Image Processing Reference
In-Depth Information
Fig. 11.3
Low resolution image with a high-resolution encrusted imagette with smoothed inner
periphery
This method provides a better simulation of the actual information at the outer
periphery and hence increases the accuracy of this area. This method mostly makes
use of the wavelet transform and multiresolution analysis. The paragraph below
summarizes the overall approach in a simplified manner without detailing the
mathematical basis of the proposed encrustation method.
The border is due to the abrupt transition from one resolution to another at the
periphery of the imagette. In the inner periphery, structures of any size are present,
including those of smaller size (high frequencies in signal theory). In the outer
periphery, only structures of larger size are present. The lower resolution means an
absence of structures of small size which can only be observed at higher resolu-
tions. The principle of our approach is that attenuation of the border discontinuities
can be made if some of smaller size structures can be injected in the outer periphery.
This will result in an increase of the effective resolution, thus creating a smooth
transition in resolution, and hence attenuating the border effects. Multiresolution
analysis allows extraction of small size structures from the imagette. Here only
the periphery is of interest. Wavelet transformation models change in information
for each pixel between two consecutive resolutions by means of the so-called wave-
let coefficients. The larger these coefficients in absolute values are, the more visi-
ble the corresponding structures will be. For higher resolutions, i.e. smaller
structures sizes, the wavelet coefficients are large at the inner periphery and null or
very weak at the outer periphery. Increasing the resolution of the latter is equivalent
to an injection of structures of small size, which is our objective. The wavelet
