Fast Diffeomorphic Image Registration via Fourier-Approximated Lie Algebras

International Journal of Computer Vision - This paper introduces Fourier-approximated Lie algebras for shooting (FLASH), a fast geodesic shooting algorithm for diffeomorphic image registration. We...     

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.     

医学影像非刚性配准的并行加速及优化

三次B样条函数拟合小形变需要大量控制点,且非刚性配准的迭代算法和归一化互信息计算量巨大,使得非刚性配准缓慢.为了提高配准速度,提出基于B样条函数的二级并行算法,其中对归一化互信息使用数据并行算法;对梯度下降流使用任务并行算法,并将数据并行算法嵌入到任务并行算法中.为减少计算量,提出图像多层次局部熵提取自由形变场活动控制点的算法,使活动控制点仅分布于待配准的目标之上,并使用B样条系数的快速算法进一步减少计算量;对由于控制点分布优化造成的各线程块并行计算量不平衡的问题,使用类似于Greedy算法的计算平衡算法使各线程块的计算量均衡.实验结果表明,使用B样条系数快速算法可以减少约50％的B样条系数计算量;与串行算法相比,使用二级并行算法以及控制点分布优化算法可以达到60～80倍的加速效果;比现有的数据并行配准算法可提速约6倍.     

Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation

In the context of large deformations by diffeomorphisms, we propose a new diffeomorphic registration algorithm for 3D images that performs the optimization directly on the set of geodesic flows. The key contribution of this work is to provide an accurate estimation of the so-called initial momentum, which is a scalar function encoding the optimal deformation between two images through the Hamiltonian equations of geodesics. Since the initial momentum has proven to be a key tool for statistics on shape spaces, our algorithm enables more reliable statistical comparisons for 3D images.     

Optimal Mass Transport for Registration and Warping

Image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times. In this paper we present a method for computing elastic registration and warping maps based on the Monge–Kantorovich theory of optimal mass transport. This mass transport method has a number of important characteristics. First, it is parameter free. Moreover, it utilizes all of the grayscale data in both images, places the two images on equal footing and is symmetrical: the optimal mapping from image A to image B being the inverse of the optimal mapping from B to A. The method does not require that landmarks be specified, and the minimizer of the distance functional involved is unique; there are no other local minimizers. Finally, optimal transport naturally takes into account changes in density that result from changes in area or volume. Although the optimal transport method is certainly not appropriate for all registration and warping problems, this mass preservation property makes the Monge–Kantorovich approach quite useful for an interesting class of warping problems, as we show in this paper. Our method for finding the registration mapping is based on a partial differential equation approach to the minimization of the L ² Kantorovich–Wasserstein or Earth Mover's Distance under a mass preservation constraint. We show how this approach leads to practical algorithms, and demonstrate our method with a number of examples, including those from the medical field. We also extend this method to take into account changes in intensity, and show that it is well suited for applications such as image morphing.     

Image Registration for Digital Subtraction Angiography

In clinical practice, Digital Subtraction Angiography (DSA) is a powerful technique for the visualization of blood vessels in the human body. The diagnostic relevance of the images is often reduced by artifacts which arise from the misalignment of successive images in the sequence, due to patient motion. In order to improve the quality of the subtraction images, several registration techniques have been proposed. However, because of the required computation times, it has never led to algorithms that are fast enough so as to be acceptable for integration in clinical applications. In this paper, a new approach to the registration of digital angiographic images is proposed. It involves an edge-based selection of control points for which the displacement is computed by means of template matching, and from which the complete displacement vector field is constructed by means of interpolation. The final warping of the images according to the calculated displacement vector field is performed real-time by graphics hardware. Experimental results with several clinical data sets show that the proposed algorithm is both effective and very fast.     

一种高效的图像匹配算法

兼顾算法的精度和效率两个方面,基于图像特征的图像匹配算法,逐渐成为众多学者研究的热点.文中提出了将多分辨率和极线约束与相关法相结合的图像匹配方法.该方法采用金字塔分层和极线约束来弥补相关匹配带来运算量大的不足,克服了图像匹配中精度低和速度慢的缺点.通过实验验证该方法不仅能够有效地缩短匹配时间,还能达到较高的匹配精度.     

