A scale-space based hierarchical representation of discrete data

A new hierarchical representation of general discrete data sets living on graphs is proposed. The approach takes advantage of recent works on graph regularization. The different levels of the hierarchy are discovered as the regularization process is performed. The role of the merging criterion that is common to hierarchical representations is greatly reduced due to the regularization step. This yields a robust representation of data sets. Moreover, the approach is particularly well adapted to the processing of digital images, where nonlocal processing allows to better handle repetitive patterns usually present in natural images.