such as MRI or CT, are first reconstructed and then registered. This approach can be effective if reconstructing using a complete set of data. However, for ill-posed, limited-angle problems such as DBT, estimating the deformation is com- plicated by the significant artefacts associated with the reconstruction, leading to severe inaccuracies in the registration. This paper presents a mathematical framework, which couples the two tasks and jointly estimates both image intensities and the parameters of a transformation. Under this framework, we compare an iterative method and a simultaneous method, both of which tackle the problem of comparing DBT data by combining reconstruction of a pair of temporal volumes with their registration. We evaluate our methods using various computational digital phantoms, uncom- pressed breast MR images, and in-vivo DBT simulations. Firstly, we compare both iter- ative and simultaneous methods to the conventional, sequential method using an affine transformation model. We show that jointly estimating image intensities and parametric transformations gives superior results with respect to reconstruction fidelity and regis- tration accuracy. Also, we incorporate a non-rigid B-spline transformation model into our simultaneous method. The results demonstrate a visually plausible recovery of the deformation with preservation of the reconstruction fidelity

Computer assisted determination of acetabular cup orientation using 2D-3D image registration

Background: 2D-3D image-based registration methods have been developed to measure acetabular cup orientation after total hip arthroplasty (THA). These methods require registration of both the prosthesis and the CT images to 2D radiographs and compute implant position with respect to a reference. The application of these methods is limited in clinical practice due to two limitations: (1) the requirement of a computer-aided design (CAD) model of the prosthesis, which may be unavailable due to the proprietary concerns of the manufacturer, and (2) the requirement of either multiple radiographs or radiograph-specific calibration, usually unavailable for retrospective studies. In this paper, we propose a new method to address these limitations. Methods: A new formulation for determination of post-operative cup orientation, which couples a radiographic measurement with 2D-3D image matching, was developed. In our formulation, the radiographic measurement can be obtained with known methods so that the challenge lies in the 2D-3D image matching. To solve this problem, a hybrid 2D-3D registration scheme combining a landmark-to-ray 2D-3D alignment with a robust intensity-based 2D-3D registration was used. The hybrid 2D-3D registration scheme allows computing both the post-operative cup orientation with respect to an anatomical reference and the pelvic tilt and rotation with respect to the X-ray imaging table/plate. The method was validated using 2D adult cadaver hips. Results: Using the hybrid 2D-3D registration scheme, our method showed a mean accuracy of 1.0 ± 0.7° (range from 0.1°to2.0°) for inclination and 1.7 ± 1.2° (range from 0.0° to 3.9°) for anteversion, taking the measurements from post-operative CT images as ground truths. Conclusions: Our new solution formulation and the hybrid 2D-3D registration scheme facilitate estimation of post-operative cup orientation and measurement of pelvic tilt and rotatio

Automatic Affine and Elastic Registration Strategies for Multi-dimensional Medical Images

Medical images have been used increasingly for diagnosis, treatment planning, monitoring disease processes, and other medical applications. A large variety of medical imaging modalities exists including CT, X-ray, MRI, Ultrasound, etc. Frequently a group of images need to be compared to one another and/or combined for research or cumulative purposes. In many medical studies, multiple images are acquired from subjects at different times or with different imaging modalities. Misalignment inevitably occurs, causing anatomical and/or functional feature shifts within the images. Computerized image registration (alignment) approaches can offer automatic and accurate image alignments without extensive user involvement and provide tools for visualizing combined images. This dissertation focuses on providing automatic image registration strategies. After a through review of existing image registration techniques, we identified two registration strategies that enhance the current field: (1) an automated rigid body and affine registration using voxel similarity measurements based on a sequential hybrid genetic algorithm, and (2) an automated deformable registration approach based upon a linear elastic finite element formulation. Both methods streamlined the registration process. They are completely automatic and require no user intervention. The proposed registration strategies were evaluated with numerous 2D and 3D MR images with a variety of tissue structures, orientations and dimensions. Multiple registration pathways were provided with guidelines for their applications. The sequential genetic algorithm mimics the pathway of an expert manually doing registration. Experiments demonstrated that the sequential genetic algorithm registration provides high alignment accuracy and is reliable for brain tissues. It avoids local minima/maxima traps of conventional optimization techniques, and does not require any preprocessing such as threshold, smoothing, segmentation, or definition of base points or edges. The elastic model was shown to be highly effective to accurately align areas of interest that are automatically extracted from the images, such as brains. Using a finite element method to get the displacement of each element node by applying a boundary mapping, this method provides an accurate image registration with excellent boundary alignment of each pair of slices and consequently align the entire volume automatically. This dissertation presented numerous volume alignments. Surface geometries were created directly from the aligned segmented images using the Multiple Material Marching Cubes algorithm. Using the proposed registration strategies, multiple subjects were aligned to a standard MRI reference, which is aligned to a segmented reference atlas. Consequently, multiple subjects are aligned to the segmented atlas and a full fMRI analysis is possible

Development and characterization of methodology and technology for the alignment of fMRI time series

This dissertation has developed, implemented and tested a novel computer based system (AUTOALIGN) that incorporates an algorithm for the alignment of functional Magnetic Resonance Image (fMRI) time series. The algorithm assumes the human brain to be a rigid body and computes a head coordinate system on the basis of three reference points that lie on the directions correspondent to two of the eigenvectors of inertia of the volume, at the intersections with the head boundary. The eigenvectors are found weighting the inertia components with the voxel\u27s intensity values assumed as mass. The three reference points are found in the same position, relative to the origin of the head coordinate system, in both test and reference brain images. Intensity correction is performed at sub-voxel accuracy by tri-linear interpolation. A test fMR brain volume in which controlled simulations of rigid-body transformations have been introduced has preliminarily assessed system performance. Further experimentation has been conducted with real fMRI time series. Rigid-body transformations have been retrieved automatically and the values of the motion parameters compared to those obtained by the Statistical Parametric Mapping (SPM99), and the Automatic Image Registration (AIR 3.08). Results indicated that AUTOALIGN offers subvoxel accuracy in correcting both misalignment and intensity among time points in fMR images time series, and also that its performance is comparable to that of SPM99 and AIR3.08