The adaptive bases algorithm for intensity-based nonrigid image registration

Nonrigid registration of medical images is important for a number of applications such as the creation of population averages, atlas-based segmentation, or geometric correction of functional magnetic resonance imaging (fMRI) images to name a few. In recent years, a number of methods have been proposed to solve this problem, one class of which involves maximizing a mutual information (MI)-based objective function over a regular grid of splines. This approach has produced good results but its computational complexity is proportional to the compliance of the transformation required to register the smallest structures in the image. Here, we propose a method that permits the spatial adaptation of the transformation's compliance. This spatial adaptation allows us to reduce the number of degrees of freedom in the overall transformation, thus speeding up the process and improving its convergence properties. To develop this method, we introduce several novelties: 1) we rely on radially symmetric basis functions rather than B-splines traditionally used to model the deformation field; 2) we propose a metric to identify regions that are poorly registered and over which the transformation needs to be improved; 3) we partition the global registration problem into several smaller ones; and 4) we introduce a new constraint scheme that allows us to produce transformations that are topologically correct. We compare the approach we propose to more traditional ones and show that our new algorithm compares favorably to those in current use.     

A comparative study of transformation functions for nonrigid image registration.

Transformation functions play a major role in nonrigid image registration. In this paper, the characteristics of thin-plate spline (TPS), multiquadric (MQ), piecewise linear (PL), and weighted mean (WM) transformations are explored and their performances in nonrigid image registration are compared. TPS and MQ are found to be most suitable when the set of control-point correspondences is not large (fewer than a thousand) and variation in spacing between the control points is not large. When spacing between the control points varies greatly, PL is found to produce a more accurate registration than TPS and MQ. When a very large set of control points is given and the control points contain positional inaccuracies, WM is preferred over TPS, MQ, and PL because it uses an averaging process that smoothes the noise and does not require the solution of a very large system of equations. Use of transformation functions in the detection of incorrect correspondences is also discussed.     

Robust weighted graph transformation matching for rigid and nonrigid image registration

This paper presents an automatic point matching algorithm for establishing accurate match correspondences in two or more images. The proposed algorithm utilizes a group of feature points to explore their geometrical relationship in a graph arrangement. The algorithm starts with a set of matches (including outliers) between the two images. A set of nondirectional graphs is then generated for each feature and its K nearest matches (chosen from the initial set). Using the angular distances between edges that connect a feature point to its K nearest neighbors in the graph, the algorithm finds a graph in the second image that is similar to the first graph. In the case of a graph including outliers, the algorithm removes such outliers (one by one, according to their strength) from the graph and re-evaluates the angles until the two graphs are matched or discarded. This is a simple intuitive and robust algorithm that is inspired by a previous work. Experimental results demonstrate the superior performance of this algorithm under various conditions, such as rigid and nonrigid transformations, ambiguity due to partial occlusions or match correspondence multiplicity, scale, and larger view variation.     

Computional cost of nonrigid registration algorithms based on fluid dynamics

Though fluid dynamics offer a good approach to nonrigid registration and give accurate results, even with large-scale deformations, its application is still very time consuming. We introduce and discuss different approaches to solve the core problem of nonrigid registration, the partial differential equation of fluid dynamics. We focus on the solvers, their computional costs and the accuracy of registration. Numerical experiments show that relaxation is currently the best approach, especially when reducing the cost/iteration by focusing the updates on deformation spots.     

Automatic nonrigid calibration of image registration for real time MR-guided HIFU ablations of mobile organs

Real time magnetic resonance imaging (MRI) is rapidly gaining importance in interventional therapies. An accurate motion estimation is required for mobile targets and can be conveniently addressed using an image registration algorithm. Since the adaptation of the control parameters of the algorithm depends on the application (targeted organ, location of the tumor, slice orientation, etc.), typically an individual calibration is required. However, the assessment of the estimated motion accuracy is difficult since the real target motion is unknown. In this paper, existing criteria based only on anatomical image similarity are demonstrated to be inadequate. A new criterion is introduced, which is based on the local magnetic field distribution. The proposed criterion was used to assess, during a preparative calibration step, the optimal configuration of an image registration algorithm derived from the Horn and Schunck method. The accuracy of the proposed method was evaluated in a moving phantom experiment, which allows the comparison with the known motion pattern and to an established criterion based on anatomical images. The usefulness of the method for the calibration of optical-flow based algorithms was also demonstrated in vivo under conditions similar to thermo-ablation for the abdomen of twelve volunteers. In average over all volunteers, a resulting displacement error of 1.5 mm was obtained (largest observed error equal to 4-5 mm) using a criterion based on anatomical image similarity. A better average accuracy of 1 mm was achieved using the proposed criterion (largest observed error equal to 2 mm). In both kidney and liver, the proposed criterion was shown to provide motion field accuracy in the range of the best achievable.     

