Deformable medical image registration: a survey

Constrained H1-regularization schemes for diffeomorphic image registration

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov regularization ensures well-posedness. Our scheme augments standard smoothness regularization operators based on H1- and H2-seminorms with a constraint on the divergence of the velocity field, which resembles variational formulations for Stokes incompressible flows. In our formulation, we invert for a stationary velocity field and a mass source map. This allows us to explicitly control the compressibility of the deformation map and by that the determinant of the deformation gradient. We also introduce a new regularization scheme that allows us to control shear. We use a globalized, preconditioned, matrix-free, reduced space (Gauss-)Newton-Krylov scheme for numerical optimization. We exploit variable elimination techniques to reduce the number of unknowns of our system; we only iterate on the reduced space of the velocity field. Our current implementation is limited to the two-dimensional case. The numerical experiments demonstrate that we can control the determinant of the deformation gradient without compromising registration quality. This additional control allows us to avoid oversmoothing of the deformation map. We also demonstrate that we can promote or penalize shear whilst controlling the determinant of the deformation gradient.

Brain shift in neuronavigation of brain tumors: A review

PURPOSE

Neuronavigation based on preoperative imaging data is a ubiquitous tool for image guidance in neurosurgery. However, it is rendered unreliable when brain shift invalidates the patient-to-image registration. Many investigators have tried to explain, quantify, and compensate for this phenomenon to allow extended use of neuronavigation systems for the duration of surgery. The purpose of this paper is to present an overview of the work that has been done investigating brain shift.

METHODS

A review of the literature dealing with the explanation, quantification and compensation of brain shift is presented. The review is based on a systematic search using relevant keywords and phrases in PubMed. The review is organized based on a developed taxonomy that classifies brain shift as occurring due to physical, surgical or biological factors.

RESULTS

This paper gives an overview of the work investigating, quantifying, and compensating for brain shift in neuronavigation while describing the successes, setbacks, and additional needs in the field. An analysis of the literature demonstrates a high variability in the methods used to quantify brain shift as well as a wide range in the measured magnitude of the brain shift, depending on the specifics of the intervention. The analysis indicates the need for additional research to be done in quantifying independent effects of brain shift in order for some of the state of the art compensation methods to become useful.

CONCLUSION

This review allows for a thorough understanding of the work investigating brain shift and introduces the needs for future avenues of investigation of the phenomenon.

Optimization of an on-board imaging system for extremely rapid radiation therapy

PURPOSE

Next-generation extremely rapid radiation therapy systems could mitigate the need for motion management, improve patient comfort during the treatment, and increase patient throughput for cost effectiveness. Such systems require an on-board imaging system that is competitively priced, fast, and of sufficiently high quality to allow good registration between the image taken on the day of treatment and the image taken the day of treatment planning. In this study, three different detectors for a custom on-board CT system were investigated to select the best design for integration with an extremely rapid radiation therapy system.

METHODS

Three different CT detectors are proposed: low-resolution (all 4×4 mm pixels), medium-resolution (a combination of 4×4 mm pixels and 2×2 mm pixels), and high-resolution (all 1×1 mm pixels). An in-house program was used to generate projection images of a numerical anthropomorphic phantom and to reconstruct the projections into CT datasets, henceforth called "realistic" images. Scatter was calculated using a separate Monte Carlo simulation, and the model included an antiscatter grid and bowtie filter. Diagnostic-quality images of the phantom were generated to represent the patient scan at the time of treatment planning. Commercial deformable registration software was used to register the diagnostic-quality scan to images produced by the various on-board detector configurations. The deformation fields were compared against a "gold standard" deformation field generated by registering initial and deformed images of the numerical phantoms that were used to make the diagnostic and treatment-day images. Registrations of on-board imaging system data were judged by the amount their deformation fields differed from the corresponding gold standard deformation fields--the smaller the difference, the better the system. To evaluate the registrations, the pointwise distance between gold standard and realistic registration deformation fields was computed.

RESULTS

By most global metrics (e.g., mean, median, and maximum pointwise distance), the high-resolution detector had the best performance but the medium-resolution detector was comparable. For all medium- and high-resolution detector registrations, mean error between the realistic and gold standard deformation fields was less than 4 mm. By pointwise metrics (e.g., tracking a small lesion), the high- and medium-resolution detectors performed similarly. For these detectors, the smallest error between the realistic and gold standard registrations was 0.6 mm and the largest error was 3.6 mm.

CONCLUSIONS

The medium-resolution CT detector was selected as the best for an extremely rapid radiation therapy system. In essentially all test cases, data from this detector produced a significantly better registration than data from the low-resolution detector and a comparable registration to data from the high-resolution detector. The medium-resolution detector provides an appropriate compromise between registration accuracy and system cost.

Feature-based multi-resolution registration of immunostained serial sections

The form and exact function of the blood vessel network in some human organs, like spleen and bone marrow, are still open research questions in medicine. In this paper, we propose a method to register the immunohistological stainings of serial sections of spleen and bone marrow specimens to enable the visualization and visual inspection of blood vessels. As these vary much in caliber, from mesoscopic (millimeter-range) to microscopic (few micrometers, comparable to a single erythrocyte), we need to utilize a multi-resolution approach. Our method is fully automatic; it is based on feature detection and sparse matching. We utilize a rigid alignment and then a non-rigid deformation, iteratively dealing with increasingly smaller features. Our tool pipeline can already deal with series of complete scans at extremely high resolution, up to 620 megapixels. The improvement presented increases the range of represented details up to smallest capillaries. This paper provides details on the multi-resolution non-rigid registration approach we use. Our application is novel in the way the alignment and subsequent deformations are computed (using features, i.e. "sparse"). The deformations are based on all images in the stack ("global"). We also present volume renderings and a 3D reconstruction of the vascular network in human spleen and bone marrow on a level not possible before. Our registration makes easy tracking of even smallest blood vessels possible, thus granting experts a better comprehension. A quantitative evaluation of our method and related state of the art approaches with seven different quality measures shows the efficiency of our method. We also provide z-profiles and enlarged volume renderings from three different registrations for visual inspection.

