PROPERTIES OF NETWORKS BUILT ON DIGITAL IMAGES

Background. It is known that some important properties of natural-language texts can be revealed when mapping a text on a network and studying the properties of this network. Here the words of a text are regarded as nodes and their co-occurrences as links. Materials and Methods. Drawing an analogy between texts and digital images, in this work we study experimentally and analyze phenomenologically the properties of a network built on an image. In this network, the nodes are pixel values and the links are assigned among those pixel values that spatially adjoin each other in an image. The neighborhood of pixels is defined by a radius r (r = 1, 2, ...). We build our networks for a test informative image and the corresponding images obtained from the initial one by adding calibrated portions of white Gaussian noise. Both weighted and non-weighted networks are analyzed and a number of practical methods for building an image network and adding a noise to an image are compared with each other. Results and Discussion. The main network parameters such as the average clustering coefficient and the average shortest-path length are measured as functions of the relative noise parameter. The main qualitative and quantitative features of the dependences are analyzed. The network characteristics are critically compared with those known for the lexical networks build upon the natural texts and the random texts obtained with randomizing words in the initial natural text. The main similarities and distinctions of the lexical and image networks are scrutinized. Conclusion. It is shown that the average clustering coefficient and path length for the networks built upon the initial informative image and the corresponding noisy images are essentially small worlds. In spite of this similarity, the above networks reveal a number of distinct features so that the dependences of the image-network parameters on the noise level can be used for distinguishing between these types of images. Finally, we analyze a number of consequences of our empirical results and some data known from the literature. Since both informative and noisy images reveal a small-worldliness, it would hardly be appropriate to associate this effect with the information load of the image.