Diffeomorphic Image Research Articles

New SPM8-based MRAC method for simultaneous PET/MR brain images: comparison with state-of-the-art non-rigid registration methods

We describe a new MR-based attenuation correction (MRAC) method for neurological studies performed using integrated PET/MR scanners. The method, combining the advantages of image segmentation and atlas-based approaches to generate a high-resolution template, is based on the widely available SPM8 software and provides robust and accurate linear attenuation coefficients (LACs) for head while requiring minimal user interaction. Atlas generation: 3T MR and CT images from 15 glioblastoma subjects were used to generate the high-resolution atlas. MR images were segmented into 6 tissue classes: GM, WM, CSF, soft tissue, bone and air)[1]. Tissue classes were then coregistered using an iterative diffeomorphic image registration algorithm [2] to form the template. Atlas validation: The template was validated on 16 subjects. SyN [3] and IRTK [4], considered state-of-the-art for non-rigid image registration[5], were used for comparison. Final attenuation maps were created from the warped CT atlas following [6]. PET images were then reconstructed using the proposed methods as well as the manufacturer’s built-in method (dual-echo Dixon-VIBE sequence) [7] and compared to the gold standard CT-based attenuation correction (CTAC). The qualitative and quantitative analysis of the attenuation maps revealed that the SPM8-based method produces very robust results (Figure ​(Figure1).1). In terms of the PET data quantification, we observed improvements of > 70% compared to the VIBE-based method (Table ​(Table11 and Figure ​Figure2).2). When compared to SyN-based image registration, the SPM8 approach showed improved global results on the brain area (Figures ​(Figures11 and ​and22). Figure 1 Comparison of LACs from a validation subject for our proposed method (A), the SyN method (B) and the manufacturer’s built-in Dixon method (C) to the gold standard CTAC (D). Image differences with respect to the gold standard CTAC of our method ... Table 1 Summary of voxel- and ROI-based results between our method (atlas) and the current manufacturer’s method (Dixon) Figure 2 PET images from a validation subject reconstructed with our proposed method (A), with the SyN method (B) and with the manufacturer’s built-in Dixon method (C), compared with the gold standard CTAC (D). Relative changes (in % with respect to gold ... We presented a new MRAC technique for brain images acquired on simultaneous PET/MR scanners. The new approach relies on segmentation- and atlas-based features to provide robust and more accurate LACs than using state-of-art non-rigid image registration while avoiding sophisticated user input or interaction.

Evaluating nonlinear coregistration of BOLD EPI and T1 images

[1] Hutton et al., 2002. Image Distortion Correction in fMRI: A Quantitative Evaluation. NeuroImage, 16:217–240. [2] Jezzard & Balaban, 1995. Correction for geometric distortion in echo planar images from B0 field variations. Magn Reson Med 34:65-73. [3] Andersson et al., 2003. How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging. NeuroImage, 20:870–88. [4] Kybic et al., 2000. Unwarping of unidirectionally distorted EPI images. IEEE Trans Med Imag , 19:80–93. [5] Studholme et al., 2000. Accurate alignment of functional EPI data to anatomical MRI using a physics-based distortion model. IEEE Trans Med Imag , 19:1115–27. [6] Gholipour et al., 2008. Cross-Validation of Deformable Registration With Field Maps, IEEE J Sel Top Sign. , 2:854–869. [7] Avants et al. , 2008. Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Med Imag Anal, 12:26–41. [8] Gorgolewski et al., 2011. Nipype: a flexible , lightweight and extensible neuroimaging data processing framework in Python. Front Neuroinform, 5:13. [9] Kahnt et al., 2012. Connectivity-based parcellation of the human orbitofrontal cortex. J Neurosci 32:6240–50. References For each method, coregistered mean EPI images of all subjects were projected into MNI space, concatenated and averaged over the 4th dimension. The four detail images depict the white box outlined in the whole brain image for each method (x=-8mm). White matter and mask edges of the MNI152 standard brain are overlayed for anatomical reference. While nonlinear coregistration achieves a better fit of the brain outline in frontal regions (white asterisks), fieldmap and topup approach show superior performance in matching gray-white matter boundaries (black asterisk). Different methods for distortion correction show characteristic coregistration outcomes 1

