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30 June 1994 Learning the identity with basic morphological operators (potato peeler algorithm)
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Abstract
Let f denote an image and F a morphological operator depending on a set of parameters {mj}. The purpose of this paper is to find a set of parameters which satisfies the equation F(f,m) equals f where F is one of the two basic morphological operator: erosion or dilation. It is obvious that there exists a trivial solution m of f equals F(f,m), which is given by m(x) equals 0 if x equals 0 and m(x) equals -(infinity) otherwise. Our approach is to consider this problem as an optimization problem: `find the best set of parameters which minimizes the error between the desired image f and the output filtered image F(f,m)'. Among various possible approaches, we have chosen a specific one introduced by Ph. Salembier for adaptative structuring elements. In our problem, we prove that Salembier algorithms always converge toward a solution distinct from m.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Juliette Mattioli and Michel Schmitt "Learning the identity with basic morphological operators (potato peeler algorithm)", Proc. SPIE 2300, Image Algebra and Morphological Image Processing V, (30 June 1994); https://doi.org/10.1117/12.179213
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