836 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 15, NO. 6, DECEMBER 1996 Registration of 3-D Images Using Weighted Geometrical Features Calvin R. Maurer, Jr.,* Student Member, IEEE, Georges B. Aboutanos, Student Member, IEEE, Benoit M. Dawant, Member, IEEE, Robert J. Maciunas, J. Michael Fitzpatrick, Member, IEEE Abstruct- In this paper, we present a weighted geometrical feature (WGF) registration algorithm. Its efficacy is demonstrated by combining points and a surface. The technique is an extension of Besl and McKay's iterative closest point (ICP) algorithm. We use the WGF algorithm to register X-ray computed tomography (CT) and T2-weighted magnetic resonance (MR) volume head im- ages acquired from eleven patients that underwent craniotomies in a neurosurgical clinical trial. Each patient had five external markers attached to transcutaneous posts screwed into the outer table of the skull. We define registration error as the distance between positions of corresponding markers that are not used for registration. The CT and MR images are registered using fidu- cial points (marker positions) only, a surface only, and various weighted combinations of points and a surface. The CT surface is derived from contours corresponding to the inner surface of the skull. The MR surface is derived from contours corresponding to the cerebrospinal fluid (CSF)-dura interface. Registration using points and a surface is found to be significantly more accurate than registration using only points or a surface. 1. INTRODUCTION EGISTRATION techniques quantitatively relate the in- formation in one image to information in another image by determining a one-to-one mapping between the points in each image. Registration of multimodal images makes it possible to superimpose features from different imaging studies. For example, skeletal structures and areas of con- trast enhancement seen in X-ray computed tomography (CT) images can be overlaid on magnetic resonance (MR) images which clearly depict soft-tissue anatomy. Likewise, functional lesions detected with positron emission tomography (PET) or single photon emission computed tomography (SPECT) can be viewed in the context of brain anatomy imaged with CT or MR. Registration of multiple data sets obtained with the same modality at different times allows quantitative comparison and thus increases the precision of treatment monitoring with Manuscript received October 3 1, 1995; revised July 23, 1996. A preliminary version of this work was presented at the SPIE Conference, Medical Imaging 1995, San Diego, CA. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was C. R. Meyer. Asterisk indicates corresponding author. *C. R. Maurer, Jr. is with the Departments of Biomedical Engineer- ing and Neurological Surgery, Vanderbilt University, Village at Vanderhilt, Rm. 452, 1500 21st Avenue South, Nashville, TN 37212 USA (e-mail: Calvin@ vuse.vanderbilt.edu). G. B. Aboutanos and B. M. Dawant are with the Department of Electrical Engineering, Vanderbilt University, Nashville, TN 37235 USA. R. J. Maciunas is with the Dqpartment of Neurological Surgery, Vanderbilt University, Nashville, TN 37232 USA. J. M. Fitzpatrick is with the Departments of Computer Science, Neurologi- cal Surgery, and Radiology, Vanderbilt University, Nashville, TN 37235 USA. Publisher Item Identifier S 0278-0062(96)08703-4. serial images. Registration techniques have recently been extended to relate image space to physical space. Stereotactic surgery and stereotactic radiosurgery require that an image or images be registered with the physical space occupied by the patient during surgery. New interactive, image-guided surgery techniques use image-to-physical space registration to track in real time the changing surgical position on a display of the preoperative image sets of the patient [35]. Many methods have been used to register medical images [39], [56]. In this paper we are primarily concerned with point-based and surface-based registration methods. We review existing point-based and surface-based methods, and present a hybrid registration technique first proposed in [38] that uses a weighted combination of multiple geometrical feature shapes. The weighted geometrical feature (WGF) registration algorithm is an extension of Besl and McKay's iterative closest point (ICP) algorithm [5] and is an improvement over an approach proposed independently in [ 131. We demonstrate the efficacy of the WGF algorithm by registering CT and MR volume head images using fiducial points (centroids of rigidly attached external markers), a surface, and various weighted combinations of points and a surface. Registration accuracy is calculated as the distance between marker positions not used to estimate the transformation. 11. REGISTRATION ALGORITHM A. Point-Based Registration Point-based registration involves the determination of the coordinates of corresponding points in different images (and/or physical space) and the estimation of the geometrical trans- formation using these corresponding points [36], [40]. The points may be either intrinsic [151, [241 or extrinsic [lll, [171, [36], [57]. Intrinsic points are derived from naturally occurring features, e.g., anatomic landmark points. Extrinsic points are derived from artificially applied markers, e.g., tubes containing copper sulfate. Registrations involving head images of the same patient are typically rigid-body transformations 7(p) = Rp + t, where R is a 3 x 3 rotation matrix, t is a 3 x 1 translation vector, and p is a 3 x 1 position vector. Let P = {pj} for j = 1, . . . , Np be a point set to be registered with another point set X = {x,} for j = 1, '.', Nz, where N = Np = N, and where each point p, corresponds to the point x3 with the same index. We wish to find the rigid-body transformation 7 that minimizes 0278-0062/96$05,00 0 1996 IEEEMAURER et al.: REGISTRATION OF 3-D lMAGES USING WEIGHTED GEOMETRICAL FEATURES 837 the cost function This problem was given the name “Orthogonal Procrustes” problem by Hurley and Cattell [26]; it is known as the “absolute orientation” problem in photogrammetry [20]. A closed-form solution was first discovered by Schonemann in 1966 [51]. Many other closed-form