TEXTURE DISCRIMINATION USING HIERARCHICAL COMPLEX NETWORKS T. Chalumeau, L. da F. Costa * Universidade de Sao Paulo IFSC Caixa Postal 369 - CEP 13560-970 Sao Carlos - SP - Brasil O. Laligant, F. Meriaudeau Universite de Bourgogne IUT Le Creusot, Le2i 12 rue de la Fonderie 71200 Le Creusot France ABSTRACT Texture analysis represents one of the main areas in image processing and computer vision. The current article describes how complex networks have been used in order to represent and characterized textures. More specifically, networks are derived from the texture images by expressing pixels as net- work nodes and similarities between pixels as network edges. Then, measurements such as the node degree, strengths and clustering coefficient are used in order to quantify properties of the connectivity and topology of the analyzed networks. Because such properties are directly related to the structure of the respective texture images, they can be used as features for characterizing and classifying textures. The latter possi- bility is illustrated with respect to images of textures, DNA chaos game, and faces. The possibility of using the network representations as a subsidy for DNA characterization is also discussed in this work. 1. INTRODUCTION Textures are everywhere: in nature as well as in human-made objects and environments. As such, texture provides impor- tant information from which to identify objects and also to infer physical properties of scenes (e.g. gradients of texture may indicate scene depth). Although the difference between textures and other images (i.e. involving objects and shapes) remains unclear, such a decision is often important because the methods applied in image processing and analysis often differ depending on the type of images (i.e. texture against shape analysis). Interestingly, the issues of texture definition and representation/characterization are therefore intensely in- tertwined. The continuing investigations in texture have considered several alternative approaches such as the Fourier and wavelet transform, co-occurrence matrices and derived measurements. Generally, textures are characterized by a high degree of dis- order and/or periodical information, or hybrids of these two principles. The presence of periodicity is closely related to * Thanks to Human Frontier for funding. spatial correlations, while large levels of disorder are associ- ated to high entropy and lack of correlations. Because these two opposing features often co-exist in textures, it is impor- tant to consider methods for representation and analysis of textures which can be capable of accounting for these two ef- fects. Introduced recently [1, 2, 3], complex networks can be conceptualized as an interface between graph theory and sta- tistical physics, two traditional and well-established research areas. Basically, complex networks are characterized by the presence of patterns of connections which are different from those observed in regular networks (e.g. lattices) or even ran- dom networks. Two important manifestations of such ”com- plexity” are the small world property, namely the fact that a pair of the network nodes tend to be interconnected through a short path, and the scale free property, indicating that the distribution of nodes is scale invariant, implying the presence of hubs. Interestingly, the complexity in such networks is also characterized by the co-existence of local and global features, in analogous fashion to the organization of textures. For in- stance, even random networks will present more densely con- nected substructures (the so-called communities) as a conse- quence of statistical fluctuations. Such an inherent representa- tional ability of complex networks has been explored in order to represent and analyze textures and images [4, 5]. One of the simplest ways to represent textures as complex networks is by expressing pixels as nodes and similarity between the gray- level or local features of the texture image as edges. Then, complex networks measurements (see [2]) can be obtained so as to provide an objective quantification of the properties of the texture in terms of the topological and connectivity of the respectively obtained network. Hierarchical extensions of these measurements [6], which consider further neighbor- hoods around each node, can also be used in order to provide additional information about the textures [7]. In particular, the ability of such hierarchical features to express from local (i.e. close node neighborhoods) to global (i.e. more distant neighborhoods) properties of the texture contributes further to integrating the local and global aspects often found in im- ages.