Pivot calibration concept for sensor attached mobile c-arms

Medical augmented reality has been actively studied for decades and many methods have been proposed torevolutionize clinical procedures. One example is the camera augmented mobile C-arm (CAMC), which providesa real-time video augmentation onto medical images by rigidly mounting and calibrating a camera to the imagingdevice. Since then, several CAMC variations have been suggested by calibrating 2D/3D cameras, trackers, andmore recently a Microsoft HoloLens to the C-arm. Different calibration methods have been applied to establishthe correspondence between the rigidly attached sensor and the imaging device. A crucial step for these methodsis the acquisition of X-Ray images or 3D reconstruction volumes; therefore, requiring the emission of ionizingradiation. In this work, we analyze the mechanical motion of the device and propose an alternatative methodto calibrate sensors to the C-arm without emitting any radiation. Given a sensor is rigidly attached to thedevice, we introduce an extended pivot calibration concept to compute the fixed translation from the sensor tothe C-arm rotation center. The fixed relationship between the sensor and rotation center can be formulated as apivot calibration problem with the pivot point moving on a locus. Our method exploits the rigid C-arm motiondescribing a Torus surface to solve this calibration problem. We explain the geometry of the C-arm motion andits relation to the attached sensor, propose a calibration algorithm and show its robustness against noise, as wellas trajectory and observed pose density by computer simulations. We discuss this geometric-based formulationand its potential extensions to different C-arm applications.