Evaluation of optimization methods for nonrigid medical image registration using mutual information and B-splines.

A popular technique for nonrigid registration of medical images is based on the maximization of their mutual information, in combination with a deformation field parameterized by cubic B-splines. The coordinate mapping that relates the two images is found using an iterative optimization procedure. This work compares the performance of eight optimization methods: gradient descent (with two different step size selection algorithms), quasi-Newton, nonlinear conjugate gradient, Kiefer-Wolfowitz, simultaneous perturbation, Robbins-Monro, and evolution strategy. Special attention is paid to computation time reduction by using fewer voxels to calculate the cost function and its derivatives. The optimization methods are tested on manually deformed CT images of the heart, on follow-up CT chest scans, and on MR scans of the prostate acquired using a BFFE, T1, and T2 protocol. Registration accuracy is assessed by computing the overlap of segmented edges. Precision and convergence properties are studied by comparing deformation fields. The results show that the Robbins-Monro method is the best choice in most applications. With this approach, the computation time per iteration can be lowered approximately 500 times without affecting the rate of convergence by using a small subset of the image, randomly selected in every iteration, to compute the derivative of the mutual information. From the other methods the quasi-Newton and the nonlinear conjugate gradient method achieve a slightly higher precision, at the price of larger computation times.     

Spatio-temporal nonrigid registration for ultrasound cardiac motion estimation

We propose a new spatio-temporal elastic registration algorithm for motion reconstruction from a series of images. The specific application is to estimate displacement fields from two-dimensional ultrasound sequences of the heart. The basic idea is to find a spatio-temporal deformation field that effectively compensates for the motion by minimizing a difference with respect to a reference frame. The key feature of our method is the use of a semi-local spatio-temporal parametric model for the deformation using splines, and the reformulation of the registration task as a global optimization problem. The scale of the spline model controls the smoothness of the displacement field. Our algorithm uses a multiresolution optimization strategy to obtain a higher speed and robustness. We evaluated the accuracy of our algorithm using a synthetic sequence generated with an ultrasound simulation package, together with a realistic cardiac motion model. We compared our new global multiframe approach with a previous method based on pairwise registration of consecutive frames to demonstrate the benefits of introducing temporal consistency. Finally, we applied the algorithm to the regional analysis of the left ventricle. Displacement and strain parameters were evaluated showing significant differences between the normal and pathological segments, thereby illustrating the clinical applicability of our method.     

Coupling dense and landmark-based approaches for nonrigid registration

In this paper, we investigate the introduction of cortical constraints for non rigid intersubject brain registration. We extract sulcal patterns with the active ribbon method, presented by Le Goualher et al. (1997). An energy based registration method (Hellier et al., 2001), which will be called photometric registration method in this paper, makes it possible to incorporate the matching of cortical sulci. The local sparse similarity and the photometric similarity are, thus, expressed in a unified framework. We show the benefits of cortical constraints on a database of 18 subjects, with global and local assessment of the registration. This new registration scheme has also been evaluated on functional magnetoencephalography data. We show that the anatomically constrained registration leads to a substantial reduction of the intersubject functional variability.     

Validation of nonrigid image registration using finite-element methods: application to breast MR images

This paper presents a novel method for validation of nonrigid medical image registration. This method is based on the simulation of physically plausible, biomechanical tissue deformations using finite-element methods. Applying a range of displacements to finite-element models of different patient anatomies generates model solutions which simulate gold standard deformations. From these solutions, deformed images are generated with a range of deformations typical of those likely to occur in vivo. The registration accuracy with respect to the finite-element simulations is quantified by co-registering the deformed images with the original images and comparing the recovered voxel displacements with the biomechanically simulated ones. The functionality of the validation method is demonstrated for a previously described nonrigid image registration technique based on free-form deformations using B-splines and normalized mutual information as a voxel similarity measure, with an application to contrast-enhanced magnetic resonance mammography image pairs. The exemplar nonrigid registration technique is shown to be of subvoxel accuracy on average for this particular application. The validation method presented here is an important step toward more generic simulations of biomechanically plausible tissue deformations and quantification of tissue motion recovery using nonrigid image registration. It will provide a basis for improving and comparing different nonrigid registration techniques for a diversity of medical applications, such as intrasubject tissue deformation or motion correction in the brain, liver or heart.     

