The use of Augmented Reality (AR) devices for surgical guidance has gained increasing traction in the medical field. Traditional registration methods often rely on external fiducial markers to achieve high accuracy and real-time performance. However, these markers introduce cumbersome calibration procedures and can be challenging to deploy in clinical settings. While commercial solutions have attempted real-time markerless tracking using the native RGB cameras of AR devices, their accuracy remains questionable for medical guidance, primarily due to occlusions and significant outliers between the live sensor data and the preoperative target anatomy point cloud derived from MRI or CT scans. In this work, we present a markerless framework that relies only on the depth sensor of AR devices and consists of two modules: a registration module for high-precision, outlier-robust target anatomy localization, and a tracking module for real-time pose estimation. The registration module integrates depth sensor error correction, a human-in-the-loop region filtering technique, and a robust global alignment with curvature-aware feature sampling, followed by local ICP refinement, for markerless alignment of preoperative models with patient anatomy. The tracking module employs a fast and robust registration algorithm that uses the initial pose from the registration module to estimate the target pose in real-time. We comprehensively evaluated the performance of both modules through simulation and real-world measurements. The results indicate that our markerless system achieves superior performance for registration and comparable performance for tracking to industrial solutions. The two-module design makes our system a one-stop solution for surgical procedures where the target anatomy moves or stays static during surgery.