Comparison and Discussion

The structural identification yields a texel-based description that characterises a texture by texels and placement rules of their arrangement. Recently, several similar works describing a texture by its primitive elements have been proposed. However, instead of `texel', the majority of the known works use an alternative term `texton', suggested by Julesz, to refer to small objects or characteristic regions that comprise a texture. Research shows that only the difference in textons or in their density can be detected pre-attentively by human early visual system [54].

Motivated by Julesz's texton theory, a few recent works [63,71,100,101,102] employ a filter-based spectral analysis technique to relate textons to the centres of clusters in filter responses of a stack of training images. Conceptually, each texton, as a feature descriptor in the spectral domain, represents a particular statistical spectral feature describing repetitive patterns of a texture in the spatial domain. All the textons form a global texton dictionary, or a feature space, allowing to characterise a texture by an empirical probability distribution of the textons, i.e. the frequency with which each texton in the dictionary occurs in the texture. A nearest-neighbour classifier with similarity metrics based on chi-square distance between texton distributions, can classify textures into different categories. But since only the occurrences of a texton are taken into account, spatial information about relationships between the textons is completely lost in the description.

A texton-based generative model of image in [112] contains local constructs at three levels: pixels, image bases, and textons. An image base is a group of pixels forming a micro geometric element like a circle or a line. In this case, a texton is actually a mini-template consisting of a number of image bases of some geometric and photometric configurations. In an image, these textons are meaningful objects like stars or birds that could be observed. The probability model with parameters $\Theta=\{\Psi,\Pi,\kappa\}$ is specified as follows:

$$\Pr(g^\circ;\Theta)=\int{\Pr(g^\circ\vert\mathbf{B};\Psi)\Pr(\mathbf{B}\vert\mathbf{T};\Pi)\Pr(\mathbf{T};\kappa)d\mathbf{B}d\mathbf{T}}$$ (6.4.2)

where $\Psi$ and $\Pi$ denote global base and texton maps containing all the image bases or textons, respectively, in the entire configuration space of images, $\mathbf{B}$ and $\mathbf{T}$ are the base and textons maps, respectively, specific to a particular image $g^\circ$, and the probability distribution $\Pr(\mathbf{T};\kappa)$ accounts for the textons and their spatial relationships in the image $g^\circ$.

The MLE of the model parameters $\Theta$ or the estimates minimising the Kullback-Leibler divergence are learned using a data-driven MCMC algorithm. Due to the complex likelihood function, the experiments were limited in several aspects in order to keep the problem tractable: (i) only a small number of image bases in the global base map, e.g., a few Laplacian-of-Gaussian and Gabor base functions; (ii) the spatially independent textons for simplicity, and (iii) only very simple textures with a priori obvious image bases and textons.

In both above mentioned and most of other known texton-based approaches, spatial relationship among the textons is either neglected or otherwise too difficult to represent. In contrast, the proposed structure identification provides a much simpler but yet more complete texture description.