Parkinson’s disease (PD) is a progressive neurodegenerative disorder whose diagnosis still relies mainly on clinical observation and rating scales, which are limited by subjectivity and variability. Spiral drawing tests have recently gained attention as a simple yet informative task for detecting subtle motor impairments, although their diagnostic value depends critically on the analytical methods applied. This study investigates the potential of Hu and Legendre image moments as shape descriptors for classifying spiral drawings from PD patients and healthy controls using two publicly available datasets, one consisting of paper-based and the other of digital spirals. To ensure consistency, all images underwent cropping, resizing, and grayscale normalization before feature extraction. Eight Hu and eight Legendre moments were computed, and Recursive Feature Elimination combined with multiple classifiers under a Leave-One-Subject-Out protocol was used to identify the most informative features. Results showed that Legendre moments consistently outperformed Hu descriptors, achieving an accuracy of 78.8% and an F1-score of 0.79. These findings demonstrate that lightweight and interpretable moment-based descriptors can serve as accessible digital biomarkers for PD, supporting efficient and reproducible tools for early diagnosis and remote motor assessment.