Digital Morse Theory gives a new way to organize and understand a volume dataset. It provides a method for recognizing and rendering all possible iso-surface bounded objects, over all thresholds, in a volume dataset.
We believe it will provide a powerful tool for volumetric data simplification and organization. In future work we will implement the criticality graph and zone labeling algorithm and further analyze the properties of each zone. We will apply this to the registration problem, Level of Detail management, and data-space navigation.
Future theoretical work will include extending the theory to arbitrary arrangements of data readings, and vector valued sampled functions (such as multi-spectral scanner data fusion).