A novel spatial-temporal image fusion method for augmented reality-based endoscopic surgery

Augmented reality (AR) has significant potential to enhance the identification of critical locations during endoscopic surgeries, where accurate endoscope calibration is essential for ensuring the quality of augmented images. In optical-based surgical navigation systems, asynchrony between the optical tracker and the endoscope can cause the augmented scene to diverge from reality during rapid movements, potentially misleading the surgeon-a challenge that remains unresolved. In this paper, we propose a novel spatial-temporal endoscope calibration method that simultaneously determines the spatial transformation from the image to the optical marker and the temporal latency between the tracking and image acquisition systems. To estimate temporal latency, we utilize a Monte Carlo method to estimate the intrinsic parameters of the endoscope's imaging system, leveraging a dataset of thousands of calibration samples. This dataset is larger than those typically employed in conventional camera calibration routines, rendering traditional algorithms computationally infeasible within a reasonable timeframe. By introducing latency as an independent variable into the principal equation of hand-eye calibration, we developed a weighted algorithm to iteratively solve the equation. This approach eliminates the need for a fixture to stabilize the endoscope during calibration, allowing for quicker calibration through handheld flexible movement. Experimental results demonstrate that our method achieves an average 2D error of 7±3 pixels and a pseudo-3D error of 1.2±0.4mm for stable scenes within 82.4±16.6 seconds-approximately 68% faster in operation time than conventional methods. In dynamic scenes, our method compensates for the virtual-to-reality latency of 11±2ms, which is shorter than a single frame interval and 5.7 times shorter than the uncompensated conventional method. Finally, we successfully integrated the proposed method into our surgical navigation system and validated its feasibility in clinical trials for transnasal optic canal decompression surgery. Our method has the potential to improve the safety and efficacy of endoscopic surgeries, leading to better patient outcomes.