Surgical tooltip localization via concentric nested square markers and depth-RGB multi-coordinate fusion.

Purpose: Accurate tooltip localization is critical in surgical navigation and other high-precision applications. Traditional ArUco marker-based systems often suffer from detection instability and reduced accuracy under varying tool poses. This study proposes a novel real-time localization method based on concentric nested square markers and multi-coordinate frame fusion, improving robustness and spatial accuracy through geometric marker enhancement and data fusion.

Methods: The proposed marker integrates an embedded ArUco code within an outer nested square structure, enabling pose estimation from multiple coordinate frames. Tooltip localization is derived by fusing the estimated poses of both structures, with optional depth data incorporated to enhance precision further. A cubic calibration object with ArUco references was used to establish ground-truth positions. Extensive experiments were conducted under varied distances, tool inclination angles, and lighting conditions.

Results: The nested square marker achieved up to 40.1% improvement in average localization accuracy compared to standard ArUco markers. Depth fusion further reduced the average error to 1.55 mm and decreased the standard deviation, indicating stronger stability. Additional comparisons with AprilTag, QR Code, and calibration patterns validated the method's superior performance across diverse marker types.

Conclusion: The proposed method offers a robust, compact, and accurate localization solution compatible with common camera systems. Its enhanced performance in various tool poses makes it well-suited for real-world surgical scenarios. Source code is available at: https://github.com/xunlizhinian1124/Real-Time-Tool-Track .