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Generalized second-order invariance in texture modeling

Hillion A., Roux C., Donescu I., Avaro O.

Machine Graphics and Vision

2006

Vol. 15, No. 1

73-97

In image processing, micro-textures are generally represented as homogeneous random fields, the term "homogeneous" indicating a second-order stationary random process. However, such a formulation is restrictive, and does not allow for the processing of anisotropic textures. The aim of this paper is to study a generalization of second-order stationarity to second-order invariance under a group of transforms, in order to apply this generalization to texture modeling and analysis. The general formulation of second-order homogeneity or G-invariance is given in relation to the framework of group theory. Two approaches are derived, taking into consideration transitive groups and generalized translations. For the latter approach, an important particular case is outlined, in which a second-order G-invariant random field X can be one-to-one associated to asecond-order stationary random field. Some examples of interesting groups of transforms are given. Finally, Cholesky factorization is applied for the synthesis of random fields showing the generalized invariance property.

Multi-scale morphological modeling of a class of structural texture

Zaremba M. B., Palenichka R. M., Missaoui R.

Machine Graphics and Vision

2005

Vol. 14, No. 2

171-199

Consistent and time-efficient modeling of textures is important both for realistic texture mapping in computer graphics and correct texture segmentation in computer vision. A large class of natural and artificial images is represented by the so-called structural textures, which contain visibly repetitive patterns. The multi-scale morphological modeling approach proposed in this paper explicitly describes shape and intensity parameters of structural textures. It is based on a cellular growth of a texture region by a sequential morphological generation of structural texture cells starting from a seed cell. Its main advantage is a concise shape representation for structural texture cells in the form of piecewise linear skeletons. Another advantage is a robust and computationally efficient estimation of texture parameters. The cell parameter estimation is based on the cell localization and adaptive segmentation using a multi-scale matched filter. The experiments reported in the paper are related to texture parameter estimation from synthetic and real textures as well as structural texture synthesis based on the estimated parameters.