SU‐E‐J‐197: A Moving Least Squares Approach for Computing Spatially Accurate Transformations That Satisfy Strict Physiologic Constraints

Purpose:To efficiently compute a physiologically realistic spatial transformation from a sparse point cloud of displacement estimates using Moving Least Squares (MLS) and any combination of upper bound, lower bound, or equality constraints placed on the Jacobian. Whereas diffeomorphic deformable image registration (DIR) requires the transformation's Jacobian determinant to be positive, within the context of thoracic CT, a more appropriate constraint is to require positive Jacobian values that reflect a strictly contracting volume (inhale to exhale DIR) or expanding volume (exhale to inhale DIR).Methods:Jacobian constraints manifest as nonlinear inequality constraints that considerably complicate DIR computation. However, MLS defines a spatial transformation from a sparse point cloud of estimated displacements and provides simple analytic derivative estimates for all voxel locations. Given displacement estimates from automated block matching algorithm, an optimal MLS spatial transformation is determined by computing the minimal perturbation to the displacement data required to yield an MLS transformation that satisfies the Jacobian constraints.Results:Five publicly available (cases 6‐10 from www.dir‐lab.com) inhale/exhale thoracic CT image pairs each with 300 landmarks (for DIR validation) were registered by first obtaining a sparse point cloud of displacement estimates via block matching. Two MLS transformations were then computed, one with no Jacobian constraints and the other with strict contraction Jacobian constraints. Both MLS fields achieved similarly low average millimeter error on all five cases (between 1.16 – 1.26). However, the constrained MLS yielded a strict contraction (all Jacobian values between 0 and 1) while the unconstrained MLS resulted in regions of expansion (Jacobian values larger than 1) despite registering from inhale to exhale.Conclusion:The proposed MLS approach is capable of producing Jacobian constrained transformations without degrading spatial accuracy. Though applied to block match estimates, the approach can be employed in conjunction with displacement estimates from any DIR algorithm.

Quantification of left ventricular deformation fields from undersampled radial, real-time cardiac MRI

Background Regional ventricular elasticity is altered in ischemic heart disease and LV hypertrophy, potentially contributing to and sustaining a ventricular remodeling process. Conventional methods to measure regional ventricular elasticity in preclinical animal models require high fidelity ventricular pressure measurement, sonomicrometry transducers and dynamic modulation of preload. These procedures are highly invasive and provide only limited regional information; patient studies are prohibitive. We dynamically measure global LV elastance using undersampled radial real-time MRI and seek to find regional LV elastance in these studies. This requires tracking LV motion derived from wall thickness measurements in a large number of real-time image frames at high accuracy. We assessed several motion tracking algorithms and characterize their fidelity with respect to true motion labeled by experts and sensitivity to residual radial streak artifact. Methods A series of short axis MR slices were acquired in 9 patients using a golden-angle radial bSSFP trajectory (total views = 4000, radial views per image = 34, shared profiles = 31, reconstructed frame rate = 98 fps) and reconstructed via conjugate gradient-SENSE based iterative reconstruction. Two independent researchers manually segmented the datasets and the movies were restricted to three full heartbeats to limit the number of images. Image registrations were performed between the initial end-diastolic frame and all subsequent frames. The image registrations were performed using b-spline and symmetric diffeomorphic (SyN) image registration across a range of spatial scales (shown in Table 1). Four separate image registration metrics were investigated (mutual information, meansquared overlap, cross-correlation, and demons). Although we expected mean squares and cross-correlation to perform better in this intramodality registration, radial streaking could potentially corrupt data integrity. The resulting deformation fields were evaluated using an array of metrics (dice coefficient, area overlap, false positive, and false negative rate) for all registrations, image frames and patients.