Phase-aware echocardiogram stabilization using keyframes

This paper presents an echocardiogram stabilization method designed to compensate for unwanted auxilliary motion. Echocardiograms contain both deformable cardiac motion and approximately rigid motion due to a number of factors. The goal of this work is to stabilize the video, while preserving the informative deformable cardiac motion. Our approach incorporates synchronized side information, extracted from electrocardiography (ECG), which provides a proxy for cardiac phase. To avoid the computational expense of pairwise alignment, we propose an efficient strategy for keyframe selection, formulated as a submodular optimization problem. We evaluate our approach quantitatively on synthetic data and demonstrate its benefit as a preprocessing step for two common echocardiogram applications: denoising and left ventricle segmentation. In both cases, preprocessing with our method improved the performance compared to no preprocessing or other alignment approaches.

Diffeomorphic Surface Registration with Atrophy Constraints

Diffeomorphic registration using optimal control on the diffeomorphism group and on shape spaces has become widely used since the development of the large deformation diffeomorphic metric mapping (LDDMM) algorithm. More recently, a series of algorithms involving sub-Riemannian constraints have been introduced in which the velocity fields that control the shapes in the LDDMM framework are constrained in accordance with a specific deformation model. Here, we extend this setting by considering, for the first time, inequality constraints in order to estimate surface deformations that only allow for atrophy, introducing for this purpose an algorithm that uses the augmented Lagrangian method. We prove the existence of solutions of the associated optimal control problem and the consistency of our approximation scheme. These developments are illustrated by numerical experiments on simulated and real data.

Automatic Extraction of Central Tendon of Rectus Femoris (CT-RF) in Ultrasound Images Using a New Intensity-Compensated Free-Form Deformation-Based Tracking Algorithm With Local Shape Refinement

Ultrasonography is an important diagnostic imaging technique for visualization of tendons, which provides useful health diagnostic and fundamental information in neuromuscular studies of human motion systems. Conventional ultrasonic-based tendon studies, however, are highly dependent on subjective experience of operators due to various impairments of ultrasound images. Dynamic changes of muscle and tendon deformation in a sequence can hardly be manually processed. Consequently, there is an urgent need for automatic analysis of tendon behavior. This paper proposes an automatic ultrasonic tendon tracking algorithm to extract the shape deformation of central tendon of rectus femoris (CT-RF) from ultrasonic image sequences. The tracking problem is complicated by the highly deformable tendon, time-varying brightness, and the inconspicuousness of the target. To address this difficult tracking problem, we proposed a new intensity-compensated free-form deformation (IC-FFD)-based tracking algorithm with local shape refinement (LSR). Experimental results and comparison show that the proposed IC-FFD-LSR algorithm outperforms IC-FFD and conventional methods such as MI-FFD in CT-RF tracking.

A survey of medical image registration - under review

A retrospective view on the past two decades of the field of medical image registration is presented, guided by the article "A survey of medical image registration" (Maintz and Viergever, 1998). It shows that the classification of the field introduced in that article is still usable, although some modifications to do justice to advances in the field would be due. The main changes over the last twenty years are the shift from extrinsic to intrinsic registration, the primacy of intensity-based registration, the breakthrough of nonlinear registration, the progress of inter-subject registration, and the availability of generic image registration software packages. Two problems that were called urgent already 20 years ago, are even more urgent nowadays: Validation of registration methods, and translation of results of image registration research to clinical practice. It may be concluded that the field of medical image registration has evolved, but still is in need of further development in various aspects.

Kernel Bundle Diffeomorphic Image Registration Using Stationary Velocity Fields and Wendland Basis Functions

In this paper, we propose a multi-scale, multi-kernel shape, compactly supported kernel bundle framework for stationary velocity field-based image registration (Wendland kernel bundle stationary velocity field, wKB-SVF). We exploit the possibility of directly choosing kernels to construct a reproducing kernel Hilbert space (RKHS) instead of imposing it from a differential operator. The proposed framework allows us to minimize computational cost without sacrificing the theoretical foundations of SVF-based diffeomorphic registration. In order to recover deformations occurring at different scales, we use compactly supported Wendland kernels at multiple scales and orders to parameterize the velocity fields, and the framework allows simultaneous optimization over all scales. The performance of wKB-SVF is extensively compared to the 14 non-rigid registration algorithms presented in a recent comparison paper. On both MGH10 and CUMC12 datasets, the accuracy of wKB-SVF is improved when compared to other registration algorithms. In a disease-specific application for intra-subject registration, atrophy scores estimated using the proposed registration scheme separates the diagnostic groups of Alzheimer's and normal controls better than the state-of-the-art segmentation technique. Experimental results show that wKB-SVF is a robust, flexible registration framework that allows theoretically well-founded and computationally efficient multi-scale representation of deformations and is equally well-suited for both inter- and intra-subject image registration.

Relationship Induced Multi-Template Learning for Diagnosis of Alzheimer's Disease and Mild Cognitive Impairment

As shown in the literature, methods based on multiple templates usually achieve better performance, compared with those using only a single template for processing medical images. However, most existing multi-template based methods simply average or concatenate multiple sets of features extracted from different templates, which potentially ignores important structural information contained in the multi-template data. Accordingly, in this paper, we propose a novel relationship induced multi-template learning method for automatic diagnosis of Alzheimer's disease (AD) and its prodromal stage, i.e., mild cognitive impairment (MCI), by explicitly modeling structural information in the multi-template data. Specifically, we first nonlinearly register each brain's magnetic resonance (MR) image separately onto multiple pre-selected templates, and then extract multiple sets of features for this MR image. Next, we develop a novel feature selection algorithm by introducing two regularization terms to model the relationships among templates and among individual subjects. Using these selected features corresponding to multiple templates, we then construct multiple support vector machine (SVM) classifiers. Finally, an ensemble classification is used to combine outputs of all SVM classifiers, for achieving the final result. We evaluate our proposed method on 459 subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, including 97 AD patients, 128 normal controls (NC), 117 progressive MCI (pMCI) patients, and 117 stable MCI (sMCI) patients. The experimental results demonstrate promising classification performance, compared with several state-of-the-art methods for multi-template based AD/MCI classification.

