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. About wavelets


Thanks to the wavelet coefficients, it is theoretically possible to differentiate textures with orientation criteria.

Figure 4: Orientation and wavelet transformation
Synthetic image
\includegraphics[scale=0.7]{carre.PS}
Wavelet transform at order one
\includegraphics[scale=1]{onde.PS}

Undecimated wavelets

The use of decimated wavelets has the drawback to be (a priori) not translation invariant.

But we want to construct a translation invariant feature for textures. So we use undecimated wavelets.

Wavelet packet transform

A large number of textures can be modelized as quasi-periodic signals (repetition of the same stucture with slight variations) whose dominant frequencies lie in median frequencies channels .

In the case of the packet wavelets, each block of the decomposition can be decomposed again (see figure 5).

Figure 5: Packet wavelet transform: at each step, all the blocks of the wavelet transform are redecomposed
\includegraphics[scale=0.7]{wavelet.eps}

Gray level independence

The mean of the gray level must not be a feature for a texture. That is why we modify the low frequency block by setting its mean to zero.


next up previous
Next: . Textures modelisation Up: Supervised classification for textured Previous: . Classification
Jean-Francois Aujol 2002-12-03