Computation of the Tree of Shapes of a Digital Image

We present here a first algorithm, the Fast Level Sets Transform, that computes the tree of shapes from an input image. Although it is applicable in any dimension, its efficiency relies on specific properties of a dimension 2 domain. Although a direct derivation of the existence of the tree of shapes in the discrete case would be possible, a judicious interpretation of the digital image as a continuous domain image leads us directly in the framework of Chap. 2, hence proving the result. This artifice avoids the necessity of a theory in the discrete case. An open source reference implementation of the algorithm presented in this chapter is freely available in the MegaWave software suite (http://megawave.cmla.ens-cachan.fr, module flst).