My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the three-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations.
GD: Graph Drawing and Network Visualization
Los Angeles, CA, United States
2015-09-24 – 2015-09-26
Edelsbrunner H. Shape, homology, persistence, and stability. 2015;9411.
Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. Presented at the GD: Graph Drawing and Network Visualization, Los Angeles, CA, United States: Springer.
Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” Lecture Notes in Computer Science. Springer, 2015.
H. Edelsbrunner, “Shape, homology, persistence, and stability,” vol. 9411. Springer, 2015.
Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 9411.
Edelsbrunner, Herbert. Shape, Homology, Persistence, and Stability. Vol. 9411, Springer, 2015.