Morse Theory

Morse theory, a branch of topology, provides a powerful framework for analyzing the shape and structure of functions and data, particularly focusing on critical points (minima, maxima, and saddles). Current research emphasizes applications in diverse fields, including computer vision (keypoint detection), surface reconstruction (e.g., of textiles), and deep learning (uncertainty quantification and improved segmentation). These applications leverage algorithms that construct Morse-Smale complexes or utilize discrete Morse theory to efficiently compute topological features, leading to improved model performance and interpretability in various scientific and engineering domains.