Soft tissue motion tracking with application to tablet-based incision planning in laser surgery

PURPOSE

Recent research has revealed that incision planning in laser surgery deploying stylus and tablet outperforms micromanipulator control. However, vision-based adaption to dynamic surgical scenes has not been addressed so far. In this study, scene motion compensation for tablet-based planning by means of tissue deformation tracking is discussed.

METHODS

A stereo-based method for motion tracking with piecewise affine deformation modeling is presented. Proposed parametrization relies on the epipolar constraint to enforce left-right consistency in the energy minimization problem. Furthermore, the method implements illumination-invariant tracking and appearance-based occlusion detection. Performance is assessed on laparoscopic and laryngeal in vivo data. In particular, tracking accuracy is measured under various conditions such as occlusions and simulated laser cuttings. Experimental validation is extended to a user study conducted on a tablet-based interface that integrates the tracking for image stabilization.

RESULTS

Tracking accuracy measurement reveals a root-mean-square error of 2.45 mm for the laparoscopic and 0.41 mm for the laryngeal dataset. Results successfully demonstrate stereoscopic tracking under changes in illumination, translation, rotation and scale. In particular, proposed occlusion detection scheme can increase robustness against tracking failure. Moreover, assessed user performance indicates significantly increased path tracing accuracy and usability if proposed tracking is deployed to stabilize the view during free-hand path definition.

CONCLUSION

The presented algorithm successfully extends piecewise affine deformation tracking to stereo vision taking the epipolar constraint into account. Improved surgical performance as demonstrated for laser incision planning highlights the potential of presented method regarding further applications in computer-assisted surgery.

Homographic Patch Feature Transform: A Robustness Registration for Gastroscopic Surgery

Image registration is a key component of computer assistance in image guided surgery, and it is a challenging topic in endoscopic environments. In this study, we present a method for image registration named Homographic Patch Feature Transform (HPFT) to match gastroscopic images. HPFT can be used for tracking lesions and augmenting reality applications during gastroscopy. Furthermore, an overall evaluation scheme is proposed to validate the precision, robustness and uniformity of the registration results, which provides a standard for rejection of false matching pairs from corresponding results. Finally, HPFT is applied for processing in vivo gastroscopic data. The experimental results show that HPFT has stable performance in gastroscopic applications.

Efficient methods for implementation of multi-level nonrigid mass-preserving image registration on GPUs and multi-threaded CPUs

BACKGROUND AND OBJECTIVE

Faster and more accurate methods for registration of images are important for research involved in conducting population-based studies that utilize medical imaging, as well as improvements for use in clinical applications. We present a novel computation- and memory-efficient multi-level method on graphics processing units (GPU) for performing registration of two computed tomography (CT) volumetric lung images.

METHODS

We developed a computation- and memory-efficient Diffeomorphic Multi-level B-Spline Transform Composite (DMTC) method to implement nonrigid mass-preserving registration of two CT lung images on GPU. The framework consists of a hierarchy of B-Spline control grids of increasing resolution. A similarity criterion known as the sum of squared tissue volume difference (SSTVD) was adopted to preserve lung tissue mass. The use of SSTVD consists of the calculation of the tissue volume, the Jacobian, and their derivatives, which makes its implementation on GPU challenging due to memory constraints. The use of the DMTC method enabled reduced computation and memory storage of variables with minimal communication between GPU and Central Processing Unit (CPU) due to ability to pre-compute values. The method was assessed on six healthy human subjects.

RESULTS

Resultant GPU-generated displacement fields were compared against the previously validated CPU counterpart fields, showing good agreement with an average normalized root mean square error (nRMS) of 0.044±0.015. Runtime and performance speedup are compared between single-threaded CPU, multi-threaded CPU, and GPU algorithms. Best performance speedup occurs at the highest resolution in the GPU implementation for the SSTVD cost and cost gradient computations, with a speedup of 112 times that of the single-threaded CPU version and 11 times over the twelve-threaded version when considering average time per iteration using a Nvidia Tesla K20X GPU.

CONCLUSIONS

The proposed GPU-based DMTC method outperforms its multi-threaded CPU version in terms of runtime. Total registration time reduced runtime to 2.9min on the GPU version, compared to 12.8min on twelve-threaded CPU version and 112.5min on a single-threaded CPU. Furthermore, the GPU implementation discussed in this work can be adapted for use of other cost functions that require calculation of the first derivatives.

Temporal mammogram image registration using optimized curvilinear coordinates

Registration of mammograms plays an important role in breast cancer computer-aided diagnosis systems. Radiologists usually compare mammogram images in order to detect abnormalities. The comparison of mammograms requires a registration between them. A temporal mammogram registration method is proposed in this paper. It is based on the curvilinear coordinates, which are utilized to cope both with global and local deformations in the breast area. Temporal mammogram pairs are used to validate the proposed method. After registration, the similarity between the mammograms is maximized, and the distance between manually defined landmarks is decreased. In addition, a thorough comparison with the state-of-the-art mammogram registration methods is performed to show its effectiveness.

Medical image registration using sparse coding of image patches

Image registration is a basic task in medical image processing applications like group analysis and atlas construction. Similarity measure is a critical ingredient of image registration. Intensity distortion of medical images is not considered in most previous similarity measures. Therefore, in the presence of bias field distortions, they do not generate an acceptable registration. In this paper, we propose a sparse based similarity measure for mono-modal images that considers non-stationary intensity and spatially-varying distortions. The main idea behind this measure is that the aligned image is constructed by an analysis dictionary trained using the image patches. For this purpose, we use "Analysis K-SVD" to train the dictionary and find the sparse coefficients. We utilize image patches to construct the analysis dictionary and then we employ the proposed sparse similarity measure to find a non-rigid transformation using free form deformation (FFD). Experimental results show that the proposed approach is able to robustly register 2D and 3D images in both simulated and real cases. The proposed method outperforms other state-of-the-art similarity measures and decreases the transformation error compared to the previous methods. Even in the presence of bias field distortion, the proposed method aligns images without any preprocessing.

