Diffeomorphic metric mapping of high angular resolution diffusion imaging based on Riemannian structure of orientation distribution functions

In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. To this end, we first review the Riemannian manifold of ODFs. We then define the reorientation of an ODF when an affine transformation is applied and subsequently, define the diffeomorphic group action to be applied on the ODF based on this reorientation. We incorporate the Riemannian metric of ODFs for quantifying the similarity of two HARDI images into a variational problem defined under the large deformation diffeomorphic metric mapping framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.     

Bilateral filtering of diffusion tensor magnetic resonance images.

We extend the well-known scalar image bilateral filtering technique to diffusion tensor magnetic resonance images (DTMRI). The scalar version of bilateral image filtering is extended to perform edge-preserving smoothing of DT field data. The bilateral DT filtering is performed in the Log-Euclidean framework which guarantees valid output tensors. Smoothing is achieved by weighted averaging of neighboring tensors. Analogous to bilateral filtering of scalar images, the weights are chosen to be inversely proportional to two distance measures: The geometrical Euclidean distance between the spatial locations of tensors and the dissimilarity of tensors. We describe the noniterative DT smoothing equation in closed form and show how interpolation of DT data is treated as a special case of bilateral filtering where only spatial distance is used. We evaluate different recent DT tensor dissimilarity metrics including the Log-Euclidean, the similarity-invariant Log-Euclidean, the square root of the J-divergence, and the distance scaled mutual diffusion coefficient. We present qualitative and quantitative smoothing and interpolation results and show their effect on segmentation, for both synthetic DT field data, as well as real cardiac and brain DTMRI data.     

DTI segmentation using an information theoretic tensor dissimilarity measure

In recent years, diffusion tensor imaging (DTI) has become a popular in vivo diagnostic imaging technique in Radiological sciences. In order for this imaging technique to be more effective, proper image analysis techniques suited for analyzing these high dimensional data need to be developed. In this paper, we present a novel definition of tensor "distance" grounded in concepts from information theory and incorporate it in the segmentation of DTI. In a DTI, the symmetric positive definite (SPD) diffusion tensor at each voxel can be interpreted as the covariance matrix of a local Gaussian distribution. Thus, a natural measure of dissimilarity between SPD tensors would be the Kullback-Leibler (KL) divergence or its relative. We propose the square root of the J-divergence (symmetrized KL) between two Gaussian distributions corresponding to the diffusion tensors being compared and this leads to a novel closed form expression for the "distance" as well as the mean value of a DTI. Unlike the traditional Frobenius norm-based tensor distance, our "distance" is affine invariant, a desirable property in segmentation and many other applications. We then incorporate this new tensor "distance" in a region based active contour model for DTI segmentation. Synthetic and real data experiments are shown to depict the performance of the proposed model.     

非刚体图像配准的变形场拓扑约束研究

利用正则化方法约束非线性变形场是非刚体图像配准领域的一个重要研究方向。为得到具有拓扑保持能力的非线性变形场,本文在分析粘流体配准和扩散模型配准算法的实现原理基础上,提出一种基于弹簧约束的变形场拓扑保持方法。该方法在可变形图像上附加不规则网格,通过保持网格结点间的连接关系不变达到控制图像变形的目的。将本文算法应用在不同人脑磁共振图像配准和脑内核结构分割中,结果表明,本文方法具有保持变形场拓扑不变的能力,且能够给出更为准确的分割结果。      

Seamless warping of diffusion tensor fields

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create ldquoseamsrdquo or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT datasets seamlessly from one imaging space to another. Once the bijection has been achieved and tensors have been correctly relocated to the template space, we can appropriately reorient tensors in the template space using a warping method based on Procrustean estimation.     

Symmetric data attachment terms for large deformation image registration

Nonrigid medical image registration between images that are linked by an invertible transformation is an inherently symmetric problem. The transformation that registers the image pair should ideally be the inverse of the transformation that registers the pair with the order of images interchanged. This property is referred to as symmetry in registration or inverse consistent registration. However, in practical estimation, the available registration algorithms have tended to produce inverse inconsistent transformations when the template and target images are interchanged. In this paper, we propose two novel cost functions in the large deformation diffeomorphic framework that are inverse consistent. These cost functions have symmetric data-attachment terms; in the first, the matching error is measured at all points along the flow between template and target, and in the second, matching is enforced only at the midpoint of the flow between the template and target. We have implemented these cost functions and present experimental results to validate their inverse consistent property and registration accuracy.     

