Geometric Structure of Texels for a Stochastic Texture.

In this case, the shape of the single central cluster defines the desired structure. Each such texel behaves like a seed, and a texture is generated by randomly scattering the seeds over the image lattice.

Figures 6.3 and 6.4 schematically illustrate several texels for stochastic and regular textures, respectively, where each texture has a distinguishing geometric structure of texels corresponding to the spatial distribution of clusters in the MBIM.

The geometric structure can be used as a mask for sampling (retrieving) texels from a texture. For example, one can superimpose a mask at an arbitrary location on an image, the group of signals covered by the mask are related to a particular texel for the texture. In a same way, texels of the same structure but different signals are retrieved at different locations from the image. Since in our experiments most texels look like a bunch of image signals, this sampling method is also called in [40] bunch sampling.

Figure 6.9: Parameters, $\Psi=(\theta_x,\theta_y, m, n)$, of the placement grid for regular texture D34.

Figure 6.10: Tessellation of regular texture D34 by the placement grid and relative positions of bunches (texels), e.g., $(0,0)$ for Bunch a and $(\delta_{x},\delta_{y})$ for Bunch b.