Edge Detection by Adaptive Splitting

Abstract

In this paper we propose an algorithm (EDAS-d) to approximate the jump discontinuity set of functions defined on subsets of ? d . We have limited our study to the 1D (EDAS-1) and 2D (EDAS-2) versions of the algorithm. Theoretical and computational results prove its effectiveness in the case of piecewise continuous 1D functions and piecewise constant 2D functions. The algorithm is based on adaptive splitting of the domain of the function guided by the value of an average integral. EDAS-d exhibits a number of attractive features: accurate determination of the jump points, fast processing, absence of oscillatory behavior, precise determination of the magnitude of the jumps, and ability to differentiate between real jumps (discontinuities) and steep gradients. Moreover, low-dimensional versions of EDAS-d can be used for solving higher dimensional problems. Computational experiments also show that EDAS-d can be applied to solve some problems involving general piecewise continuous functions. EDAS-1 and EDAS-2 have been used to determine edges in 2D-images. The results are quite satisfactory for practical purposes.