Synthesis of Weakly-Homogeneous Textures

Figure 7.6: Textures that cannot be synthesised using bunch sampling.

MBIM
	D75

MBIM
	Brick04

Bunch sampling cannot directly mimic local geometric deformations and signal deviation commonly seen in weakly homogeneous textures. Since the spatial variation, usually resulted from imperfection of image devices or defects of materials, is rather random and singular, global signal statistics like GLCHs are ineffective in modelling them. Figure 7.5 presents some results of the bunch sampling on several typical weakly-homogeneous textures. In these examples, the rectified, or homogenised synthetic textures D03 (Crocodile skin) and `Fabrics0010' are obtained, while local deformations of texture primitives in the original images are not preserved. In another example, the repetitive global structure of the texture `Ukrainian parade' is also reproduced although details of each single solder are missed and long strokes in the training texture `Paint0411' are cut short to the average size in the synthetic texture.

All the examples show the bunch sampling only rectifies a weakly-homogeneous texture. This problem is caused by the initial assumption that all the texels in a training texture have the same geometric structure. By the assumption, a single texel related to the MMP probabilities of image signals is used as a representative for each relative shift. The representative averages variations of all texels in both the geometric structure and the signal configurations, and results in the bunch sampling producing an idealised (precisely periodic) synthetic image for a weakly-homogeneous texture.

In addition, the bunch sampling fails dramatically on a class of aperiodic textures with irregular shapes and/or arbitrary placement of local objects, e.g. pebbles and brick tiles shown in Fig 7.6. In these cases, second-order signal statistics only simply cannot adequately model the training images.