Augmented Reality Spinal Surgery Navigation: A Spatial Registration Method Using Personalized Markers

2.1 Registration Process\n\nThe spatial registration method proposed in this paper is applied to the augmented reality spinal surgery navigation system developed by us, which operates on a high-performance computer. The system hardware includes a personalized marker, an intraoperative X-ray imaging system, a monocular camera, and a screen as an augmented reality display tool, as shown in Figure 1.\n\nFigure 1: The use environment of the augmented reality spinal surgery navigation system\n\nTo achieve patient medical image registration with the world space, we define the monocular camera coordinate system as the world coordinate system and unify the medical image coordinate system and patient coordinate system within it. A personalized marker is used and rigidly fixed to the patient during surgery. The marker and patient are registered as a whole. As medical images are obtained from patients' scans, this study completes the registration based on the characteristic that patients and markers exist in both the real world and image space. The spatial registration process of medical images is shown in Figure 2.\n\nFigure 2: Spatial registration of medical images\n\nTo achieve the conversion from the CT image coordinate system to the world space coordinate system, the transformation matrix, denoted as \u03A9, needs to be solved, which can be expressed as equation (1):\n(1)\n\nIn the equation, the matrix \u03A3 is the transformation matrix from the personalized marker coordinate system () to the world coordinate system (). The matrix \u03C4 is the transformation matrix from the two-dimensional X-ray image coordinate system () to the three-dimensional CT image coordinate system, which can be obtained by 2D/3D image registration. The matrix \u03B1 is the transformation matrix from to , which needs to be solved by determining the pose of the marker in the X-ray image.\n\n2.2 Personalized Marker to Camera Registration\n\nThe personalized marker we designed, shown in Figure 3, can be detected using X-ray and monocular cameras to obtain the transformation matrices \u03A3 and \u03B1.\n\nThe personalized marker relies on ArUco design. ArUco [25] is a binary-coded square marker that can be arbitrarily sized and numbered. As shown in Figure 3(a), each ArUco reference marker consists of internal coding and a black border. The internal coding contains basic information such as the four corner points' data and the marker's dictionary number. Given the reference marker's size and dictionary type, the corner points' three-dimensional coordinates in the marker's own coordinate system and the marker's pose can be calculated using the camera's imaging model and parameters.\n\nTo ensure the marker is clear and distinguishable in optical and X-ray spectral imaging, we printed the ArUco marker's internal coding portion using resin material and connected it to a white outer frame. The ArUco black part was made using stainless steel material, which strongly attenuates X-ray radiation, as shown in Figure 3(b). Due to the metal's high attenuation, the marker is equally visible in X-ray spectra and monocular camera images.\n\nFigure 3: The personalized marker\n(a) ArUco marker; (b) Marker entity\n\nSince the personalized marker's shape and size