Higher-order spatial accuracy in diffeomorphic image registration

Abstract: We discretize a cost functional for image registration problems by deriving Taylor expansions for the matching term. Minima of the discretized cost functionals can be computed with no spatial discretization error, and the optimal solutions are equivalent to minimal energy curves in the space of k-jets. We show that the solutions convergence to optimal solutions of the original cost functional as the number of particles increases with a convergence rate of O(hd+k) where h is a resolution parameter. The effect of this approach over traditional particle methods is illustrated on synthetic examples and real images.

Spatially-varying metric learning for diffeomorphic image registration: a variational framework.

This paper introduces a variational strategy to learn spatially-varying metrics on large groups of images, in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. Spatially-varying metrics we learn not only favor local deformations but also correlated deformations in different image regions and in different directions. In addition, metric parameters can be efficiently estimated using a gradient descent method. We first describe the general strategy and then show how to use it on 3D medical images with reasonable computational ressources. Our method is assessed on the 3D brain images of the LPBA40 dataset. Results are compared with ANTS-SyN and LDDMM with spatially-homogeneous metrics.

Splines for diffeomorphic image regression.

This paper develops a method for splines on diffeomorphisms for image regression. In contrast to previously proposed methods to capture image changes over time, such as geodesic regression, the method can capture more complex spatio-temporal deformations. In particular, it is a first step towards capturing periodic motions for example of the heart or the lung. Starting from a variational formulation of splines the proposed approach allows for the use of temporal control points to control spline behavior. This necessitates the development of a shooting formulation for splines. Experimental results are shown for synthetic and real data. The performance of the method is compared to geodesic regression.

Normalization of Ventilation Data from 4D-CT to Facilitate Comparison between Datasets Acquired at Different Times

PurposeThe 4D-CT data used for comparing a patient’s ventilation distributions before and after lung radiotherapy are acquired at different times. As a result, an additional variable – the tidal volume (TV) – can alter the results. Therefore, in this paper we propose to normalize the ventilation to the same TV to eliminate that uncertainty. MethodsAbsolute ventilation (AV) data were generated for 6 stereotactic body radiation therapy (SBRT) cases before and after treatment, using the direct geometric algorithm and diffeomorphic morphons deformable image registration (DIR). Each pair of AV distributions was converted to TV-normalized, percentile ventilation (PV) and low-dose well-ventilated-normalized ventilation (LDWV) distributions. The ventilation change was calculated in various dose regions based on the treatment plans using the DIR-registered before and after treatment data sets. The ventilation change based on TV-normalized ventilation was compared with the AV as well as the data normalized by PV and LDWV.ResultsAV change may be misleading when the TV differs before and after treatment, which was found to be up to 6.7%. All three normalization methods produced a similar trend in ventilation change: the higher the dose to a region of lung, the greater the degradation in ventilation. In low dose regions (<5 Gy), ventilation appears relatively improved after treatment due to the relative nature of the normalized ventilation. However, the LDWV may not be reliable when the ventilation in the low-dose regions varies. PV exhibited a similar ventilation change trend compared to the TV-normalized in all cases. However, by definition, the ventilation distribution in the PV is significantly different from the original distribution. ConclusionNormalizing ventilation distributions by the TV is a simple and reliable method for evaluation of ventilation changes.

