Edge Detection by Adaptive Splitting II. The Three-Dimensional Case

In Lianas and Lantaron, J. Sci. Comput. 46, 485-518 (2011) we proposed an algorithm (EDAS-<i) to approximate the jump discontinuity set of functions defined on subsets of R. This procedure is based on adaptive splitting of the domain of the function guided by the value of an average integral. The above study was limited to the ID and 2D versions of the algorithm. In this paper we address the three-dimensional problem. We prove an integral inequality (in the case d = 3) which constitutes the basis of EDAS-3. We have performed detailed computational experiments demonstrating effective edge detection in 3D function models with different interface topologies. EDAS-1 and EDAS-2 appealing properties are extensible to the 3D case.