A fast nonrigid image registration with constraints on the Jacobian using large scale constrained optimization

This paper presents a new nonrigid monomodality image registration algorithm based on B-splines. The deformation is described by a cubic B-spline field and found by minimizing the energy between a reference image and a deformed version of a floating image. To penalize noninvertible transformation, we propose two different constraints on the Jacobian of the transformation and its derivatives. The problem is modeled by an inequality constrained optimization problem which is efficiently solved by a combination of the multipliers method and the L-BFGS algorithm to handle the large number of variables and constraints of the registration of 3-D images. Numerical experiments are presented on magnetic resonance images using synthetic deformations and atlas based segmentation.     

A review of geometric transformations for nonrigid body registration

This paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration. It explains the theoretical foundation of the models and classifies them according to this basis. This results in two categories, physically based models described by partial differential equations of continuum mechanics (e.g., linear elasticity and fluid flow) and basis function expansions derived from interpolation and approximation theory (e.g., radial basis functions, B-splines and wavelets). Recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described. The final section reviews some recent evaluation studies. The paper concludes by explaining under what conditions a particular transformation model is appropriate.     

Analysis of 3-D myocardial motion in tagged MR images using nonrigid image registration

Tagged magnetic resonance imaging (MRI) is unique in its ability to noninvasively image the motion and deformation of the heart in vivo, but one of the fundamental reasons limiting its use in the clinical environment is the absence of automated tools to derive clinically useful information from tagged MR images. In this paper, we present a novel and fully automated technique based on nonrigid image registration using multilevel free-form deformations (MFFDs) for the analysis of myocardial motion using tagged MRI. The novel aspect of our technique is its integrated nature for tag localization and deformation field reconstruction using image registration and voxel based similarity measures. To extract the motion field within the myocardium during systole we register a sequence of images taken during systole to a set of reference images taken at end-diastole, maximizing the normalized mutual information between the images. We use both short-axis and long-axis images of the heart to estimate the full four-dimensional motion field within the myocardium. We also present validation results from data acquired from twelve volunteers.     

Automatic generation of boundary conditions using demons nonrigid image registration for use in 3-D modality-independent elastography

Modality-independent elastography (MIE) is a method of elastography that reconstructs the elastic properties of tissue using images acquired under different loading conditions and a biomechanical model. Boundary conditions are a critical input to the algorithm and are often determined by time-consuming point correspondence methods requiring manual user input. This study presents a novel method of automatically generating boundary conditions by nonrigidly registering two image sets with a demons diffusion-based registration algorithm. The use of this method was successfully performed in silico using magnetic resonance and X-ray-computed tomography image data with known boundary conditions. These preliminary results produced boundary conditions with an accuracy of up to 80% compared to the known conditions. Demons-based boundary conditions were utilized within a 3-D MIE reconstruction to determine an elasticity contrast ratio between tumor and normal tissue. Two phantom experiments were then conducted to further test the accuracy of the demons boundary conditions and the MIE reconstruction arising from the use of these conditions. Preliminary results show a reasonable characterization of the material properties on this first attempt and a significant improvement in the automation level and viability of the method.     

An automatic nonrigid registration for stained histological sections.

Automatic computer-based analyses of histological sections which are differently stained require that they are related to each other. Most registration methods are only able to perform rigid-body motion and are sensitive to noise and artifacts. Histological images, however, are accompanied by several artifacts and different contrasts, which require a nonrigid registration. In this paper, we present a hierarchical nonrigid registration algorithm able to align images, which contain minor image artifacts. The algorithm requires no a priori knowledge of the true image. The hierarchical design of the algorithm enhances robustness and accuracy, and saves computational costs. The proposed algorithm is decomposed into a fast, coarse, rigid registration step and a slower, but finer, nonrigid step. For the coarse registration, we use image pyramids, while for the second step, we combine a point-based registration with an elastic thin-plate spline interpolation. Accuracy tests, performed for 20 histological images obtained from human arteries, have shown that the error measure is acceptable, and that the image noise does not cause a problem. The associated convergence rate of the mean pixel displacement error during the rigid and nonrigid registrations is satisfying. The algorithm can be applied to various multicontrast elastic registration problems in medical imaging and may be extended to three dimensions.     