Estimating Brain Lesion Volume Change in Multiple Sclerosis by Subtraction of Magnetic Resonance Images

BACKGROUND

Change in lesion volume over time, measured on brain magnetic resonance imaging (MRI) scans, is an important outcome measure for natural history studies and clinical trials in multiple sclerosis (MS).

PURPOSE

To develop and test image analysis methods for quantification of lesion volume change in order to improve reliability.

METHODS

The technique is based on registration and subtraction, and was evaluated in a cohort of 20 MS patients with dual-echo images acquired annually over a period of four years. The study protocol was approved by the local ethics review boards of participating centers, and all subjects gave written informed consent. The repeatability was compared to that obtained by the standard method for obtaining lesion volume change by evaluating the total volume at each time point, and then subtracting the volumes to obtain the difference.

RESULTS

Compared to the standard method, the subtraction method had improved intrarater correlation (0.95 and 0.72 for the subtraction method and the standard method, respectively) and interrater correlation (0.51 and 0.28, respectively). Furthermore, the mean time required to analyze the scans from one patient was 41 minutes for the subtraction method compared to 125 minutes for the standard method.

CONCLUSION

Use of the subtraction algorithm leads to improved reliability and lower operator fatigue in clinical trials and studies of the natural history of MS.

Hierarchical and symmetric infant image registration by robust longitudinal-example-guided correspondence detection

PURPOSE

To investigate anatomical differences across individual subjects, or longitudinal changes in early brain development, it is important to perform accurate image registration. However, due to fast brain development and dynamic tissue appearance changes, it is very difficult to align infant brain images acquired from birth to 1-yr-old.

METHODS

To solve this challenging problem, a novel image registration method is proposed to align two infant brain images, regardless of age at acquisition. The main idea is to utilize the growth trajectories, or spatial-temporal correspondences, learned from a set of longitudinal training images, for guiding the registration of two different time-point images with different image appearances. Specifically, in the training stage, an intrinsic growth trajectory is first estimated for each training subject using the longitudinal images. To register two new infant images with potentially a large age gap, the corresponding images patches between each new image and its respective training images with similar age are identified. Finally, the registration between the two new images can be assisted by the learned growth trajectories from one time point to another time point that have been established in the training stage. To further improve registration accuracy, the proposed method is combined with a hierarchical and symmetric registration framework that can iteratively add new key points in both images to steer the estimation of the deformation between the two infant brain images under registration.

RESULTS

To evaluate image registration accuracy, the proposed method is used to align 24 infant subjects at five different time points (2-week-old, 3-month-old, 6-month-old, 9-month-old, and 12-month-old). Compared to the state-of-the-art methods, the proposed method demonstrated superior registration performance.

CONCLUSIONS

The proposed method addresses the difficulties in the infant brain registration and produces better results compared to existing state-of-the-art registration methods.

Cardiac motion correction based on partial angle reconstructed images in x-ray CT

PURPOSE

Cardiac x-ray CT imaging is still challenging due to heart motion, which cannot be ignored even with the current rotation speed of the equipment. In response, many algorithms have been developed to compensate remaining motion artifacts by estimating the motion using projection data or reconstructed images. In these algorithms, accurate motion estimation is critical to the compensated image quality. In addition, since the scan range is directly related to the radiation dose, it is preferable to minimize the scan range in motion estimation. In this paper, the authors propose a novel motion estimation and compensation algorithm using a sinogram with a rotation angle of less than 360°. The algorithm estimates the motion of the whole heart area using two opposite 3D partial angle reconstructed (PAR) images and compensates the motion in the reconstruction process.

METHODS

A CT system scans the thoracic area including the heart over an angular range of 180° + α + β, where α and β denote the detector fan angle and an additional partial angle, respectively. The obtained cone-beam projection data are converted into cone-parallel geometry via row-wise fan-to-parallel rebinning. Two conjugate 3D PAR images, whose center projection angles are separated by 180°, are then reconstructed with an angular range of β, which is considerably smaller than a short scan range of 180° + α. Although these images include limited view angle artifacts that disturb accurate motion estimation, they have considerably better temporal resolution than a short scan image. Hence, after preprocessing these artifacts, the authors estimate a motion model during a half rotation for a whole field of view via nonrigid registration between the images. Finally, motion-compensated image reconstruction is performed at a target phase by incorporating the estimated motion model. The target phase is selected as that corresponding to a view angle that is orthogonal to the center view angles of two conjugate PAR images. To evaluate the proposed algorithm, digital XCAT and physical dynamic cardiac phantom datasets are used. The XCAT phantom datasets were generated with heart rates of 70 and 100 bpm, respectively, by assuming a system rotation time of 300 ms. A physical dynamic cardiac phantom was scanned using a slowly rotating XCT system so that the effective heart rate will be 70 bpm for a system rotation speed of 300 ms.

RESULTS

In the XCAT phantom experiment, motion-compensated 3D images obtained from the proposed algorithm show coronary arteries with fewer motion artifacts for all phases. Moreover, object boundaries contaminated by motion are well restored. Even though object positions and boundary shapes are still somewhat different from the ground truth in some cases, the authors see that visibilities of coronary arteries are improved noticeably and motion artifacts are reduced considerably. The physical phantom study also shows that the visual quality of motion-compensated images is greatly improved.

CONCLUSIONS

The authors propose a novel PAR image-based cardiac motion estimation and compensation algorithm. The algorithm requires an angular scan range of less than 360°. The excellent performance of the proposed algorithm is illustrated by using digital XCAT and physical dynamic cardiac phantom datasets.