Spectral Log-Demons: Diffeomorphic Image Registration with Very Large Deformations

This paper presents a new framework for capturing large and complex deformations in image registration and atlas construction. This challenging and recurrent problem in computer vision and medical imaging currently relies on iterative and local approaches, which are prone to local minima and, therefore, limit present methods to relatively small deformations. Our general framework introduces to this effect a new direct feature matching technique that finds global correspondences between images via simple nearest-neighbor searches. More specifically, very large image deformations are captured in Spectral Forces, which are derived from an improved graph spectral representation. We illustrate the benefits of our framework through a new enhanced version of the popular Log-Demons algorithm, named the Spectral Log-Demons, as well as through a groupwise extension, named the Groupwise Spectral Log-Demons, which is relevant for atlas construction. The evaluations of these extended versions demonstrate substantial improvements in accuracy and robustness to large deformations over the conventional Demons approaches.

SU-D-WAB-05: Image-Based Proton Range Verification Using Intensity-Corrected CBCT

Purpose: Using CBCT to detect variations in proton beam path prior to treatment is an important step in the quality assurance of proton therapy. However, the Hounsfield Units (HUs) from a CBCT differs slightly from a simulation CT, thereby introducing additional uncertainties in the conversion from HUs to proton stopping power. The aim of this work is to demonstrate the feasibility of using deformable image registration to map simulation CT HUs onto a treatment CBCT for range verification during proton therapy. Methods: A simulation CT and two simulated proton CBCT of a head and neck patient were used in this study. We used a diffeomorphic deformable image registration algorithm with symmetric normalization in conjunction with cross correlation similarity metrics (ANTs: Advanced Normalization Tools) to deform the simulation CT onto the CBCTs. Polar plots of proton beam water equivalent thickness (WET) were generated using a ray tracing algorithm at different gantry angles in the unmodified CBCT, corrected CBCT and simulation CT for analysis. Results: With no anatomical variation, corrected CBCT and simulation CT image exhibited excellent agreement in WETs (mean difference of 1.26 mm, interquartile range 0.42∼1.79mm). In the unmodified CBCT image, larger difference in WETs (mean value 3.38 mm, interquartile range 1.90∼5.03mm) attributed to errors in HU to stopping power conversion were observed. With tumor shrinkage the differences in the WET polar plots between planning CT and corrected CBCT correlated with the location of anatomical change in the nasal/oral cavity, indicating potential deviations in proton dose deposition. Conclusion: It is feasible to use deformable image registration to correct CBCT HUs for image based proton range verification. Polar plots of deviations in WET between CBCT and simulation CT is potentially an efficient and practical quality assurance tool in the use of CBCT for proton therapy applications.

SU‐E‐J‐69: Normalization of Ventilation Data From 4D‐CT for Comparison Before and After Treatment

Purpose: If one were to evaluate ventilation distributions before and after radiotherapy derived from 4D‐CT scans, changes in tidal volume (TV) might potentially bias the results. This is important because differences in TV were found to be large in some cases. To eliminate this uncertainty we proposed to normalize the ventilation to the TV. Methods: Absolute ventilation (AV) data were generated for 6 SBRT cases before and after treatment, using the direct geometric algorithm and diffeomorphic morphons deformable image registration (DIR). Each pair of AV distributions was converted to TV‐normalized, percentile ventilation (PV) and low‐dose well‐ventilated‐normalized ventilation (LDWV) distributions. The latter two were described in previous publications. The ventilation change was calculated in various dose regions based on the treatment plans using the DIR‐registered before and after treatment data sets. The ventilation change based on TV‐normalized ventilation was compared with the AV as well as the data normalized by PV and LDWV. Results: AV change may be misleading when the TV differs before and after treatment which was found to be up to 6.7% in the cases studied. All three normalization methods produced a similar trend in ventilation change: the higher the dose to a region of lung, the greater the degradation in ventilation. In low dose regions (&lt;5 Gy), ventilation appears relatively improved after treatment due to the relative nature of the normalized ventilation. However, the LDWV may not be reliable when the ventilation in the low‐dose regions varies. As an example, in one case LDWV appeared degraded regardless of dose. PV exhibited a similar ventilation change trend compared to the TV‐normalized in all cases. However, by definition, the ventilation distribution in the PV is significantly different from the original distribution. Conclusion: Normalizing ventilation distributions by the TV is a simple and reliable method for evaluation of ventilation changes. This work was partially supported by a research grant from Varian Medical Systems, Inc., Palo Alto, CA.

