A variational formulation-based edge focussing algorithm

Abstract

Many edge detection techniques exhibit scale-dependent distortion of edges. We develop two ideas, which may also be of independent interest, to produce sharp edge localization at all scales. The first is approximation of the functional associated with the variational formulation via epi-convergence, replacing the edge set with a function. We provide a fast algorithm for minimizing the approximate functional. The second is to scale parameters and data to focus the edges. The resulting edge detector is a singular perturbation of a coupled pair of partial differential equations, yielding an elegant structure, suitable for digital or analog parallel implementation on mesh-connected arrays. © 1997 Indian Academy of Sciences.