Variational Snake Theory

Abstract

In this chapter, we review briefly the theory of edge detection and its non local versions, the ”snakes”. We support the idea that the class of snake energies proposed recently by Kimmel and Bruckstein, namely the ”average contrast across the snake” is optimal. We reduce this class to a single model by proving a particular form of their contrast function to be optimal. This form is as close as possible to a threshold function of the image contrast accross the snake. Eventually, we show by arguments and experiments that the resulting snakes simply coincide with the well contrasted level lines of the image. For a sake of completeness, we give all formal computations needed for deriving the main models, their evolution equation and steady state equation. If, as we sustain, the snakes can be replaced in most practical cases by optimal level lines, the topological changes are simply handled by using their nested inclusion tree.