IEEE TRANSACTIONS ON MEDICAL IMAGING VOL 15 NO 6 DECEMBER 1996 836 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 images 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 fiducial 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 information 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 contrast 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 Engineering 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 Neurological 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 transformation using these corresponding points 36 40 The points may be either intrinsic 151 241 or extrinsic l l l 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 N z where N N p 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 IEEE MAURER et al REGISTRATION OF 3 D lMAGES USING WEIGHTED GEOMETRICAL FEATURES 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 solutions have been independently discovered including the solution of Arun et al 21 that is based on the singular value decomposition SVD of the position vectors in the two spaces B Surface Based Registration Surface based registration involves the determination of corresponding surfaces in different images andlor physical space and the estimation of the geometrical transformation using these corresponding structures The surfaces are generally represented as sets of