Next: . Complete functional
Up: Supervised classification for textured
Previous: . About wavelets
We characterize textures through their wavelet decomposition.
Idea
We consider that a texture is characterized by the energy of its wavelets coefficients.
If we note the function which represents this texture, we can write:

(4.1) 
where is the mother wavelet, the scaling function and the order of the decomposition.
Thus, we consider that a texture is characterized by the sequence:

(4.2) 
Probability distribution of the energy
S.G. Mallat checked experimentally that the distribution of the modulus of the wavelets coefficients in a subband follows a generalized gaussian law of the form:

(4.3) 
For the energy, we get, thanks to (4.3) (with ):

(4.4) 
Experimentally, we have checked that the distribution of the energy inside a subband is well approximated by a law of this type (see figure 6).
Figure 6:
Theoretical graph of the energy distribution in a subband (law (4.4)) and experimental histogram
Theoretical graph of the energy distribution in a subband (law (4.4)) 

Histogram of the energy distribution in a subband 


Next: . Complete functional
Up: Supervised classification for textured
Previous: . About wavelets
JeanFrancois Aujol
20021203