The preservation, analysis, and dissemination of digital heritage have become critical in addressing the challenges of safeguarding cultural artifacts in an increasingly digital world. The representation and comparison of 3D objects within digital heritage require robust, interpretable, and efficient methodologies that account for the diverse, intricate geometries of cultural assets. Despite advancements in computational geometry and machine learning, achieving invariance to transformations, scalability, and topological interpretability remains a significant challenge. This paper introduces a novel pipeline tailored for digital heritage applications, leveraging Reeb graphs as topological descriptors alongside a rigorous normalization framework and a multi-methodological similarity assessment strategy. The proposed approach constructs Reeb graphs from scalar fields defined on 3D objects, normalizes them to ensure invariance to scale, translation, and rotation, and applies a suite of similarity measures, including Persistent Homology combined with Euclidean Distance, Hausdorff Distance, and Jaccard Index. A key application of this methodology is demonstrated in the similarity-based study of ancient masks, where the method identifies and categorizes masks with shared morphological and topological features. This capability provides invaluable insights into historical, cultural, and artistic contexts, fostering deeper understanding and cross-cultural analyses. Extensive experiments on heritage-inspired datasets validate the approach, showing superior performance in terms of accuracy, robustness, and interpretability. By addressing key limitations in current 3D object analysis methods, this work offers a scalable, interpretable, and modular framework, empowering digital heritage scientists to preserve cultural legacies more effectively. The proposed solution not only enhances the scientific understanding of artifact morphology but also facilitates the development of digital heritage repositories, enabling sophisticated similarity searches and fostering interdisciplinary collaborations.