A regular mosaic is a special case of spatially homogeneous textures formed by tiling where each tile represents the same prototype (texel). Let the texel have a rectangular shape. Then the Gibbs random field model with multiple pairwise pixel interactions permits us to quantitatively estimate both the orientation and size of the rectangle so that the texel can be cut out from a given training sample. Of course, there are a big number of equivalent cut-outs differing by "phase", that is, by relative position of the tiling borders with respect to the image pattern.
Given the estimated tiling of the training texture, the texel can be easily obtained by joint processing of all its samples (tiles). But even each tile itself acts as the approximate texel, as is shown, for example, in my recent paper (pdf-file) submitted to the "Vision Interface 2002" conference in Canada.
The following examples show more in detail how a large-size prototype of some natural regular mosaics can be simulated fast by estimating its rectangular texel: