Stochastic simulation
Statistical Inference for Spatial Processes
Statistical Inference for Spatial Processes
Group theoretical methods in image processing
Group theoretical methods in image processing
A taxonomy for texture description and identification
A taxonomy for texture description and identification
Shape from texture and contour by weak isotropy
Artificial Intelligence
Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
Log-Polar Wavelet Energy Signatures for Rotation and Scale Invariant Texture Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Signal modeling and parameter estimation for 1/f processes using scale stationary models
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 05
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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 a second-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.