3.3.2
Two experimental results are presented in the following (More results can be found in Chapter 3 of [Li 1991].). The first is
the reconstruction of a real image of size 
(Fig.3.3). Here, APF 1 (
) is used and
the parameters are empirically chosen as 
, 
. The
result shows that the reconstructed image is much cleaner with
discontinuities well preserved.
Figure 3.4: Step and roof edges (right) detected from a pyramid image (left).
Step edges are shown in dots and roof edges in crosses.
From (Li 1995b) with permission; © 1995 IEEE.
The second experiment is the detection of step and roof edges from a
simulated noisy pyramid image of size 
(Fig.3.4). The detection process runs in three stages:
1) regularizing the input image and computing images of first
derivatives in the two directions from the regularized image using
finite difference, 2) regularizing the derivative images and 3)
detecting steps and roofs by thresholding the regularized derivative
images. APF 2 (
) is used and the parameters are
empirically chosen as 
, 
for the first
stage of the regularization and 
, 
for the second stage.
Edges in the horizontal and vertical directions are best detected while those in the diagonal directions are not so well done. This is because only derivatives in the two axes directions are considered in the DA discussed so far; changes in the diagonal directions are largely ignored. Regularizers using the 8-neighborhood system (see the footnote for Eq.(3.53) should help improve the detection of diagonal changes.