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.     

Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity

In this paper a variational method for registering or mapping like points in medical images is proposed and analyzed. The proposed variational principle penalizes a departure from rigidity and thereby provides a natural generalization of strictly rigid registration techniques used widely in medical contexts. Difficulties with finite displacements are elucidated, and alternative infinitesimal displacements are developed for an optical flow formulation which also permits image interpolation. The variational penalty against non-rigid flows provides sufficient regularization for a well-posed minimization and yet does not rule out irregular registrations corresponding to an object excision. Image similarity is measured by penalizing the variation of intensity along optical flow trajectories. The approach proposed here is also independent of the order in which images are taken. For computations, a lumped finite element Eulerian discretization is used to solve for the optical flow. Also, a Lagrangian integration of the intensity along optical flow trajectories has the advantage of prohibiting diffusion among trajectories which would otherwise blur interpolated images. The subtle aspects of the methods developed are illustrated in terms of simple examples, and the approach is finally applied to the registration of magnetic resonance images.Supported by the Fonds zur Förderung der wissenschaftliche Forschung under SFB 03, Optimierung und Kontrolle.Stephen Keeling was born in 1956 in Louisville, KY, USA. He received the B.S. in Biology and Chemistry from Eastern Kentucky University in 1978, the M.S. in Biomedical Engineering (bioelectric phenomena) from Case Western Reserve University in 1981, and the Ph.D. in Mathematics (numerical analysis for PDEs) from the University of Tennessee in 1986. His postdoctoral research at ICASE and at Vanderbilt University focused on active noise control until 1989. From 1989 until 1998 he worked as Senior and then Principal Scientist in the CFD Group at the Arnold Engineering Development Center specializing in flow control and imaging. From 1998 until 2001 he worked with the mathematics and radiology faculties of the University of Graz as a Research Associate of the Special Research Center on Optimization and Control. Since 2001 he is Assistant Professor at the Institute of Mathematics of the University of Graz. His research interests include early vision problems in medical imaging with emphasis on MRI applications.Wolfgang Ring was born on November 6, 1965 in Zeltweg, Austria. He received his Masters Degree from the University of Graz in 1991 and his Ph.D. in Mathematics from the Technical University of Graz in 1994. He worked as an Assistant Professor at the Institute of Mathematics at the Technical University of Graz between 1993 and 1996. Since 1997 he is Assistant Professor at the Institute of Mathematics at the University of Graz. His main scientific interests are geometric inverse problems, mathematical imaging and optimal shape design.     

基于改进光流场模型的医学图像配准方法

基于光流场模型的图像配准方法计算简单快速,但采用原始光流场模型进行图像配准会使图像出现严重的模糊导致不能使用。提出了对原始光流场模型的正则项进行改进,同时引入运动模糊图像复原算法,改进的算法改善了原始光流场模型造成的图像模糊。实验结果表明,基于改进光流场模型的医学图像配准算法配准结果准确,具有较快的配准速度。     

基于改进的SIFT算法的红外图像配准

电路板红外图像具有分辨率低、对比度低、信噪比低、视觉效果模糊的特点,目前的图像配准算法用于电路板红外图像配准时,运算时间长且匹配准确度低.针对电路板红外图像的特点,梳理了图像配准方面的国内外研究现状,分析了SIFT算法的基本原理,对原有的SIFT算法进行了修改.对特征点的提取方式进行了改进,减少了不必要的特征点;改进了...     

Gradient-based approach for fine registration of panorama images

This paper studies the application of gradient-based motion detection techniques (i.e., optical flow methods) for registration of adjacent images taken using a hand-held camera for the purposes of building a panorama. A general 8-parameter model or a more compact 3-parameter model is commonly used for transformation estimation. However, both models are approximations to the real situation when viewpoint position is not absolutely fixed but includes a small translation, and thus distortion and blurring are sometimes present in the final registration results. This paper proposes a new 5-parameter model that shows better result and has less strict requirement on good choice of unknown initial parameters. An analysis of disparity recovery range and its enlargement using Gaussian filter is also given.     

基于Co-motion的可见光--热红外图像序列自动配准算法

提出了一种基于Co-motion的可见光--热红外图像序列自动配准方法, 引入Co-motion运动统计特征来解决异源图像序列配准问题, 从而避开了异源图像相似图像特征提取和精确运动检测的难题. 由于可见光和热红外成像机理不同, 在运用运动统计特征时, 会面临与同源配准不同的诸多问题, 如难以提取相似前景、大量外点干扰和易受大尺度变化的影响等. 本文通过对所面临难题的分析 提出了适合于异源图像序列配准的同名点对选取方法和外点去除方法, 并精确迭代优化变换模型. 对俄亥俄州大学红外--可见光数据库和自建数据库共8组数据的实验分析结果表明, 该算法在大尺度、旋转、平移及视场角变化下均能精确配准.     