A comparative study of automatic image segmentation algorithms for target tracking in MR-IGRT

On-board magnetic resonance (MR) image guidance during radiation therapy offers the potential for more accurate treatment delivery. To utilize the real-time image information, a crucial prerequisite is the ability to successfully segment and track regions of interest (ROI). The purpose of this work is to evaluate the performance of different segmentation algorithms using motion images (4 frames per second) acquired using a MR image-guided radiotherapy (MR-IGRT) system. Manual con-tours of the kidney, bladder, duodenum, and a liver tumor by an experienced radiation oncologist were used as the ground truth for performance evaluation. Besides the manual segmentation, images were automatically segmented using thresholding, fuzzy k-means (FKM), k-harmonic means (KHM), and reaction-diffusion level set evolution (RD-LSE) algorithms, as well as the tissue tracking algorithm provided by the ViewRay treatment planning and delivery system (VR-TPDS). The performance of the five algorithms was evaluated quantitatively by comparing with the manual segmentation using the Dice coefficient and target registration error (TRE) measured as the distance between the centroid of the manual ROI and the centroid of the automatically segmented ROI. All methods were able to successfully segment the bladder and the kidney, but only FKM, KHM, and VR-TPDS were able to segment the liver tumor and the duodenum. The performance of the thresholding, FKM, KHM, and RD-LSE algorithms degraded as the local image contrast decreased, whereas the performance of the VP-TPDS method was nearly independent of local image contrast due to the reference registration algorithm. For segmenting high-contrast images (i.e., kidney), the thresholding method provided the best speed (< 1 ms) with a satisfying accuracy (Dice = 0.95). When the image contrast was low, the VR-TPDS method had the best automatic contour. Results suggest an image quality determination procedure before segmentation and a combination of different methods for optimal segmentation with the on-board MR-IGRT system.

Deformable medical image registration of pleural cavity for photodynamic therapy by using finite-element based method

When the pleural cavity is opened during the surgery portion of pleural photodynamic therapy (PDT) of malignant mesothelioma, the pleural volume will deform. This impacts the delivered dose when using highly conformal treatment techniques. To track the anatomical changes and contour the lung and chest cavity, an infrared camera-based navigation system (NDI) is used during PDT. In the same patient, a series of computed tomography (CT) scans of the lungs are also acquired before the surgery. The reconstructed three-dimensional contours from both NDI and CTs are imported into COMSOL Multiphysics software, where a finite element-based (FEM) deformable image registration is obtained. The CT contour is registered to the corresponding NDI contour by overlapping the center of masses and aligning their orientations. The NDI contour is considered as the reference contour, and the CT contour is used as the target one, which will be deformed. Deformed Geometry model is applied in COMSOL to obtain a deformed target contour. The distortion of the volume at X, Y and Z is mapped to illustrate the transformation of the target contour. The initial assessment shows that FEM-based image deformable registration can fuse images acquired by different modalities. It provides insights into the deformation of anatomical structures along X, Y and Z-axes. The deformed contour has good matches to the reference contour after the dynamic matching process. The resulting three-dimensional deformation map can be used to obtain the locations of other critical anatomic structures, e.g., heart, during surgery.

Evaluation of Medical Image Registration Techniques Based on Nature and Domain of the Transformation

A lot of research has been done during the past 20 years in the area of medical image registration for obtaining detailed, important, and complementary information from two or more images and aligning them into a single, more informative image. Nature of the transformation and domain of the transformation are two important medical image registration techniques that deal with characters of objects (motions) in images. This article presents a detailed survey of the registration techniques that belong to both categories with detailed elaboration on their features, issues, and challenges. An investigation estimating similarity and dissimilarity measures and performance evaluation is the main objective of this work. This article also provides reference knowledge in a compact form for researchers and clinicians looking for the proper registration technique for a particular application.

Effects of Spatial Resolution on Image Registration

This paper presents a theoretical analysis of the effect of spatial resolution on image registration. Based on the assumption of additive Gaussian noise on the images, the mean and variance of the distribution of the sum of squared differences (SSD) were estimated. Using these estimates, we evaluate a distance between the SSD distributions of aligned images and non-aligned images. The experimental results show that by matching the resolutions of the moving and fixed images one can get a better image registration result. The results agree with our theoretical analysis of SSD, but also suggest that it may be valid for mutual information as well.

MUSE: MUlti-atlas region Segmentation utilizing Ensembles of registration algorithms and parameters, and locally optimal atlas selection

Atlas-based automated anatomical labeling is a fundamental tool in medical image segmentation, as it defines regions of interest for subsequent analysis of structural and functional image data. The extensive investigation of multi-atlas warping and fusion techniques over the past 5 or more years has clearly demonstrated the advantages of consensus-based segmentation. However, the common approach is to use multiple atlases with a single registration method and parameter set, which is not necessarily optimal for every individual scan, anatomical region, and problem/data-type. Different registration criteria and parameter sets yield different solutions, each providing complementary information. Herein, we present a consensus labeling framework that generates a broad ensemble of labeled atlases in target image space via the use of several warping algorithms, regularization parameters, and atlases. The label fusion integrates two complementary sources of information: a local similarity ranking to select locally optimal atlases and a boundary modulation term to refine the segmentation consistently with the target image's intensity profile. The ensemble approach consistently outperforms segmentations using individual warping methods alone, achieving high accuracy on several benchmark datasets. The MUSE methodology has been used for processing thousands of scans from various datasets, producing robust and consistent results. MUSE is publicly available both as a downloadable software package, and as an application that can be run on the CBICA Image Processing Portal (https://ipp.cbica.upenn.edu), a web based platform for remote processing of medical images.

Robust CPD Algorithm for Non-Rigid Point Set Registration Based on Structure Information

Recently, the Coherent Point Drift (CPD) algorithm has become a very popular and efficient method for point set registration. However, this method does not take into consideration the neighborhood structure information of points to find the correspondence and requires a manual assignment of the outlier ratio. Therefore, CPD is not robust for large degrees of degradation. In this paper, an improved method is proposed to overcome the two limitations of CPD. A structure descriptor, such as shape context, is used to perform the auxiliary calculation of the correspondence, and the proportion of each GMM component is adjusted by the similarity. The outlier ratio is formulated in the EM framework so that it can be automatically calculated and optimized iteratively. The experimental results on both synthetic data and real data demonstrate that the proposed method described here is more robust to deformation, noise, occlusion, and outliers than CPD and other state-of-the-art algorithms.

