Stochastic Optimization based Design of C-Arm Calibration Phantoms

C-arm fluoroscopy is commonly used in Computer-Assisted Surgery, enabling real-time imaging. Calibrating such images enable the use of 2D/3D registration or advanced reconstruction algorithms, making a well designed calibration approach is essential. Most prior work mainly focuses on the calibration methods, with limited attention given to the optimal design of C-arm calibration phantoms. This work introduces a stochastic optimization framework for designing sphere based calibration phantoms. Our approach optimizes sphere placement to satisfy key criteria: robustness to segmentation noise, visibility in clinically relevant views, and adherence to physical size constraints. We model the calibration process using a pinhole camera representation, employing the Direct Linear Transform (DLT) algorithm employed to estimate extrinsic and intrinsic parameters from 2D-3D correspondences. Introducing normally distributed noise to the projected coordinates, we simulate realistic segmentation inaccuracies. We designed a tunable cost function incorporating components to minimize calibration errors under noisy conditions, penalize occlusions, and enforce visibility. This cost is optimized to define the 3D coordinates for the spheres of the calibration phantom using the stochastic optimizer Dual Annealing. Results demonstrate that phantoms optimized using our method doubles the calibration accuracy of phantoms with randomly placed spheres in terms of both intrinsic and extrinsic parameters. In addition, occlusions are minimized, ensuring that the phantom can be well calibrated within all relevant images. This method offers an automated solution for creating calibration phantoms aligning with specific clinical requirements, increasing the robustness and accuracy of existing calibration approaches.