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

Authors:
Bernardo Llanas;Sagrario Lantarón
Affiliations:
Departamento de Matemática Aplicada, ETSI de Caminos, Universidad Politécnica de Madrid, Madrid, Spain 28040;Departamento de Matemática Aplicada, ETSI de Caminos, Universidad Politécnica de Madrid, Madrid, Spain 28040
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

In Llanas and Lantarón, J. Sci. Comput. 46, 485---518 (2011) we proposed an algorithm (EDAS-d) to approximate the jump discontinuity set of functions defined on subsets of 驴 d . 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 1D 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.