A "twisting and bending" model-based nonrigid image registration technique for 3-D ultrasound carotid images

Atherosclerosis at the carotid bifurcation resulting in cerebral emboli is a major cause of ischemic stroke. Most strokes associated with carotid atherosclerosis can be prevented by lifestyle/dietary changes and pharmacological treatments if identified early by monitoring carotid plaque changes. Registration of 3-D ultrasound (US) images of carotid plaque obtained at different time points is essential for sensitive monitoring of plaque changes in volume and surface morphology. This registration technique should be nonrigid, since different head positions during image acquisition sessions cause relative bending and torsion in the neck, producing nonlinear deformations between the images. We modeled the movement of the neck using a “twisting and bending” model with only six parameters for nonrigid registration. We evaluated the algorithm using 3-D US carotid images acquired at two different head positions to simulate images acquired at different times. We calculated the mean registration error (MRE) between the segmented vessel surfaces in the target image and the registered image using a distance-based error metric after applying our “twisting and bending” model-based nonrigid registration algorithm. We achieved an average registration error of $0.80 pm 0.26$ mm using our nonrigid registration technique, which was a significant improvement in registration accuracy over rigid registration, even with reduced degrees-of-freedom compared to the other nonrigid registration algorithms.      

图像配准中基于最大熵的模板选取算法研究

图像配准是对多幅相关图像匹配与融合,其中匹配特征空间的选择是图像配准的基础,直接关系着最终的配准效果.为此针对空域相关配准,提出一种基于最大熵的模板选取算法,首先计算候选匹配模板平滑直方图的信息熵,选择熵值最大的图像块作为配准模板,再对搜索空间计算相似性测度得到最佳配准.通过大量抗干扰仿真试验证明,算法鲁棒性很好.     

新的Jensen-Schur测度在医学图像配准中的应用

针对传统的互信息和归一化互信息运算时间长、收敛性能和抗噪声能力差的缺点,提出了一种新的医学图像配准测度,Jensen-Schur测度.从理论上分析了该测度可用于图像配准的性质,并构造了三类Jensen-Schur测度:Jensen-Schur-alpha、Jensen-Rényi-alpha、JenserrSchur-w测度.通过对人体脑部MR/CI"和MR/PET图像的刚体配准实验,从运算时间、收敛性能、抗噪鲁棒性方面,对这三类测度、互信息和归一化互信息进行了比较和分析.实验结果表明,Jensen-Schur-alpha(alpha=2或3)和Jensen-Schur-w测度的收敛性能优于其它测度,运算速度快于其它测度,对噪声有很强的鲁棒性.最后用Jensen-Sehur-alpha(alpha=2)测度进行多模态医学图像的配准实验,结果表明效果良好.     

基于互信息和多智能体优化的合成孔径雷达图像配准

提出了一种基于互信息的多智能体优化方法,并将其用于合成孔径雷达(Synthetic Aperture Radar,SAR)图像的配准.采用归一化互信息作为度量准则,直接利用图像的灰度数据进行配准,没有假设图像间灰度值的线性关系,不需要对图像做分割、特征提取等预处理,并利用多智能体优化算法寻找最佳匹配参数,以得到最优的配准结果.实验表明,该算法在SAR图像配准方面有更好的普适性和更高的配准精度.     

Mutual information-based rigid and nonrigid registration of ultrasound volumes

We investigated the registration of ultrasound volumes based on the mutual information measure, a technique originally applied to multimodality registration of brain images. A prerequisite for successful registration is a smooth, quasi-convex mutual information surface with an unambiguous maximum. We discuss the necessary preprocessing to create such a surface for ultrasound volumes. Abdominal and thoracic organs imaged with ultrasound typically move relative to the exterior of the body and are deformable. Consequently, four specific instances of image registration involving progressively generalized transformations were studied: rigid-body, rigid-body + uniform scaling, rigid-body + nonuniform scaling, and affine. Registration was applied to clinically acquired volumetric images. The accuracy was comparable with the voxel dimension for all transformation modes, although it degraded as the transformation grew more complex. Likewise, the capture range became narrower with the complexity of transformation. As the use of real-time three-dimensional ultrasound becomes more prevalent, the method we present should work well for a variety of applications examining serial anatomic and physiologic changes. Developers of these clinical applications would match the deformation model of their problem to one of the four transformation models presented here.     

基于MMI的存在旋转的异类图匹配方法

为了解决存在旋转的异类图匹配问题,在互信息（MMI,Maximum of Mutual Information）匹配方法的基础上,利用穷举法在参考图中找出实时图的对应匹配位置,并作为控制点,利用模型以及最小二乘方法找出两幅图像的对应关系。利用参考图的旋转变换较好地解决了存在旋转的异类图匹配问题;把控制点理论应用于灰度匹配得到的匹配点;把景象匹配的新成果（MMI）用于解决旋转异类图匹配。仿真实验表明此方法可较好地解决存在旋转的异类图匹配问题。