MOTIVATION: Dendritic spines, postsynaptic structures characterized by their complex shapes, provide the essential structural foundation for synaptic function. Their shape is dynamic, undergoing alterations in various conditions, notably during neurodegenerative disorders like Alzheimer's disease. The dramatically increasing prevalence of such diseases highlights an urgent need for effective treatments. A key strategy in developing these treatments involves evaluating how dendritic spine morphology responds to potential therapeutic compounds. Although a link between spine shape and function is recognized, its precise nature is still not fully elucidated. Consequently, advancing our understanding of dendritic spines in both health and disease necessitates the urgent development of more effective methods for assessing their morphology. RESULTS: This study introduces qualitatively new 3D dendritic shape descriptors based on spherical harmonics and Zernike moments and proposes a bases on them clustering approach for grouping dendritic spines with similar shapes applied to 3D polygonal spines meshes acquired from Z-stack dendrite images. By integrating these methods, we achieve improved differentiation between normal and pathological spines represented by the Alzheimer's disease in vitro model, offering a more precise representation of morphological diversity. Additionally, the proposed spherical harmonics approach enables dendritic spine reconstruction from vector-based shape representations, providing a novel tool for studying structural changes associated with neurodegeneration and possibilities for synthetic dendritic spines dataset generation. AVAILABILITY AND IMPLEMENTATION: The software used for experiments is public and available at https://github.com/Biomed-imaging-lab/SpineTool with the DOI: 10.5281/zenodo.17359066. Descriptors codebase is available at https://github.com/Biomed-imaging-lab/Spine-Shape-Descriptors with the DOI: 10.5281/zenodo.17302859.