Deformable Medical Image Registration: A Survey <s> III. MATCHING CRITERIA <s> Guidance systems designed for neurosurgery, hip surgery, and spine surgery, and for approaches to other anatomy that is relatively rigid can use rigid-body transformations to accomplish image registration. These systems often rely on point-based registration to determine the transformation, and many such systems use attached fiducial markers to establish accurate fiducial points for the registration, the points being established by some fiducial localization process. Accuracy is important to these systems, as is knowledge of the level of that accuracy. An advantage of marker-based systems, particularly those in which the markers are bone-implanted, is that registration error depends only on the fiducial localization error (FLE) and is thus to a large extent independent of the particular object being registered. Thus, it should be possible to predict the clinical accuracy of marker-based systems on the basis of experimental measurements made with phantoms or previous patients. This paper presents two new expressions for estimating registration accuracy of such systems and points out a danger in using a traditional measure of registration accuracy. The new expressions represent fundamental theoretical results with regard to the relationship between localization error and registration error in rigid-body, point-based registration. Rigid-body, point-based registration is achieved by finding the rigid transformation that minimizes "fiducial registration error" (FRE), which is the root mean square distance between homologous fiducials after registration. Closed form solutions have been known since 1966. The expected value (FRE/sup 2/) depends on the number N of fiducials and expected squared value of FLE, (FLE/sup 2/), but in 1979 it was shown that (FRE/sup 2/) is approximately independent of the fiducial configuration C. The importance of this surprising result seems not yet to have been appreciated by the registration community: Poor registrations caused by poor fiducial configurations may appear to be good due to a small FRE value. A more critical and direct measure of registration error is the "target registration error" (TRE), which is the distance between homologous points other than the centroids of fiducials. Efforts to characterize its behavior have been made since 1989. Published numerical simulations have shown that (TRE/sup 2/) is roughly proportional to (FLE/sup 2/)/N and, unlike (FRE/sup 2/), does depend in some way on C. Thus, FRE, which is often used as feedback to the surgeon using a point-based guidance system, is in fact an unreliable indicator of registration-accuracy. In this work the authors derive approximate expressions for (TRE/sup 2/), and for the expected squared alignment error of an individual fiducial. They validate both approximations through numerical simulations. The former expression can be used to provide reliable feedback to the surgeon during surgery and to guide the placement of markers before surgery, or at least to warn the surgeon of potentially dangerous fiducial placements; the latter expression leads to a surprising conclusion: Expected registration accuracy (TRE) is worst near the fiducials that are most closely aligned! This revelation should be of particular concern to surgeons who may at present be relying on fiducial alignment as an indicator of the accuracy of their point-based guidance systems. <s> BIB001 </s> Deformable Medical Image Registration: A Survey <s> III. MATCHING CRITERIA <s> Motivated by the problem of retinal image registration, this paper introduces and analyzes a new registration algorithm called Dual-Bootstrap Iterative Closest Point (Dual-Bootstrap ICP). The approach is to start from one or more initial, low-order estimates that are only accurate in small image regions, called bootstrap regions. In each bootstrap region, the algorithm iteratively: 1) refines the transformation estimate using constraints only from within the bootstrap region; 2) expands the bootstrap region; and 3) tests to see if a higher order transformation model can be used, stopping when the region expands to cover the overlap between images. Steps 1): and 3), the bootstrap steps, are governed by the covariance matrix of the estimated transformation. Estimation refinement [Step 2)] uses a novel robust version of the ICP algorithm. In registering retinal image pairs, Dual-Bootstrap ICP is initialized by automatically matching individual vascular landmarks, and it aligns images based on detected blood vessel centerlines. The resulting quadratic transformations are accurate to less than a pixel. On tests involving approximately 6000 image pairs, it successfully registered 99.5% of the pairs containing at least one common landmark, and 100% of the pairs containing at least one common landmark and at least 35% image overlap. <s> BIB002 </s> Deformable Medical Image Registration: A Survey <s> III. MATCHING CRITERIA <s> A crucial part of image-guided therapy is registration of preoperative and intraoperative images, by which the precise position and orientation of the patient's anatomy is determined in three dimensions. This paper presents a novel approach to register three-dimensional (3-D) computed tomography (CT) or magnetic resonance (MR) images to one or more two-dimensional (2-D) X-ray images. The registration is based solely on the information present in 2-D and 3-D images. It does not require fiducial markers, intraoperative X-ray image segmentation, or timely construction of digitally reconstructed radiographs. The originality of the approach is in using normals to bone surfaces, preoperatively defined in 3-D MR or CT data, and gradients of intraoperative X-ray images at locations defined by the X-ray source and 3-D surface points. The registration is concerned with finding the rigid transformation of a CT or MR volume, which provides the best match between surface normals and back projected gradients, considering their amplitudes and orientations. We have thoroughly validated our registration method by using MR, CT, and X-ray images of a cadaveric lumbar spine phantom for which "gold standard" registration was established by means of fiducial markers, and its accuracy assessed by target registration error. Volumes of interest, containing single vertebrae L1-L5, were registered to different pairs of X-ray images from different starting positions, chosen randomly and uniformly around the "gold standard" position. CT/X-ray (MR/ X-ray) registration, which is fast, was successful in more than 91% (82% except for L1) of trials if started from the "gold standard" translated or rotated for less than 6 mm or 17 degrees (3 mm or 8.6 degrees), respectively. Root-mean-square target registration errors were below 0.5 mm for the CT to X-ray registration and below 1.4 mm for MR to X-ray registration. <s> BIB003
We can distinguish three groups of registration methods according to how they exploit the available information to drive the matching process (see Fig. 2 ). On one hand, geometric methods opt for the establishment of correspondences between landmarks. The landmarks are assumed to be placed in salient image locations which are considered to correspond to meaningful anatomical locations. The underlying assumption is that saliency in the image level is equivalent to anatomical regions of interest. Geometric registration is robust with respect to the initial conditions and the existence of large deformations. The solution of the registration problem is obtained in a relatively straightforward way once landmarks have been extracted. However, locating reliable landmarks is an open problem and an active topic of research. Most importantly, the sparse set of directly obtained correspondences gives rise to the need for extrapolation. Interpolation results in a decrease in accuracy as the distance from the landmarks increases. The interest regarding geometric methods has decreased during the past decade. Nevertheless, geometric methods constitute a reliable approach for specific applications. They are of interest when intensity information is undermined due to the presence of pathologies while geometric structures remain stable (e.g., retina registration BIB002 ). Geometric registration has also important applications in image-guided interventions BIB001 , BIB003 . On the other hand, iconic methods, often referred to as either voxel-based or intensity-based methods, quantify the alignment of the images by evaluating an intensity-based criterion over the whole image domain. When compared to the geometric methods, this approach has the potential to better quantify and represent the accuracy of the estimated dense deformation field. Nonetheless, it comes at the cost of increased computational expense. Where geometric methods use a small subset of image voxels to evaluate the matching criterion, iconic methods may use them all. Moreover, due to the fact that salient points are not explicitly taken into account by the matching criterion, the important information they contain is not fully exploited to drive the registration. In addition, initial conditions greatly influence the quality of the obtained result due to the nonconvexity of the problem. Hybrid methods combine both types of information in an effort to get the best of both worlds. 