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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.

Transient texture synthesis based on multiple templates

Saitoh T., Sato M., Kaneko T., Kuriyama S.

Machine Graphics and Vision

2003

Vol. 12, No. 4

525-537

Texture synthesis based upon a sample image or template has attracted much attention recently. This paper describes a new blending algorithm for synthesizing a transient texture based upon two or more templates that gives an impression of a gradual transition from one template to another. Based upon a pair combination out of four templates, we synthesize six transitional textures. Then, we shown that various blending patterns can be designed by controlling the blending ratio maps. Based upon investigations of unsuccessful results of blending, we derive some necessary conditions on the statistical properties of templates for the applicability of this synthesis method.

Fast 2D vector field visualization using a 2D texture synthesis based on an autoregressive filter : Application to cardiac imaging

Khouas L., Clarysse P., Friboulet D., Odet C.

Machine Graphics and Vision

1998

Vol. 7, No. 4

751-764

This paper presents a new technique for vectoe field visualization and its application to the motion estimation of the heart. Our approach is based on the principle of filtering a texture over the data to visualize. For this purpose, we have first developed a texture model that allows 2D synthesis of furlike texture. The technique is based on a non stationary two dimensional Autoregressive synthesis (2D AR). The texture generator allows a local control of orientation and length of the synthesized texture (the orientation and length of filaments). We have experimented the use of this texture model to represent 2D vector field. We use orientation, lenght and color attributes of our furlike texture to visualize local orientation and magnitude of a 2D vector field. The visual representations produced seem satisfying since complete information about local orientation is easily perceived. In addition, due to the AR formulation, the obtained technique is computationally efficient. In particular, the application of this twchnique to the visualization of the myocardial motion has proven very useful.