Accurate fingertip detection is critical for translating hand gestures into actionable commands in vision-based human‒computer interaction (HCI) systems. However, challenges such as complex backgrounds, dynamic hand postures, and real-time processing constraints hinder reliable detection. This paper introduces a robust framework integrating three key innovations: (1) an adaptive Gaussian mixture model (GMM) enhanced with neighborhood pixel connectivity for precise motion extraction; (2) a weighted YCbCr color-space shadow removal algorithm to eliminate false positives; and (3) a centroid distance method refined with circularity constraints for accurate fingertip localization. Extensive experiments demonstrate a recognition accuracy of 97.26% across diverse scenarios, including varying illuminations, occlusions, and hand rotations. The algorithm processes each frame in 23.43 ms on average, satisfying real-time requirements. Comparative evaluations against state-of-the-art methods reveal significant improvements in precision (8.3%), recall (6.1%), and F-measure (7.8%). This work advances HCI applications such as virtual keyboards, gesture-controlled interfaces, and augmented reality systems.