Research On Small-World Properties Of Image Gray Neighborhood Model

This article is a earlier research on the complex theory applied to image processing, and mainly focus on small-world properties of image gray neighborhood model. According to the gray neighborhood model in this paper, we abstract each testing image in the picture database for a network, and establish a network model about image. By researching and quantitative analysising of each network of the testing image, we prove that in this type of networks of the testing images exist the small-world properties:there are smaller average path length and clustering coefficient in image network.In this paper, according to the commonly used image gray neighborhood model, each pixel of the image as a node of image network. The connections between the nodes are defined as follows:using the relationship between the geometry distance about two different pixels in the image and neighborhood radius value of a certain pixel center, then other pixels within a certain radius of any pixel as its neighbor points, and connect them, so we have established an image neighborhood network; basing on the image neighborhood network, according to the relationship between the gray difference of different pixels and gray difference threshold, selectively connect two different pixels with a edge, at last we have got a image network.In order to calculate the average path length of image network, firstly we establish connection matrix of each image network, then we use power iterative algorithm to calculate the shortest path length between pixels. Because of image network have huge number of nodes, using connection matrix to calculate the shortest path length between pixels of the image network become a very difficult problem, by designing numerical calculation method cleverly we prove that the network based on image have smaller average path length and larger clustering coefficient, it means that this type of the testing image networks are small-world network.Our main contributions in this paper are:according to the image gray neighborhood model, we establish image network; using connection matrix of image network model and power iterative algorithm, we get the shortest path length between any two pixels of image network; prove the model of image network is small-world network. In addition, this article provides new ideas for establishing model of image network and researching small-world properties of image model, and we believe that our research can help to solve some image processing problems in the future.