基于归一化SIFT算法的不同光学影像配准

由不同传感器摄取的遥感影像因成像模式、拍摄角度和分辨率不同,给两者之间的配准造成困难。针对该问题,提出归一化SIFT算法,通过对SIFT描述子归一化的处理,降低不同光学影像色调差异大的影响,并通过与最小二乘法和双线性内插法的结合,完成自动配准。选取角度和尺度偏差较大的SPOT与ASTER影像、ASTER与TM影像2组数据进行实验。结果证明,该算法鲁棒性强,配准精度高。     

一种新的面向超分辨率的图像配准方法

图像配准是超分辨率图像恢复的关键技术之一,现有的图像配准算法没有考虑目标运动幅度变化大和目标在视场中远离镜头或靠近镜头的情况,针对于此,该文提出了基于运动轨迹的面向超分辨率图像恢复的配准方法,用以解决目标运动幅度变化大和目标分辨率改变情况下的图像配准问题,试验表明该文提出的算法能够有效地解决实际问题,效果很好。     

基于全局运动模型配准的图像超分辨重建

把全局运动模型配准算法运用到序列图像超分辨重建中,通过与优化的基于频域的配准法进行对比,在运动模型可以准确地反映物体运动状态的情况下,该算法能够更精确地估计运动参数,从而确保重建后的高分辨率图像拥有更多细节信息。同时,阐述了参与重建的低分辨率图像帧数越多,重建精度会越高,但随着帧数的增多,重建误差降低幅度会越低,而算法复杂度及其耗时会过多地增加,因此提出应根据对重建精度的要求而确定参与重建的低分辨率图像的帧数。     

非刚性医学图像配准研究综述

非刚性配准技术是医学图像配准中的一个重要研究课题,是非刚性组织配准,不同个体之间的配准以及个体同图谱配准的基础。该文提出了多项式法、样条函数法等基于空间变换的配准方法,以及弹性模型、粘性流体模型和光流场模型等基于物理模型的配准方法两大类方法。同刚性配准相比,非刚性配准技术还不成熟,计算效率和稳定性还需要进一步提高,仍是一个非常活跃的研究领域。     

Curvature Based Image Registration

A fully automated, non-rigid image registration algorithm is presented. The deformation field is found by minimizing a suitable measure subject to a curvature based constraint. It is a well-known fact that non-rigid image registration techniques may converge poorly if the initial position is not sufficiently near to the solution. A common approach to address this problem is to perform a time consuming rigid pre-registration step. In this paper we show that the new curvature registration not only produces accurate and smooth solutions but also allows for an automatic rigid alignment. Thus, in contrast to other popular registration schemes, the new method no longer requires a pre-registration step. Furthermore, we present an implementation of the new scheme based on the numerical solution of the underlying Euler-Lagrange equations. The real discrete cosine transform is the backbone of our implementation and leads to a stable and fast O(N log N) algorithm, where N denotes the number of voxels. Finally, we report on some numerical test runs.     

一种应用于图像配准中大尺度位移估计的改进光流法

本文介绍了一种改进的光流法来对图像进行配准. 其新颖之处在于, 引入了一种初始运动估计器 (扩展相位相关法) 来改善光流法的性能. 光流法配准可达到亚像素级精度, 并能计算某些复杂的运动模式, 如 chirping 和 tilting, 但它处理大尺度位移的能力较弱. 相对而言, 因为扩展相位相关法可在像素级精度上对大尺度的旋转和平移进行估计, 且计算效率较高, 所以, 它可以作为光流法一种较好的运动预估器. 实验表明, 这种改进的光流法可显著提高配准精度, 特别是对存在大尺度位移的图像, 并且对随机噪声不敏感.     

Correspondence-free Structure from Motion

We present a novel approach for the estimation of 3D-motion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a similarity function on feature pairs with a Dirac function embedding the epipolar constraint. The maxima in this five dimensional motion space will correspond to compatible rigid motions. The main novelty is in the realization that the Radon transform is a filtering operator: If we assume that the similarity and Dirac functions are defined on spheres and the epipolar constraint is a group action of rotations on spheres, then the Radon transform is a correlation integral. We propose a new algorithm to compute this integral from the spherical Fourier transform of the similarity and Dirac functions. Generating the similarity function now becomes a preprocessing step which reduces the complexity of the Radon computation by a factor equal to the number of feature pairs processed. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions. The authors are grateful for support through the following grants: NSF-IIS-0083209, NSF-IIS-0121293, NSF-EIA-0324977, NSF-CNS-0423891, NSF-IIS-0431070, and ARO/MURI DAAD19-02-1-0383. The author is grateful for the generous support of the ARO MURI program (DAAD-19-02-1-0383) while at U. C. Berkeley.     

Image Registration Using Wavelet-Based Motion Model

An image registration algorithm is developed to estimate dense motion vectors between two images using the coarse-to-fine wavelet-based motion model. This motion model is described by a linear combination of hierarchical basis functions proposed by Cai and Wang (SIAM Numer. Anal., 33(3):937–970, 1996). The coarser-scale basis function has larger support while the finer-scale basis function has smaller support. With these variable supports in full resolution, the basis functions serve as large-to-small windows so that the global and local information can be incorporated concurrently for image matching, especially for recovering motion vectors containing large displacements. To evaluate the accuracy of the wavelet-based method, two sets of test images were experimented using both the wavelet-based method and a leading pyramid spline-based method by Szeliski et al. (International Journal of Computer Vision, 22(3):199–218, 1996). One set of test images, taken from Barron et al. (International Journal of Computer Vision, 12:43–77, 1994), contains small displacements. The other set exhibits low texture or spatial aliasing after image blurring and contains large displacements. The experimental results showed that our wavelet-based method produced better motion estimates with error distributions having a smaller mean and smaller standard deviation.     

Geometrical Analysis of Two Sets of 3D Correspondence Data Patterns for the Registration of Free-Form Shapes

The iterative closest point (ICP) algorithm represents an efficient method to establish an initial set of possible correspondences between two overlapping range images. An inherent limitation of the algorithm is the introduction of false matches, a problem that has been tackled by a variety of schemes mainly based on local invariants described in a single coordinate frame. In this paper we propose using global rigid motion constraints to deal with false matches. Such constraints are derived from geometric properties of correspondence vectors bridging the points described in different coordinate frames before and after a rigid motion. In order to accurately and efficiently estimate the parameters of interest, the Monte Carlo resampling technique is used and motion parameter candidates are then synthesised by a median filter. The proposed algorithm is validated based on both synthetic data and real range images. Experimental results show that the proposed algorithm has advantages over existing registration methods concerning robustness, accuracy, and efficiency.     

基于卫星图像数据的大范围风场重建

在机载气象雷达早期开发中,数值天气模型是一个非常重要的环节,而天气模型中风场的准确性直接影响整个模型的准确性。为解决数值天气模型中的连续图像运动分析问题,提出一种基于运动场Helmholtz分解的低维流体运动估计方法。通过少量涡流粒子和源粒子的演化,得到光流场的低维参数化表达,即非旋旋转量和螺旋量基函数的线性组合,其中基函数由格林核梯度构成,系数值和基函数参数通过最小化代价函数获得。实验结果表明,与传统光流法相比,该方法的计算速度快了近4倍,风场更为准确地反映了实际的天气状况,在风场反演中更为可靠。     

基于迭代重加权的非刚性图像配准

非刚性图像配准问题是当今重要的研究课题. 本文提出一类基于能量最小化方法的非刚性图像配准模型, 其中包括单模态和多模态两个模型. 在单模态模型中,正则项采用迭代重加权的L2范数度量, 一方面克服了迭代收敛不同步的问题, 另一方面使新模型既能保持图像的边缘几何结构, 又能避免块效应的产生. 在多模态模型中, 不同模态的图像被转化为同一模态进行处理, 提高了配准的效率. 在模型求解方面, 利用算子分裂和交替最小化的方法, 将原问题转化为阈值和加性算子分裂的迭代格式进行求解. 数值实验表明, 本文的方法对含噪以及变形较大的图像都能实现较好的配准.     

基于自适应薄板样条全变分的肺CT/PET图像配准

全变分正则项虽然能够在具有滑移运动的肺等胸腹部器官图像配准时校正边界不连续位移场，但仍然无法保留图像的局部特征，损失配准精度。针对肺图像CT单模配准和CT/PET双模配准，通过像素点空间位置权重将薄板样条能量算子与全变分算子进行空间加权建立自适应薄板样条全变分正则项。然后，将正则项与CRMI相似性测度以及L-BFGS优化方法结合建立非刚性配准算法。通过DIR-Lab 4D-CT公共数据集和CT/PET临床数据集上的实验结果表明，提出的方法能够在保证边界不连续运动的同时保证图像内部的平滑性，具有更高的配准精度。     

运动估计与运动补偿在电子稳像中的应用

电子稳像系统的核心是运动估计和运动补偿。为了提供运动估计的精度和降低时间开销，达到实时应用的要求，该文提出了基于宏块的步进全局运动估计算法，获得图像序列的全局运动矢量；给出了一个新的应用于电子稳像系统中运动估计与运动补偿模块的运动估计、运动补偿原理框图；采用两步补偿算法完成对图像序列的运动补偿，得到稳定的图像序列输出。仿真结果表明，采用的方法是高效、可行的。