Fiber continuity: an anisotropic prior for ODF estimation

The accurate and reliable estimation of fiber orientation distributions, based on diffusion-sensitized magnetic resonance images is a major prerequisite for tractography algorithms or any other derived statistical analysis. In this work, we formulate the principle of fiber continuity (FC), which is based on the simple observation that the imaging of fibrous tissue implies certain expectations for the measured images. From this principle we derive a prior for the estimation of fiber orientation distributions based on high angular resolution diffusion imaging (HARDI). We demonstrate on simulated, phantom, and in vivo data the superiority of the proposed approach. Further, we propose another application of the FC principle, named FC flow, a method to resolve complex crossing regions solely based on diffusion tensor imaging (DTI). The idea is to infer directional information in crossing regions from adjacent anisotropic areas.     

Nonlinear diffusion for orientation estimation

This letter presents an image orientation estimation method which is based on a combination of two techniques： quadrature filtering and nonlinear diffusion. The quadrature filters are used to get the orientation tensors for edges, then the orientation tensors are smoothed through nonlinear diffusion. Experimental resuits and analysis show the robustness of the proposed method.     

基于边缘和互信息法的红外图像配准

用红外图像配准技术对多帧图像进行配准,不仅可以实现平台防抖等电子稳像功能,而且还可以通过对配准后的图像进行多帧累加来积累目标能量,增强图像的性噪比,从而为红外图像弱小目标识别提供帮助。将传统的单纯基于图像整体灰度和基于图像结构特征的配准方法相结合,利用边缘检测得到边缘图像,然后以交互方差为配准测度,以向下加速度法为寻优算法进行图像配准。     

Anisotropic diffusion for image denoising based on diffusion tensors

In this paper, the anisotropic diffusion for image denoising is considered. A new method to construct diffusion tensors is proposed. The tensors obtained by our approach depend on four directional derivatives of the intensity of an image, and hence they are adaptively determined by local image structure. It is shown that the proposed diffusion filter is isotropic in the interior of a region, whereas it is anisotropic at edges. This property of tensors allows us to efficiently remove noise in an image, particularly noise at edges. Several numerical experiments are conducted on both synthetic and real images.     

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.     

Spatially regularized compressed sensing for high angular resolution diffusion imaging

Despite the relative recency of its inception, the theory of compressive sampling (aka compressed sensing) (CS) has already revolutionized multiple areas of applied sciences, a particularly important instance of which is medical imaging. Specifically, the theory has provided a different perspective on the important problem of optimal sampling in magnetic resonance imaging (MRI), with an ever-increasing body of works reporting stable and accurate reconstruction of MRI scans from the number of spectral measurements which would have been deemed unacceptably small as recently as five years ago. In this paper, the theory of CS is employed to palliate the problem of long acquisition times, which is known to be a major impediment to the clinical application of high angular resolution diffusion imaging (HARDI). Specifically, we demonstrate that a substantial reduction in data acquisition times is possible through minimization of the number of diffusion encoding gradients required for reliable reconstruction of HARDI scans. The success of such a minimization is primarily due to the availability of spherical ridgelet transformation, which excels in sparsifying HARDI signals. What makes the resulting reconstruction procedure even more accurate is a combination of the sparsity constraints in the diffusion domain with additional constraints imposed on the estimated diffusion field in the spatial domain. Accordingly, the present paper describes an original way to combine the diffusion- and spatial-domain constraints to achieve a maximal reduction in the number of diffusion measurements, while sacrificing little in terms of reconstruction accuracy. Finally, details are provided on an efficient numerical scheme which can be used to solve the aforementioned reconstruction problem by means of standard and readily available estimation tools. The paper is concluded with experimental results which support the practical value of the proposed reconstruction methodology.     

基于各向异性热扩散方程的SAR图像分割方法

提出了一种非监督SAR图像快速分割算法。该方法利用固体热扩散模型与图像尺度空间的等价性,在SAR图像初始分割的基础上,引入最大后验概率矩阵的各向异性多尺度平滑,在保持图像结构信息的同时滤除斑点噪声对于分割的影响。利用本算法对仿真数据和实测SAR数据分割的结果,均证明了本文方法的有效性。     

红外与微光图像开窗配准融合处理方法

为解决图像实时融合以及红外与微光图像视场大小不一致等问题,提出一种基于仿射变换的红外与微光图像开窗配准融合处理方法。首先以大视场微光图像为背景,对图像中人眼感兴趣的目标区域信息进行开窗,窗口的大小由系统硬件速度和配准融合算法的运算量决定,然后在相同的目标窗口区域,通过双线性插值和仿射变换建立一种红外与微光图像各个像素点的对应匹配关系来完成窗口图像的快速配准与融合,实验对开窗融合结果进行了分析与评价。结果表明,该方法在满足人眼观察需求的条件下既减小图像融合处理数据,又保留了重要的细节融合信息,有效地提高了图像融合的实时性,对兼顾硬件速度与实时性要求的图像融合系统具有较高的应用价值。     

3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization.