基于GPU的遥感图像配准并行程序设计与存储优化

遥感图像配准是遥感图像应用的一个重要处理步骤.随着遥感图像数据规模与遥感图像配准算法计算复杂度的增大,遥感图像配准面临着处理速度的挑战.最近几年,GPU计算能力得到极大提升,面向通用计算领域得到了快速发展.结合GPU面向通用计算领域的优势与遥感图像配准面临的处理速度问题,研究了GPU加速处理遥感图像配准的算法.选取计算量大计算精度高的基于互信息小波分解配准算法进行GPU并行设计,提出了GPU并行设计模型;同时选取GPU程序常用面向存储级的优化策略应用于遥感图像配准GPU程序,并利用CUDA(compute unified device architecture)编程语言在nVIDIA Tesla M2050GPU上进行了实验.实验结果表明,提出的并行设计模型与面向存储级的优化策略能够很好地适用于遥感图像配准领域,最大加速比达到了19.9倍.研究表明GPU通用计算技术在遥感图像处理领域具有广阔的应用前景.     

干涉合成孔径雷达复图像配准解析搜索方法

图像配准是干涉SAR数据处理中关键步骤之一,它的处理精度直接影响着高程重建的质量.为了克服经典方法带来误差的影响,本文构建了一种解析代价函数,利用双迭代优化算法与弦割法求取亚像元级偏移量,实现了在连续域内搜索,避免了传统的在离散域搜索带来的误差,提高了配准精度,在插值意义上,配准精度达到最优.基于实测数据的实验结果表明,该算法具有较高精度.     

基于对等差异进化算法的医学图像配准方法

差异进化算法是一种简单、可靠和有效的全局优化算法.本文在差异进化算法的基础上,将对等学习方法应用到种群初始化和进化中,提出一种基于对等差异进化算法的图像配准方法.该方法在种群进化过程中由对等跃变率决定是否生成对等种群,文中对不同对等跃变率及动态对等跃变率的不同情况进行三维医学图像配准实验.实验结果表明,只要选取合适的对等跃变率,该方法比传统差异进化算法的图像配准具有更高的精度和更好的稳定性;并且线性递减跃变率的对等差异进化配准算法比固定对等跃变率和线性递增跃变率的配准更精确、更稳定.     

Image Registration, Optical Flow and Local Rigidity

We address the theoretical problems of optical flow estimation and image registration in a multi-scale framework in any dimension. Much work has been done based on the minimization of a distance between a first image and a second image after applying deformation or motion field. Usually no justification is given about convergence of the algorithm used. We start by showing, in the translation case, that convergence to the global minimum is made easier by applying a low pass filter to the images hence making the energy convex enough. In order to keep convergence to the global minimum in the general case, we introduce a local rigidity hypothesis on the unknown deformation. We then deduce a new natural motion constraint equation (MCE) at each scale using the Dirichlet low pass operator. This transforms the problem to solving the energy minimization in a finite dimensional subspace of approximation obtained through Fourier Decomposition. This allows us to derive sufficient conditions for convergence of a new multi-scale and iterative motion estimation/registration scheme towards a global minimum of the usual nonlinear energy instead of a local minimum as did all previous methods. Although some of the sufficient conditions cannot always be fulfilled because of the absence of the necessary a priori knowledge on the motion, we use an implicit approach. We illustrate our method by showing results on synthetic and real examples in dimension 1 (signal matching, Stereo) and 2 (Motion, Registration, Morphing), including large deformation experiments.     

一种基于特征的SAR图像自动配准方法

由于SAR图像固有的相干斑噪声的影响,使得SAR图像的自动配准不能直接使用光学遥感图像自动配准.基于特征的SAR图像配准方法是一种有效的配准方法,但是特征的提取一直以来是一个很难解决的问题.针对SAR图像自身的特性提出了一种基于特征的SAR图像自动配准方法.首先进行了对SAIl图像进行了合适的区域分割,然后利用不变性特征进行区域匹配,最后求取扩展质心作为匹配控制点.通过对真实SAR图像进行实验,取得了较好的配准结果,充分证明了算法的有效性.     

基于粗配准和互信息的脑部MR图像配准算法

现有的医学图像配准算法一般都存在需要人工介入、配准时间过长等问题.为了寻找快速、精确、鲁棒性强的自动配准算法,在采用主轴矩方法进行脑部MR(核磁共振)图像的初始配准的基础上,提出局部搜索算法对图像求得更精确的配准.实验表明,该方法的配准精度和现有的Powell算法都可以达到亚像素级,但局部搜索方法和Powell算法相比较,平均配准时间大大缩短;即便和采用了主轴矩粗配准的Powell算法相比较,配准效率也提高了一倍左右.主轴矩粗配准算法提高了配准效率,局部搜索算法则保证了配准的精度.     