Fast Automatic Step Size Estimation for Gradient Descent Optimization of Image Registration

Fast automatic image registration is an important prerequisite for image-guided clinical procedures. However, due to the large number of voxels in an image and the complexity of registration algorithms, this process is often very slow. Stochastic gradient descent is a powerful method to iteratively solve the registration problem, but relies for convergence on a proper selection of the optimization step size. This selection is difficult to perform manually, since it depends on the input data, similarity measure and transformation model. The Adaptive Stochastic Gradient Descent (ASGD) method is an automatic approach, but it comes at a high computational cost. In this paper, we propose a new computationally efficient method (fast ASGD) to automatically determine the step size for gradient descent methods, by considering the observed distribution of the voxel displacements between iterations. A relation between the step size and the expectation and variance of the observed distribution is derived. While ASGD has quadratic complexity with respect to the transformation parameters, fast ASGD only has linear complexity. Extensive validation has been performed on different datasets with different modalities, inter/intra subjects, different similarity measures and transformation models. For all experiments, we obtained similar accuracy as ASGD. Moreover, the estimation time of fast ASGD is reduced to a very small value, from 40 s to less than 1 s when the number of parameters is 105, almost 40 times faster. Depending on the registration settings, the total registration time is reduced by a factor of 2.5-7 × for the experiments in this paper.

Confidence Estimation for Medical Image Registration Based On Stereo Confidences

In this paper, we propose a novel method to estimate the confidence of a registration that does not require any ground truth, is independent from the registration algorithm and the resulting confidence is correlated with the amount of registration error. We first apply a local search to match patterns between the registered image pairs. Local search induces a cost space per voxel which we explore further to estimate the confidence of the registration similar to confidence estimation algorithms for stereo matching. We test our method on both synthetically generated registration errors and on real registrations with ground truth. The experimental results show that our confidence measure can estimate registration errors and it is correlated with local errors.

Towards Personalized Statistical Deformable Model and Hybrid Point Matching for Robust MR-TRUS Registration

Registration and fusion of magnetic resonance (MR) and 3D transrectal ultrasound (TRUS) images of the prostate gland can provide high-quality guidance for prostate interventions. However, accurate MR-TRUS registration remains a challenging task, due to the great intensity variation between two modalities, the lack of intrinsic fiducials within the prostate, the large gland deformation caused by the TRUS probe insertion, and distinctive biomechanical properties in patients and prostate zones. To address these challenges, a personalized model-to-surface registration approach is proposed in this study. The main contributions of this paper can be threefold. First, a new personalized statistical deformable model (PSDM) is proposed with the finite element analysis and the patient-specific tissue parameters measured from the ultrasound elastography. Second, a hybrid point matching method is developed by introducing the modality independent neighborhood descriptor (MIND) to weight the Euclidean distance between points to establish reliable surface point correspondence. Third, the hybrid point matching is further guided by the PSDM for more physically plausible deformation estimation. Eighteen sets of patient data are included to test the efficacy of the proposed method. The experimental results demonstrate that our approach provides more accurate and robust MR-TRUS registration than state-of-the-art methods do. The averaged target registration error is 1.44 mm, which meets the clinical requirement of 1.9 mm for the accurate tumor volume detection. It can be concluded that the presented method can effectively fuse the heterogeneous image information in the elastography, MR, and TRUS to attain satisfactory image alignment performance.

Registration of coronary arteries in computed tomography angiography images using Hidden Markov Model

Computed tomography angiography (CTA) allows for not only diagnosis of coronary artery disease (CAD) with high spatial resolution but also monitoring the remodeling of vessel walls in the progression of CAD. Alignment of coronary arteries in CTA images acquired at different times (with a 3-7 years interval) is required to visualize and analyze the geometric and structural changes quantitatively. Previous work in image registration primarily focused on large anatomical structures and leads to suboptimal results when applying to registration of coronary arteries. In this paper, we develop a novel method to directly align the straightened coronary arteries in the cylindrical coordinate system guided by the extracted centerlines. By using a Hidden Markov Model (HMM), image intensity information from CTA and geometric information of extracted coronary arteries are combined to align coronary arteries. After registration, the pathological features in two straightened coronary arteries can be directly visualized side by side by synchronizing the corresponding cross-sectional slices and circumferential rotation angles. By evaluating with manually labeled landmarks, the average distance error is 1.6 mm.

Image Registration Based on Autocorrelation of Local Structure

Registration of images in the presence of intra-image signal fluctuations is a challenging task. The definition of an appropriate objective function measuring the similarity between the images is crucial for accurate registration. This paper introduces an objective function that embeds local phase features derived from the monogenic signal in the modality independent neighborhood descriptor (MIND). The image similarity relies on the autocorrelation of local structure (ALOST) which has two important properties: 1) low sensitivity to space-variant intensity distortions (e.g., differences in contrast enhancement in MRI); 2) high distinctiveness for 'salient' image features such as edges. The ALOST method is quantitatively compared to the MIND approach based on three different datasets: thoracic CT images, synthetic and real abdominal MR images. The proposed method outperformed the NMI and MIND similarity measures on these three datasets. The registration of dynamic contrast enhanced and post-contrast MR images of patients with Crohn's disease led to relative contrast enhancement measures with the highest correlation (r=0.56) to the Crohn's disease endoscopic index of severity.