Multi-subject atlas built from structural tongue magnetic resonance images

Magnetic resonance imaging (MRI) is a widely used technology for non-invasive tongue imaging. MRI can detail tongue and muscle shapes and their variability in both healthy and diseased populations. Such detail can aid significantly in the interpretation of muscle interactions in the tongue for both normal and disordered speech production. However, the size or shape of the tongue and muscles may vary from one subject to another. In addition, there exists no comprehensive and systematic framework to assess the difference and variability of tongue and muscles in a normalized space. In the present work, we built a multi-subject atlas from 20 normal subjects that are acquired using structural MRI to offer a normalized space on which all subjects from a target population can be mapped and compared. In order to find accurate one-to-one correspondences, we bounded the tongue so that each volume had the same vocal tract features. For registration, we used symmetric diffeomorphic image registration with a cross-correlation similarity metric, which is widely used in brain image analysis. The atlas facilitates a template-based segmentation in assigning anatomical labels in the images. The tongue atlas is unprecedented and opens new vistas for exploring normal and diseased oral structures and function.

A VECTOR MOMENTA FORMULATION OF DIFFEOMORPHISMS FOR IMPROVED GEODESIC REGRESSION AND ATLAS CONSTRUCTION.

This paper presents a novel approach for diffeomorphic image regression and atlas estimation that results in improved convergence and numerical stability. We use a vector momenta representation of a diffeomorphism's initial conditions instead of the standard scalar momentum that is typically used. The corresponding variational problem results in a closed-form update for template estimation in both the geodesic regression and atlas estimation problems. While we show that the theoretical optimal solution is equivalent to the scalar momenta case, the simplification of the optimization problem leads to more stable and efficient estimation in practice. We demonstrate the effectiveness of our method for atlas estimation and geodesic regression using synthetically generated shapes and 3D MRI brain scans.

Explicit B-spline regularization in diffeomorphic image registration

Diffeomorphic mappings are central to image registration due largely to their topological properties and success in providing biologically plausible solutions to deformation and morphological estimation problems. Popular diffeomorphic image registration algorithms include those characterized by time-varying and constant velocity fields, and symmetrical considerations. Prior information in the form of regularization is used to enforce transform plausibility taking the form of physics-based constraints or through some approximation thereof, e.g., Gaussian smoothing of the vector fields [a la Thirion's Demons (Thirion, 1998)]. In the context of the original Demons' framework, the so-called directly manipulated free-form deformation (DMFFD) (Tustison et al., 2009) can be viewed as a smoothing alternative in which explicit regularization is achieved through fast B-spline approximation. This characterization can be used to provide B-spline “flavored” diffeomorphic image registration solutions with several advantages. Implementation is open source and available through the Insight Toolkit and our Advanced Normalization Tools (ANTs) repository. A thorough comparative evaluation with the well-known SyN algorithm (Avants et al., 2008), implemented within the same framework, and its B-spline analog is performed using open labeled brain data and open source evaluation tools.

Geodesics, Parallel Transport &amp; One-Parameter Subgroups for Diffeomorphic Image Registration