Mesh Topological Optimization for Improving Piecewise-Linear Image Registration

This paper presents a mutual-information based optimization algorithm for improving piecewise-linear (PWL) image registration. PWL-registration techniques, which are well-suited for registering images of the same scene with relative local distortions, divide the images in conjugate triangular patches that are individually mapped through affine transformations. For this process to be accurate, each pair of corresponding image triangles must be the projections of a planar surface in space; otherwise, the registration incurs in errors that appear in the resultant registered image as local distortions (distorted shapes, broken lines, etc.). Given an initial triangular mesh onto the images, we propose an optimization algorithm that, by swapping edges, modifies the mesh topology looking for an improvement in the registration. For detecting the edges to be swapped we employ a cost function based on the mutual information (MI), a metric for registration consistency more robust to image radiometric differences than other well-known metrics such as normalized cross correlation (NCC). The proposed method has been successfully tested with different sets of test images, both synthetic and real, acquired from different angles and lighting conditions.     

A Full Curvature Based Algorithm for Image Registration

Image registration, i.e., finding an optimal displacement field u which minimizes a distance functional D(u) is known to be an ill-posed problem. In this paper a novel variational image registration method is presented, which matches two images acquired from the same or from different medical imaging modalities. The approach proposed here is also independent of the image dimension. The proposed variational penalty against oscillations in the solutions is the standard H²(Ω) Sobolev semi-inner product for each component of the displacement. We investigate the associated Euler-Lagrange equation of the energy functional. Furthermore, we approach the solution of the underlying system of biharmonic differential equations with higher order boundary conditions as the steady-state solution of a parabolic partial differential equation (PDE). One of the important aspects of this approach is that the kernel of the Euler-Lagrange equation is spanned by all rigid motions. Hence, the presented approach includes a rigid alignment. Experimental results on both synthetic and real images are presented to illustrate the capabilities of the proposed approach. Stefan Henn obtained his diploma (1997) and his Ph.D. in mathematics (2001), both from the Heinrich-Heine University (HHU) of Düsseldorf (Germany). From 1997–1999 he had a researcher position at the Institute for Brain Research at the HHU Düsseldorf. Since 1999 he is a research assistant at the Institute of Mathematics at the HHU Düsseldorf. He received the SIAM outstanding paper prize in 2003 for the paper (Iterative Multigrid Regularization Techniques for Image Matching, SIAM Journal on Scientific Computing, 23(4), pp. 1077-1093). His research interests include Multiscale methods in Scientific Computing and Image Processing, nonlinear large-scale optimization, and numerical analysis of partial differential equations.     

Adaptive Stochastic Gradient Descent Optimisation for Image Registration

We present a stochastic gradient descent optimisation method for image registration with adaptive step size prediction. The method is based on the theoretical work by Plakhov and Cruz (J. Math. Sci. 120(1):964–973, 2004). Our main methodological contribution is the derivation of an image-driven mechanism to select proper values for the most important free parameters of the method. The selection mechanism employs general characteristics of the cost functions that commonly occur in intensity-based image registration. Also, the theoretical convergence conditions of the optimisation method are taken into account. The proposed adaptive stochastic gradient descent (ASGD) method is compared to a standard, non-adaptive Robbins-Monro (RM) algorithm. Both ASGD and RM employ a stochastic subsampling technique to accelerate the optimisation process. Registration experiments were performed on 3D CT and MR data of the head, lungs, and prostate, using various similarity measures and transformation models. The results indicate that ASGD is robust to these variations in the registration framework and is less sensitive to the settings of the user-defined parameters than RM. The main disadvantage of RM is the need for a predetermined step size function. The ASGD method provides a solution for that issue.     

基于SURF特征的高动态范围图像配准算法

同一场景的多曝光图像序列被广泛的应用于高动态范围图像（HighDynamicRangeImage）的合成中。但是,在多曝光图像序列的采集过程中,相机抖动、场景运动等因素会对合成图像的质量产生较大的影响。此外,离镜头较近的大目标往往由于显著的三维形状,在序列图中产生较大的视差效应,也会对合成图像产生消极影响。该文提出一种基于SURF特征点的三维图像配准算法,实验证明该算法在近距离大目标情形下较之传统配准算法MTB（MeanThresholdBitmap,均值二值化）可以获得更好效果。     

一种快速稳健的图像配准算法

本文对图像配准问题进行了研究,提出了一种快速、稳健的基于特征点匹配的配准算法。采用小波变换建立图像金字塔,从分辨率最低的图像层开始进行特征点匹配,在次一层匹配时以上层匹配结果为粗值,在原始图像上得到初始匹配点后采用RANSAC算法稳健估计变换矩阵H;为了提高配准算法的精度,采用变换矩阵H引导两幅原始图像上的所有特征点重新进行匹配,对得到的匹配点集重新用RANSAC算法估计变换矩阵,并采用LM非线性优化算法进一步优化。通过实验分析对比,本文的算法比原算法速度更快,更稳健。