A Variational Approach To Edge Detection

In this paper, using the variational framework and elements of topological asymptotic analysis, we derive an algorithm for edge detection in a digital image in which an optimal value for the threshold is computed automatically. In order to examine this algorithm, we perform a simple experiment on synthetic images composed of two objects with different values of intensity and size. In this case, we are be able to find an exact condition which has to be satisfied so that an edge of object with lower contrast would be detected. At the end, we compare results of numerical experiments obtained by application of our algorithm and the algorithm proposed by Desolneux et al. [7, x]. We indicate some similarities between these two approaches to edge detection and discuss their differences.