  An increasing abstraction has marked some recent investigations in network
science. Examples include the development of algorithms that map time series
data into networks whose vertices and edges can have different interpretations,
beyond the classical idea of parts and interactions of a complex system. These
approaches have proven useful for dealing with the growing complexity and
volume of diverse data sets. However, the use of such algorithms is mostly
limited to one-dimension data, and there has been little effort towards
extending these methods to higher-dimensional data such as images. Here we
propose a generalization for the ordinal network algorithm for mapping images
into networks. We investigate the emergence of connectivity constraints
inherited from the symbolization process used for defining the network nodes
and links, which in turn allows us to derive the exact structure of ordinal
networks obtained from random images. We illustrate the use of this new
algorithm in a series of applications involving randomization of periodic
ornaments, images generated by two-dimensional fractional Brownian motion and
the Ising model, and a data set of natural textures. These examples show that
measures obtained from ordinal networks (such as average shortest path and
global node entropy) extract important image properties related to roughness
and symmetry, are robust against noise, and can achieve higher accuracy than
traditional texture descriptors extracted from gray-level co-occurrence
matrices in simple image classification tasks.
