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1、1.Elastic registration:The estimation of the geometric deformation is reduced to the search for the best parameters. This idea were introduced by Bajcsy et al10 and is often called elastic registration.In the elastic registration, the images are viewed as pieces of a rubber sheet, on which external
2、forces stretching the image and the internal forces defined by stiffness or smoothness constraints are applied to bring them into alignment with the minimal amount of bending and Stretching. The feature matching and mapping function design stepsof the registration are done simultaneously. This is on
3、e of advantages ofthe elastic methods, because feature descriptors invariant to complicated deformations are not known and the feature correspondence is difficult to establish in the traditional way. The registration is achieved by locating the minimum energy in an iterative fashion. The external fo
4、rces can be derived from the local optimization of the similarity function which is defined by the intensity values or the correspondence of boundary structures among others.Disadvantage of elastic registration is in situations when image deformations are very localized. 弹性形变的弹性形变的 百度百科定义百度百科定义 在外力的
5、作用下，物体发生形变，当外力撤消后，物体能恢复原状，则这样的形变叫做弹性形变，如弹簧的形变等。 在外力的作用下，物体发生形变，当外力撤去后，物体不能恢复原状，则称这样的形变叫做塑性形变，如橡皮泥的形变等。因物体弹性形变弹性形变受力情况不同，在弹性限度内，弹性形变有四种基本类型：即拉伸和压缩形变；切变；弯曲形变和扭转形变。2.Affine registration(维基百科维基百科)In geometry, an affine transformation or affine map 1 or an affinity (from the Latin, affinis, “connected wi
6、th“) is a transformation which preserves straight lines and ratios of distances between points lying on a straight lineAn affine transformation does not necessarily preserve angles or lengths. Translation, geometric contraction, expansion, dilation, reflection, rotation, shear, similarity transforma
7、tions, and spiral similarities are all affine transformations, as are their combinations. It is equivalent to a translation followed by a linear transformation.3 Non-rigid transformation/ registration 维基百科维基百科The second category of transformations allow elastic or nonrigid transformations.（在这位维基百科编辑
8、人的认识中个，非刚性就是弹性） These transformations are capable of locally warping the target image to align with the reference image. Nonrigid transformations include radial basis functions (thin-plate or surface splines, multiquadrics, and compactly-supported transformations2), physical continuum models (viscou
9、s fluids), and large deformation models (diffeomorphisms).4.四种定义的区别四种定义的区别 (1) 刚性的, (2) 仿射的, (3) 投影的, (4) 弹性的。不考虑坐标轴尺度缩放时, 如果仅存在坐标轴的平移和旋转, 图像的坐标变换是刚体变换, 这时直线的平行性和垂直性在映射后保持不变。如果只能保持平行性, 不能保持垂直性, 坐标变换是仿射变换。如果只能将直线映射成直线, 平行性和垂直线都不能保持时, 坐标变换是投影变换。如果将直线映射成曲线, 坐标变换就是弹性变换。这四类变换依次包含, 即弹性变换包含投影变换, 投影变换包含仿射变换
10、, 仿射变换包含刚体变换。3D 的刚体或仿射变换用一个常数矩阵 A 表示, 刚体变换的 A 可表示为三个参数的平移矢量 t 和三个参数决定的 3*3 的旋转矩阵R , M B = R * M A + t, 三次平移的顺序对 A 没有影响, R 有九种表示方法, 最流行的是 Eu ler 角表示法。用 U,H,7 角表示依次围绕X、Y、Z 坐标轴的连续旋转。变换的域有局部和全局两类。如果交换应用于整个图像, 那么变换是全局的, 如果图像的每个子块都有自已定义的变换, 那么变换就是局部的。刚体变换和仿射变换是全局的, 弹性变换是局部的, 仿射变换一般应用在求解图像的坐标轴尺度因子, 投影变换极少见
11、于文献报道。局部交换不能直接使用, 而是在全局变换的基础上, 使用在整个图像中感兴趣的局部区域(子图像)。局部的仿射和投影变换在文献中少见报道, 局部刚体变换经常是嵌入局部弹性变换。在医学图像配准中, 解剖结构可视为刚体或近似刚体, 最常用到的变换是全局刚体变换, 这样只需求解相对较少的变换参数, 最常应用的场合是头部的图像配准。平移变换是一种“刚体变换”，平移不会改变图形的形状。 “旋转变换”也是刚体变换，而“缩放”、 “错切”都是会改变图形形状的。5. 非刚性变换和刚性变换非刚性变换和刚性变换刚性变换即为仿射变换。非刚性变换包括：6.Evaluation on Similarity Mea
12、sures of a Surface-to-Image Registration Technique for Ultrasound Images文章阅读，一般性总结文章阅读，一般性总结It shown that the selection of the similarity function is related to the ultrasound characteristics of the object to be registered.the key to the intensity-based techniques is that there must be a comparable
13、percentage of mutual information existing in both of the images;Different from the traditional surface-to-surface and image-to-image registration patterns, the surface-to-image registration technique would be a good compromise between simplicity and flexibility.This gave us an idea that the similari
14、ty measure behaves differently when it applied to different organs.To evaluate the algorithms performance, we first conducted a self-registration test, i.e., registering the pubic arch surface segmented from TRUS image to the image itself. Intuitively, this surface was used not only as the input from other modalities, but also as the “ground truth” of the output. This manner established a so-called“bronze truth” 12 of the transformation.
