Study of the Materials Microstructure using Topological Properties of Complex Networks

A method for mapping a two-dimensional color image of the microstructure of the material to a complex network is proposed. Each image elements is assigned to node network. A weighted combination of distance metrics - the Euclidean distance and the Manhattan distance - defines whether there is or not an edge between corresponding nodes. The first metric is used to calculate the spatial distance between the picture elements (pixels), the second metric takes into account the contrast between the brightness of pixels in the gray scale. On the basis of the topological properties of the constructed network the edge pixels were detected that allows us to identify the border areas in the microstructure of materials. The proposed method can be used in automated systems of materialographic analysis.