Hierarchical Queues: general description and implementation in MAMBA image library

Hierarchical queues (HQ) are extremely efficient structures for fast computation of morphological transformations such as watershed lines or geodesic reconstructions. The recent development of MAMBA, new morphological image processing library, led the authors of this paper to review the definition and implementation of the watersheds and geodesic reconstructions algorithms based on these hierarchical queues. This library incorporates very fast implementations of these operators, based on HQ. These implementations increase deeply the performances of MAMBA in real-time applications. Indeed, the documents describing HQ are quite succinct [4, 6]. Unfortunately, these descriptions are far from being accurate and complete. The HQ implementation as it is described in these documents will be used as a starting point for the description of its implementation in the MAMBA library. Regarding the watershed transform, two implementations are available: the first one where only the catchment basins are generated and the second one where these catchment basins are separated by the watershed lines. However, only the first implementation is described in the above mentioned documents. The second one is not addressed although it is more difficult to achieve. The two implementations however are available in some software libraries [7, 8]. The HQ implementation as it is realised in these libraries will be used as a starting point for the description of its implementation in the MAMBA library. Some of its peculiarities and defects will be recalled before indicating which enhancements have been achieved in MAMBA. Regarding geodesic reconstruction, the description of HQ implementations in the above documents exhibits a peculiar feature which makes this algorithm to be tautological. We shall come back to this characteristic and we shall describe an implementation that avoids this problem.