Computational anatomy aims at developing models to understand the anatomical variability of organs and tissues. A widely used and validated instrument for comparing the anatomy in medical images is non-linear diffeomorphic registration which is based on a rich mathematical background. For instance, the large deformation diffeomorphic metric mapping (LDDMM) framework defines a Riemannian setting by providing a right invariant metric on the tangent spaces, and solves the registration problem by computing geodesics parametrized by time-varying velocity fields. A simpler alternative based on stationary velocity fields (SVF) has been proposed, using the one-parameter subgroups from Lie groups theory. In spite of its better computational efficiency, the geometrical setting of the SVF is more vague, especially regarding the relationship between one-parameter subgroups and geodesics. In this work, we detail the properties of finite dimensional Lie groups that highlight the geometric foundations of one-parameter subgroups. We show that one can define a proper underlying geometric structure (an affine manifold) based on the canonical Cartan connections, for which one-parameter subgroups and their translations are geodesics. This geometric structure is perfectly compatible with all the group operations (left, right composition and inversion), contrarily to left- (or right-) invariant Riemannian metrics. Moreover, we derive closed-form expressions for the parallel transport. Then, we investigate the generalization of such properties to infinite dimensional Lie groups. We suggest that some of the theoretical objections might actually be ruled out by the practical implementation of both the LDDMM and the SVF frameworks for image registration. This leads us to a more practical study comparing the parameterization (initial velocity field) of metric and Cartan geodesics in the specific optimization context of longitudinal and inter-subject image registration.Our experimental results suggests that stationarity is a good approximation for longitudinal deformations, while metric geodesics notably differ from stationary ones for inter-subject registration, which involves much larger and non-physical deformations. Then, we turn to the practical comparison of five parallel transport techniques along one-parameter subgroups. Our results point out the fundamental role played by the numerical implementation, which may hide the theoretical differences between the different schemes. Interestingly, even if the parallel transport generally depends on the path used, an experiment comparing the Cartan parallel transport along the one-parameter subgroup and the LDDMM (metric) geodesics from inter-subject registration suggests that our parallel transport methods are not so sensitive to the path.

Fractal curvature measures and Minkowski content for self-conformal subsets of the real line

We show that the fractal curvature measures of invariant sets of one-dimensional conformal iterated function systems satisfying the open set condition exist if the associated geometric potential function is nonlattice. Moreover, we prove that if the maps of the conformal iterated function system are all analytic, then the fractal curvature measures do not exist in the lattice case. Further, in the nonlattice situation we obtain that the Minkowski content exists and prove that the fractal curvature measures are constant multiples of the δ-conformal measure, where δ denotes the Minkowski dimension of the invariant set. For the first fractal curvature measure, this constant factor coincides with the Minkowski content of the invariant set. In the lattice situation we give sufficient conditions for the Minkowski content of the invariant set to exist, disproving a conjecture of Lapidus and standing in contrast with the fact that the Minkowski content of a self-similar lattice fractal never exists. However, every self-similar set satisfying the open set condition exhibits a Minkowski measurable C1+α diffeomorphic image. Both in the lattice and in the nonlattice situation, average versions of the fractal curvature measures are shown to always exist.

The TVDMFFDVR Algorithm

The recent ITKv4 refactoring includes several enhancements to the existing registration framework. These additional transform classes provide access to mappings described by dense displacement fields and their corresponding optimization which complement the popular free-form deformation (FFD) ap- proach already in ITK. Innovation motivated by previous work [5] and recent diffeomorphic image regis- tration developments in which the characteristic velocity field is represented by spatiotemporal B-splines [2], resulted in a diffeomorphic B-spline-based image registration algorithm combining and extending these techniques which we make available in ITK through the gerrit system. Additionally, we include two command line tools showcasing the new elements of the registration refactoring for 1) computing mappings between two images (antsRegistration) including the family of transforms discussed in this article and 2) applying those transformations to images (antsApplyTransforms). NB: The user must download the patch available at http://review.source.kitware.com/#/c/3606/ in or- der to compile the code accompanying this article.

Diffeomorphic image registration of diffusion MRI using spherical harmonics.

