Topological Simplification of Voxelized Data

Explore topological simplification techniques for voxelized data in this 25-minute conference talk. Delve into the challenges of analyzing graphical data generated by MRI and CT scans, represented as intensity fields. Learn about segmentation methods used to construct voxelized shapes and the inherent errors in spatial and intensity domains. Discover how homological simplification can be applied to denoise these shapes by defining neighborhoods and cores. Examine the process of adding voxels to fill noisy holes or voids and connecting disconnected components, as well as subtracting voxels not in the core. Gain insights into the accuracy and efficiency of these heuristic simplification methods and discuss potential future improvements in the field of applied algebraic topology.

Intro
Motivation
Homological Simplification Problem
Algorithm
Persistence Candidates
Experimental Results
Conclusion