This paper deals with topology preservation in three-dimensional (3-D) deformable image registration. This work is a nontrivial extension of, which addresses the case of two-dimensional (2-D) topology preserving mappings. In both cases, the deformation map is modeled as a hierarchical displacement field, decomposed on a multiresolution B-spline basis. Topology preservation is enforced by controlling the Jacobian of the transformation. Finding the optimal displacement parameters amounts to solving a constrained optimization problem: The residual energy between the target image and the deformed source image is minimized under constraints on the Jacobian. Unlike the 2-D case, in which simple linear constraints are derived, the 3-D B-spline-based deformable mapping yields a difficult (until now, unsolved) optimization problem. In this paper, we tackle the problem by resorting to interval analysis optimization techniques. Care is taken to keep the computational burden as low as possible. Results on multipatient 3-D MRI registration illustrate the ability of the method to preserve topology on the continuous image domain.     

Local frequency representations for robust multimodal image registration

Automatic registration of multimodal images involves algorithmically estimating the coordinate transformation required to align the data sets. Most existing methods in the literature are unable to cope with registration of image pairs with large nonoverlapping field of view (FOV). We propose a robust algorithm, based on matching dominant local frequency image representations, which can cope with image pairs with large nonoverlapping FOV. The local frequency representation naturally allows for processing the data at different scales/resolutions, a very desirable property from a computational efficiency view point. Our algorithm involves minimizing-over all rigid/affine transformations--the integral of the squared error (ISE or L2 E) between a Gaussian model of the residual and its true density function. The residual here refers to the difference between the local frequency representations of the transformed (by an unknown transformation) source and target data. We present implementation results for image data sets, which are misaligned magnetic resonance (MR) brain scans obtained using different image acquisition protocols as well as misaligned MR-computed tomography scans. We experimently show that our L2E-based scheme yields better accuracy over the normalized mutual information.     

Spatial transformations of diffusion tensor magnetic resonanceimages

We address the problem of applying spatial transformations (or "image warps") to diffusion tensor magnetic resonance images. The orientational information that these images contain must be handled appropriately when they are transformed spatially during image registration. We present solutions for global transformations of three-dimensional images up to 12-parameter affine complexity and indicate how our methods can be extended for higher order transformations. Several approaches are presented and tested using synthetic data. One method, the preservation of principal direction algorithm, which takes into account shearing, stretching and rigid rotation, is shown to be the most effective. Additional registration experiments are performed on human brain data obtained from a single subject, whose head was imaged in three different orientations within the scanner. All of our methods improve the consistency between registered and target images over na?ve warping algorithms.     

对图像配准误差稳健的分布式星载SAR地面运动目标检测及高精度的测速定位方法

图像配准误差、杂波相关性以及阵列误差等对分布式星载合成孔径雷达地面运动目标检测的性能有很大影响.针对这种情况,研究了一种基于多通道、多像素联合自适应处理的运动目标检测及测速定位联合实现方法,首先将多通道、多像素联合数据等效为一个简单的阵列模型,通过空间投影的方法估计出存在图像配准误差情况下的运动目标真实的导向矢量形式,然后利用最优波束形成的方法在抑制杂波的同时,通过搜索代价函数的峰值来估计动目标的径向速度,从而对其进行重新定位.性能分析及仿真结果表明,此方法大大提高了动目标检测性能及测速定位精度,对图像配准误差具有较强的稳健性.     

基于PDE的自适应各向异性图像配准方法研究

针对传统光流场配准模型会造成图像模糊和细节丢失的问题,提出了一种基于偏微分方程的自适应各向异性配准模型。新模型将具有自适应性的扩散滤波方法引入图像配准,定义具有图像结构保持能力的各向异性扩散函数作为模型的正则项;数据项采用作用于亮度常量假设的非二次惩罚函数以增加模型的稳健性。实验结果表明,新模型能够有效保持图像特征,实现对大脑等复杂图像的有效配准。     

Edge matching rate based on generalized acreage for images registration

This paper proposes an enhanced Edge Matching Rate (EMR) to gain good image registration based on Generalized Acreage (GA). Traditional EMR considers only matched pixels sum without concerns of the cause of unmatched pixels and the relationship between matched pixels. The modified EMR introduces the new concept of generalized acreage to measure the overlaying parts between the target image and the model. It also defines similarity of local occlusion and of local dithering to measure interference degree. Not only edge points are considered but also non-edge points, occlusion, and dithering. Using the same preprocessing, the experiments match images based on traditional EMR and the proposed EMR separately. Based on the proposed EMR the paper achieves more stable registration and higher precision.