New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones
This work addresses representation challenges in image processing and hierarchical data analysis, offering incremental theoretical advancements with practical applications.
The paper tackles the problem of representing hierarchies of partitions in image processing by establishing a new bijection between saliency maps and hierarchies based on quasi-flat zones, and characterizes saliency maps and minimum spanning trees as solutions to constrained minimization problems. The result provides a toolkit for developing new hierarchical methods and extends morphological hierarchies to non-image data.
We study three representations of hierarchies of partitions: dendrograms (direct representations), saliency maps, and minimum spanning trees. We provide a new bijection between saliency maps and hierarchies based on quasi-flat zones as used in image processing and characterize saliency maps and minimum spanning trees as solutions to constrained minimization problems where the constraint is quasi-flat zones preservation. In practice, these results form a toolkit for new hierarchical methods where one can choose the most convenient representation. They also invite us to process non-image data with morphological hierarchies.