The Utility of Cloud Computing in Analyzing GPU-Accelerated Deformable Image Registration of CT and CBCT Images in Head and Neck Cancer Radiation Therapy

The images generated during radiation oncology treatments provide a valuable resource to conduct analysis for personalized therapy, outcomes prediction, and treatment margin optimization. Deformable image registration (DIR) is an essential tool in analyzing these images. We are enhancing and examining DIR with the contributions of this paper: 1) implementing and investigating a cloud and graphic processing unit (GPU) accelerated DIR solution and 2) assessing the accuracy and flexibility of that solution on planning computed tomography (CT) with cone-beam CT (CBCT). Registering planning CTs and CBCTs aids in monitoring tumors, tracking body changes, and assuring that the treatment is executed as planned. This provides significant information not only on the level of a single patient, but also for an oncology department. However, traditional methods for DIR are usually time-consuming, and manual intervention is sometimes required even for a single registration. In this paper, we present a cloud-based solution in order to increase the data analysis throughput, so that treatment tracking results may be delivered at the time of care. We assess our solution in terms of accuracy and flexibility compared with a commercial tool registering CT with CBCT. The latency of a previously reported mutual information-based DIR algorithm was improved with GPUs for a single registration. This registration consists of rigid registration followed by volume subdivision-based nonrigid registration. In this paper, the throughput of the system was accelerated on the cloud for hundreds of data analysis pairs. Nine clinical cases of head and neck cancer patients were utilized to quantitatively evaluate the accuracy and throughput. Target registration error (TRE) and structural similarity index were utilized as evaluation metrics for registration accuracy. The total computation time consisting of preprocessing the data, running the registration, and analyzing the results was used to evaluate the system throughput. Evaluation showed that the average TRE for GPU-accelerated DIR for each of the nine patients was from 1.99 to 3.39 mm, which is lower than the voxel dimension. The total processing time for 282 pairs on an Amazon Web Services cloud consisting of 20 GPU enabled nodes took less than an hour. Beyond the original registration, the cloud resources also included automatic registration quality checks with minimal impact to timing. Clinical data were utilized in quantitative evaluations, and the results showed that the presented method holds great potential for many high-impact clinical applications in radiation oncology, including adaptive radio therapy, patient outcomes prediction, and treatment margin optimization.

Accurate Interactive Visualization of Large Deformations and Variability in Biomedical Image Ensembles

Large image deformations pose a challenging problem for the visualization and statistical analysis of 3D image ensembles which have a multitude of applications in biology and medicine. Simple linear interpolation in the tangent space of the ensemble introduces artifactual anatomical structures that hamper the application of targeted visual shape analysis techniques. In this work we make use of the theory of stationary velocity fields to facilitate interactive non-linear image interpolation and plausible extrapolation for high quality rendering of large deformations and devise an efficient image warping method on the GPU. This does not only improve quality of existing visualization techniques, but opens up a field of novel interactive methods for shape ensemble analysis. Taking advantage of the efficient non-linear 3D image warping, we showcase four visualizations: 1) browsing on-the-fly computed group mean shapes to learn about shape differences between specific classes, 2) interactive reformation to investigate complex morphologies in a single view, 3) likelihood volumes to gain a concise overview of variability and 4) streamline visualization to show variation in detail, specifically uncovering its component tangential to a reference surface. Evaluation on a real world dataset shows that the presented method outperforms the state-of-the-art in terms of visual quality while retaining interactive frame rates. A case study with a domain expert was performed in which the novel analysis and visualization methods are applied on standard model structures, namely skull and mandible of different rodents, to investigate and compare influence of phylogeny, diet and geography on shape. The visualizations enable for instance to distinguish (population-)normal and pathological morphology, assist in uncovering correlation to extrinsic factors and potentially support assessment of model quality.

A New Approach to Evaluate Drug Treatment Response of Ovarian Cancer Patients Based on Deformable Image Registration

Although Response Evaluation Criteria in Solid Tumors (RECIST) is the current clinical guideline to assess size change of solid tumors after therapeutic treatment, it has a relatively lower association to the clinical outcome of progression free survival (PFS) of the patients. In this paper, we presented a new approach to assess responses of ovarian cancer patients to new chemotherapy drugs in clinical trials. We first developed and applied a multi-resolution B-spline based deformable image registration method to register two sets of computed tomography (CT) image data acquired pre- and post-treatment. The B-spline difference maps generated from the co-registered CT images highlight the regions related to the volumetric growth or shrinkage of the metastatic tumors, and density changes related to variation of necrosis inside the solid tumors. Using a testing dataset involving 19 ovarian cancer patients, we compared patients' response to the treatment using the new image registration method and RECIST guideline. The results demonstrated that using the image registration method yielded higher association with the six-month PFS outcomes of the patients than using RECIST. The image registration results also provided a solid foundation of developing new computerized quantitative image feature analysis schemes in the future studies.

Learning intervention-induced deformations for non-rigid MR-CT registration and electrode localization in epilepsy patients

This paper describes a framework for learning a statistical model of non-rigid deformations induced by interventional procedures. We make use of this learned model to perform constrained non-rigid registration of pre-procedural and post-procedural imaging. We demonstrate results applying this framework to non-rigidly register post-surgical computed tomography (CT) brain images to pre-surgical magnetic resonance images (MRIs) of epilepsy patients who had intra-cranial electroencephalography electrodes surgically implanted. Deformations caused by this surgical procedure, imaging artifacts caused by the electrodes, and the use of multi-modal imaging data make non-rigid registration challenging. Our results show that the use of our proposed framework to constrain the non-rigid registration process results in significantly improved and more robust registration performance compared to using standard rigid and non-rigid registration methods.

Topology preserving non-rigid image registration using time-varying elasticity model for MRI brain volumes

In this paper, we present a new non-rigid image registration method that imposes a topology preservation constraint on the deformation. We propose to incorporate the time varying elasticity model into the deformable image matching procedure and constrain the Jacobian determinant of the transformation over the entire image domain. The motion of elastic bodies is governed by a hyperbolic partial differential equation, generally termed as elastodynamics wave equation, which we propose to use as a deformation model. We carried out clinical image registration experiments on 3D magnetic resonance brain scans from IBSR database. The results of the proposed registration approach in terms of Kappa index and relative overlap computed over the subcortical structures were compared against the existing topology preserving non-rigid image registration methods and non topology preserving variant of our proposed registration scheme. The Jacobian determinant maps obtained with our proposed registration method were qualitatively and quantitatively analyzed. The results demonstrated that the proposed scheme provides good registration accuracy with smooth transformations, thereby guaranteeing the preservation of topology.

