Abstract
Neurodegenerative diseases present complex challenges that demand advanced analytical techniques to decode intricate brain structures and their changes over time. Curvature estimation within datasets has emerged as a critical tool in areas like neuroimaging and pattern recognition, with significant applications in diagnosing and understanding neurodegenerative diseases. This systematic review assesses state-of-the-art curvature estimation methodologies, covering classical mathematical techniques, machine learning, deep learning, and hybrid methods. Analysing 105 research papers from 2010 to 2023, we explore how each approach enhances our understanding of structural variations in neurodegenerative pathology. Our findings highlight a shift from classical methods to machine learning and deep learning, with neural network regression and convolutional neural networks gaining traction due to their precision in handling complex geometries and data-driven modelling. Hybrid methods further demonstrate the potential to merge classical and modern techniques for robust curvature estimation. This comprehensive review aims to equip researchers and clinicians with insights into effective curvature estimation methods, supporting the development of enhanced diagnostic tools and interventions for neurodegenerative diseases.