GEOMETRIC AND STATISTICAL ANALYSIS OF FINGERTIP LANDMARK FEATURES FOR REAL-TIME AMERICAN SIGN LANGUAGE RECOGNITION

This paper presents a mathematical and computational study of real-time American Sign Language (ASL) alphabet recognition using fingertip landmark geometry. We formalize each hand observation as a point X∈ℝ¹⁰ composed of the (x,y)-coordinates of the five fingertip landmarks detected by MediaPipe, introduce a canonical normalization map that enforces translation and scale invariance, and analyze the resulting feature space using covariance (PCA) and linear discriminant analysis. We propose a lightweight classification pipeline whose decision rule is either linear in the normalized feature coordinates or based on a learned Mahalanobis metric; we provide complexity estimates and a sample-complexity bound for reliable generalization. Experiments on the publicly available ASL alphabet dataset demonstrate that compact geometric and statistical features achieve high accuracy (≈92%) while enabling inference at <100 ms per frame on consumer hardware. The combination of geometric preprocessing, principled metric design, and statistical analysis yields a mathematically transparent and computationally efficient approach suitable for deployment in assistive technologies. Future extensions include temporal modeling and rigorous generalization theory for dynamic signs.