The expressions of [a'.sub.k] and [b'.sub.k] in the WGIF can be obtained according to (4)-(7) as shown below:
It is noted that the edge-aware weighting [[GAMMA].sub.g-k] is spatially varying in the WGIF; that is, [[GAMMA].sub.g-k] is larger than 1 when the pixel k locates in the edge area, and [[GAMMA].sub.g-k] is smaller than 1 when the pixel k locates in the flat area.
The comparison of [[??].sub.g-k] and [[GAMMA].sub.g-k] in WGIF of an image is shown in Figure 3.
When the input image [p.sub.i] and guided image [g.sub.i] are the same, the GDGIF has better edge preserving and smoother features than the GIF and the WGIF due to the following two points.
In fact, the value of [a".sub.k] in GDGIF is much closer to 1 than it is in GIF and WGIF. Hence, GDGIF has the best edge preserving feature.
As a result, we can select larger [epsilon] in GDGIF than that in WGIF and GIF, so that better smoothing is achieved without affecting the edge preserving .