Efficient Schemes for Computing α-tree Representations

Hierarchical image representations have been addressed by various models by the past, the max-tree being probably its best representative within the scope of Mathematical Morphology. However, the max-tree model requires to impose an ordering relation between pixels, from the lowest values (root) to the highest (leaves). Recently, the α-tree model has been introduced to avoid such an ordering. Indeed, it relies on image quasi-flat zones, and as such focuses on local dissimilarities. It has led to successful attempts in remote sensing and video segmentation. In this paper, we deal with the problem of α-tree computation, and propose several efficient schemes which help to ensure real-time (or near-real time) morphological image processing.