The Tree of Shapes Turned into a Max-Tree: A Simple and Efficient Linear Algorithm

The Tree of Shapes (ToS) is a morphological, tree-based representation of an image, translating the inclusion of its level lines. It features many invariants to image changes, which make it well-suited for many applications in image processing and pattern recognition. In this paper, we propose a way of turning a ToS computation into a Max-Tree computation. The latter has been widely studied, and many efficient algorithms (including parallel ones) have been developed. Furthermore, we develop a specific optimization to speed-up the common 2D case. It follows a simple and efficient algorithm, running in linear time with a low memory footprint, that outperforms other currently used algorithms. For Reproducible Research purpose, we distribute our code as free software.