Graph morphology

Authors:
H. J. A. M. Heumans;P. Nacken;A. Toet;L. Vincent
Affiliations:
Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands;Institute for Perception TNO, Kampweg 5, 3769 DE Soesterberg, The Netherlands;Institute for Perception TNO, Kampweg 5, 3769 DE Soesterberg, The Netherlands;Division of Applied Sciences, Harvard University, Cambridge, Massachusetts, 02138, USA
Venue:
Journal of Visual Communication and Image Representation
Year:
1992

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Abstract

This paper presents a systematic theory for the construction of morphological operators on graphs. Graph morphology extracts structural information from graphs using predefined test probes called structuring graphs. Structuring graphs have a simple structure and are relatively small compared to the graph that is to be transformed. A neighborhood function on the set of vertices of a graph is constructed by relating individual vertices to each other whenever they belong to a local instantiation of the structuring graph. This function is used to construct dilations and erosions. The concept of the structuring graph is also used to define openings and closings. The resulting morphological operators are invariant under symmetries of the graph. Graph morphology resembles classical morphology (which uses structuring elements to obtain translation-invariant operators) to a large extent. However, not all results from classical morphology have analogues in graph morphology because the local graph structure may be different at different vertices.