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In this work we have chosen the Kullback distance
between two Gaussian models of textures :
Clearly, one is interested in being able to define a distance measure,
which is invariant to translation and rotation.To achieve the desired invariance, we have implemented the following
procedure:
 Estimate the parametric model of each texture patch.
 For textures with harmonic components, the texture is
first rotated so that its dominant harmonic component is aligned with
a predefined direction (the xaxis, for example).
 For textures with evanescent components, the dominant evanescent
component is considered the one whose modulating 1D
purelyindeterministic processes have maximal variance. Thus, the texture is first rotated so that its dominant evanescent component has
.
 For textures with harmonic components where the phase of the
dominant component is not zero, we crop a subpicture of the original in which the phase of the dominant component is zero.
 Reestimate the texture parameters to find the parameters of
all the model components.
Figure:
Textures ordered using the Kullback distance. The test texture is structured, dominantly harmonic.

Test Texture 

The Kullback distance is computationally expensive. Therefore we
derived a hierarchical approach :
 if both textures are deterministic : the
distance becomes the euclidean norm between spectral
densities
 if both textures are purely random : the distance is
reduced to the ItakuraSaito distance
 if one texture is purely random and one texture is
deterministic : the distance is infinity
Figure:
Textures ordered using the hierarchical distance. The test texture is structured, dominantly harmonic.

Test Texture 

Next: Unsupervised segmentation of textures
Up: Indexing and segmentation of
Previous: Estimation of the model
Radu Stoica
19990521