RISM: Single-Modal Image Registration via Rank-Induced Similarity Measure

Similarity measure is an important block in image registration. Most traditional intensity-based similarity measures (e.g., sum-of-squared-difference, correlation coefficient, and mutual information) assume a stationary image and pixel-by-pixel independence. These similarity measures ignore the correlation between pixel intensities; hence, perfect image registration cannot be achieved, especially in the presence of spatially varying intensity distortions. Here, we assume that spatially varying intensity distortion (such as bias field) is a low-rank matrix. Based on this assumption, we formulate the image registration problem as a nonlinear and low-rank matrix decomposition (NLLRMD). Therefore, image registration and correction of spatially varying intensity distortion are simultaneously achieved. We illustrate the uniqueness of NLLRMD, and therefore, we propose the rank of difference image as a robust similarity in the presence of spatially varying intensity distortion. Finally, by incorporating the Gaussian noise, we introduce rank-induced similarity measure based on the singular values of the difference image. This measure produces clinically acceptable registration results on both simulated and real-world problems examined in this paper, and outperforms other state-of-the-art measures such as the residual complexity approach.

Statistical Biomechanical Surface Registration: Application to MR-TRUS Fusion for Prostate Interventions

A common challenge when performing surface-based registration of images is ensuring that the surfaces accurately represent consistent anatomical boundaries. Image segmentation may be difficult in some regions due to either poor contrast, low slice resolution, or tissue ambiguities. To address this, we present a novel non-rigid surface registration method designed to register two partial surfaces, capable of ignoring regions where the anatomical boundary is unclear. Our probabilistic approach incorporates prior geometric information in the form of a statistical shape model (SSM), and physical knowledge in the form of a finite element model (FEM). We validate results in the context of prostate interventions by registering pre-operative magnetic resonance imaging (MRI) to 3D transrectal ultrasound (TRUS). We show that both the geometric and physical priors significantly decrease net target registration error (TRE), leading to TREs of 2.35 ± 0.81 mm and 2.81 ± 0.66 mm when applied to full and partial surfaces, respectively. We investigate robustness in response to errors in segmentation, varying levels of missing data, and adjusting the tunable parameters. Results demonstrate that the proposed surface registration method is an efficient, robust, and effective solution for fusing data from multiple modalities.

Brain extraction in pediatric ADC maps, toward characterizing neuro-development in multi-platform and multi-institution clinical images

Apparent Diffusion Coefficient (ADC) maps can be used to characterize myelination and to detect abnormalities in the developing brain. However, given the normal variation in regional ADC with myelination, detection of abnormalities is difficult when based on visual assessment. Quantitative and automated analysis of pediatric ADC maps is thus desired but requires accurate brain extraction as the first step. Currently, most existing brain extraction methods are optimized for structural T1-weighted MR images of fully myelinated brains. Due to differences in age and image contrast, these approaches do not translate well to pediatric ADC maps. To address this problem, we present a multi-atlas brain extraction framework that has 1) specificity: designed and optimized specifically for pediatric ADC maps; 2) generality: applicable to multi-platform and multi-institution data, and to subjects at various neuro-developmental stages across the first 6 years of life; 3) accuracy: highly accurate compared to expert annotations; and 4) consistency: consistently accurate regardless of sources of data and ages of subjects. We show how we achieve these goals, via optimizing major components in a multi-atlas brain extraction framework, and via developing and evaluating new criteria for its atlas ranking component. Moreover, we demonstrate that these goals can be achieved with a fixed set of atlases and a fixed set of parameters, which opens doors for our optimized framework to be used in large-scale and multi-institution neuro-developmental and clinical studies. In a pilot study, we use this framework in a dataset containing scanner-generated ADC maps from 308 pediatric patients collected during the course of routine clinical care. Our framework leads to successful quantifications of the changes in whole-brain volumes and mean ADC values across the first 6 years of life.

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

Optimal mass transport for shape matching and comparison

Surface based 3D shape analysis plays a fundamental role in computer vision and medical imaging. This work proposes to use optimal mass transport map for shape matching and comparison, focusing on two important applications including surface registration and shape space. The computation of the optimal mass transport map is based on Monge-Brenier theory, in comparison to the conventional method based on Monge-Kantorovich theory, this method significantly improves the efficiency by reducing computational complexity from O(n(2)) to O(n) . For surface registration problem, one commonly used approach is to use conformal map to convert the shapes into some canonical space. Although conformal mappings have small angle distortions, they may introduce large area distortions which are likely to cause numerical instability thus resulting failures of shape analysis. This work proposes to compose the conformal map with the optimal mass transport map to get the unique area-preserving map, which is intrinsic to the Riemannian metric, unique, and diffeomorphic. For shape space study, this work introduces a novel Riemannian framework, Conformal Wasserstein Shape Space, by combing conformal geometry and optimal mass transport theory. In our work, all metric surfaces with the disk topology are mapped to the unit planar disk by a conformal mapping, which pushes the area element on the surface to a probability measure on the disk. The optimal mass transport provides a map from the shape space of all topological disks with metrics to the Wasserstein space of the disk and the pullback Wasserstein metric equips the shape space with a Riemannian metric. We validate our work by numerous experiments and comparisons with prior approaches and the experimental results demonstrate the efficiency and efficacy of our proposed approach.

SIRF: Simultaneous Satellite Image Registration and Fusion in a Unified Framework

In this paper, we propose a novel method for image fusion with a high-resolution panchromatic image and a low-resolution multispectral (Ms) image at the same geographical location. The fusion is formulated as a convex optimization problem which minimizes a linear combination of a least-squares fitting term and a dynamic gradient sparsity regularizer. The former is to preserve accurate spectral information of the Ms image, while the latter is to keep sharp edges of the high-resolution panchromatic image. We further propose to simultaneously register the two images during the fusing process, which is naturally achieved by virtue of the dynamic gradient sparsity property. An efficient algorithm is then devised to solve the optimization problem, accomplishing a linear computational complexity in the size of the output image in each iteration. We compare our method against six state-of-the-art image fusion methods on Ms image data sets from four satellites. Extensive experimental results demonstrate that the proposed method substantially outperforms the others in terms of both spatial and spectral qualities. We also show that our method can provide high-quality products from coarsely registered real-world IKONOS data sets. Finally, a MATLAB implementation is provided to facilitate future research.