From min tree to watershed lake tree: Theory and implementation

Segmentation is a classical problem in image processing that has been an active research topic for more than three decades. Classical tools provided by mathematical morphology for segmenting images are the connected set operators and the watershed transformation. Both of these operations can be applied to form hierarchies of nested partitions at increasing scales. This paper studies two image partition hierarchies founded in mathematical morphology, namely the max/min tree and the watershed lake tree. By considering watershed and max/min tree image descriptions we show that a watershed lake tree comprises a subset of min tree vertices.