Nonrigid registration of diffusion magnetic resonance imaging (MRI) is crucial for group analyses and building white matter and fiber tract atlases. Most current diffusion MRI registration techniques are limited to the alignment of diffusion tensor imaging (DTI) data. We propose a novel diffeomorphic registration method for high angular resolution diffusion images by mapping their orientation distribution functions (ODFs). ODFs can be reconstructed using q-ball imaging (QBI) techniques and represented by spherical harmonics (SHs) to resolve intra-voxel fiber crossings. The registration is based on optimizing a diffeomorphic demons cost function. Unlike scalar images, deforming ODF maps requires ODF reorientation to maintain its consistency with the local fiber orientations. Our method simultaneously reorients the ODFs by computing a Wigner rotation matrix at each voxel, and applies it to the SH coefficients during registration. Rotation of the coefficients avoids the estimation of principal directions, which has no analytical solution and is time consuming. The proposed method was validated on both simulated and real data sets with various metrics, which include the distance between the estimated and simulated transformation fields, the standard deviation of the general fractional anisotropy and the directional consistency of the deformed and reference images. The registration performance using SHs with different maximum orders were compared using these metrics. Results show that the diffeomorphic registration improved the affine alignment, and registration using SHs with higher order SHs further improved the registration accuracy by reducing the shape difference and improving the directional consistency of the registered and reference ODF maps.

Statistical Modeling of 4D Respiratory Lung Motion Using Diffeomorphic Image Registration

Modeling of respiratory motion has become increasingly important in various applications of medical imaging (e.g., radiation therapy of lung cancer). Current modeling approaches are usually confined to intra-patient registration of 3D image data representing the individual patient's anatomy at different breathing phases. We propose an approach to generate a mean motion model of the lung based on thoracic 4D computed tomography (CT) data of different patients to extend the motion modeling capabilities. Our modeling process consists of three steps: an intra-subject registration to generate subject-specific motion models, the generation of an average shape and intensity atlas of the lung as anatomical reference frame, and the registration of the subject-specific motion models to the atlas in order to build a statistical 4D mean motion model (4D-MMM). Furthermore, we present methods to adapt the 4D mean motion model to a patient-specific lung geometry. In all steps, a symmetric diffeomorphic nonlinear intensity-based registration method was employed. The Log-Euclidean framework was used to compute statistics on the diffeomorphic transformations. The presented methods are then used to build a mean motion model of respiratory lung motion using thoracic 4D CT data sets of 17 patients. We evaluate the model by applying it for estimating respiratory motion of ten lung cancer patients. The prediction is evaluated with respect to landmark and tumor motion, and the quantitative analysis results in a mean target registration error (TRE) of 3.3 ±1.6 mm if lung dynamics are not impaired by large lung tumors or other lung disorders (e.g., emphysema). With regard to lung tumor motion, we show that prediction accuracy is independent of tumor size and tumor motion amplitude in the considered data set. However, tumors adhering to non-lung structures degrade local lung dynamics significantly and the model-based prediction accuracy is lower in these cases. The statistical respiratory motion model is capable of providing valuable prior knowledge in many fields of applications. We present two examples of possible applications in radiation therapy and image guided diagnosis.

An ITK Implementation of the Symmetric Log-Domain Diffeomorphic Demons Algorithm

This article provides an implementation of the symmetric log-domain diffeomorphic image registration algorithm, or symmetric demons algorithm for short. It generalizes Thirion’s demons and the diffeomorphic demons algorithm. The main practical advantages of the symmetric demons with respect to the other demons variants is that is provides the inverse of the spatial transformation at no additional computational cost and ensures that the registration of image A to image B provides the inverse of the registration from image B to image A. The algorithm works completely in the log-domain, i.e. it uses a stationary velocity field to encode the spatial transformation as its exponential. Within the Insight Toolkit (ITK), the classical demons algorithm is implemented as part of the finite difference solver framework. Our code reuses and extends this generic framework. The source code is composed of a set of reusable ITK filters and classes together with their unit tests. We also provide a small example program that allows the user to compare the different variants of the demons algorithm. This paper gives an overview of the algorithm, an overview of its implementation and a small user guide to ease the use of the registration executable.