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Pairwise Pixel Interactions in Texture Pyramids

This paper investigates how structures of pairwise pixel interactions are changing at subsequent levels of Gaussian or Laplacian pyramids representing spatially homogeneous image textures. Structural differences between the parent and child levels of the pyramid are analysed using the modelbased interaction maps (MBIM) describing relative interaction energies in a generic Gibbs random field model of the texture. It is shown that characteristic interaction structures at most levels in the pyramid remain almost the same in spite of the reduced image scales. The periodic structures for regular mosaics are closely related between the neighboring pyramid levels. The like dependencies hold for the close-range characteristic interactions in stochastic textures.