We describe new methods for rigid registration of a preoperative computed tomography (CT)-scan image to a set of intraoperative X-ray fluoroscopic images, for guiding a surgical robot to its trajectory planned from CT. Our goal is to perform the registration, i.e., compute a rotation and translation of one data set with respect to the other to within a prescribed accuracy, based upon bony anatomy only, without external fiducial markers. With respect to previous approaches, the following aspects are new: 1) we correct the geometric distortion in fluoroscopic images and calibrate them directly with respect to the robot by affixing to it a new calibration device designed as a radiolucent rod with embedded metallic markers, and by moving the device along two planes, while radiographs are being acquired at regular intervals; 2) the registration uses an algorithm for computing the best transformation between a set of lines in three space, the (intraoperative) X-ray paths, and a set of points on the surface of the bone (imaged preoperatively), in a statistically robust fashion, using the Cayley parameterization of a rotation; and 3) to find corresponding sets of points to the X-ray paths on the surfaces, our new approach consists of extracting the surface apparent contours for a given viewpoint, as a set of closed three-dimensional nonplanar curves, before registering the apparent contours to X-ray paths. Aside from algorithms, there are a number of major technical difficulties associated with engineering a clinically viable system using anatomy and image-based registration. To detect and solve them, we have so far conducted two experiments with the surgical robot in an operating room (OR), using CT and fluoroscopic image data of a cadaver bone, and attempting to faithfully simulate clinical conditions. Such experiments indicate that intraoperative X-ray-based registration is a promising alternative to marker-based registration for clinical use with our proposed method.
