OPTIMAL EDGE DETECTION BY TOPOLOGICAL ASYMPTOTIC ANALYSIS
Monika Muszkieta · Mathematical Models and Methods in Applied Sciences · 2009
In this paper, we consider a variational approach to the problem of edge detection without using a priori information. To begin with, we derive an asymptotic expansion of a functional inspired by the Mumford–Shah model at its global minimum. Then, we show that, according to our model, the optimal set of image edges is indicated by the set of points for which the dominant term of this expansion is minimal and the topological derivative associated with the considered functional is equal to zero. These two conditions form the basis for the introduced method to edge detection, which does not require prior setting of parameters. The analytical results presented in this paper are additionally validated by numerical experiments.