186
7: Hua-mei Chen, Pramod K. Varshney
Table 7.1. Image pyramid constructed from digital aerial photograph
Level
Image size
Resolution Scaling
[pixel x pixel]
(m)
factor
0
4000x4000
0.1508
0.0222
2000x2000
0.3016
0.0444
2
1000xlOOO
0.6032
0.0887
3
500x500
1.2064
0.1774
4
250x250
2.4128
0.3548
5
125x125
4.8256
0.7096
image pyramid (Burt and Adelson 1983; Burt 1984; Toet 1992). Here we used
Haar wavelet decomposition to accomplish this task because of its simplicity.
For the experiment, an image pyramid of 6 levels (level 0 ~ level 5, level
o is the original resolution) was constructed. Table 7.1 lists the image size
and corresponding spatial resolution at each level. To apply the multi-scale
optimization strategy, we start with the registration of the HyMap image and
the aerial photograph at levelS. The aerial photograph at level 5 is served
as the floating image because of the reason mentioned previously. We denote
the transformation parameter set obtained at this level (i. e. scale, rotation, xdisplacement (in pixel), y-displacement (in pixel)) as [55, rs, dxs, dys], then the
parameter set [55/2, rs, dxs, dys] is used as the initial search point to optimize
the MI similarity measure between the HyMap image (reference image) and
the aerial photograph at level 4 (floating image). The reason for doubling the
scaling factor is that the resolution of the digital aerial photograph is doubled
when we move from levelS to level 4, as a result, the scaling factor between
the photograph at level 4 and the HyMap image is decreased by the same
factor 2. The above procedure is repeated until the digital aerial photograph at
level 0 (original resolution) is reached. Figure 7.4 summarizes the multi-scale
optimization procedure stated above.
In Fig. 7.4, {Fdf:Ol forms an image pyramid of L levels and the image at
each level is used in consecutive iterations, from i = L - 1 to i = 0, as the
~
ng
Floati
Image Fi
L
-'" ...
~
renee
Refe
image R
Maximization of MI
[SOi_I,'ili_l.dxOi_I,dYOi_l]
. .
using any local optimizer
= [Si 12, r"dx"dYi I
with initial search point [Si' lj,dxi,dYi]
[SOirOi,dxoi,dyo, ]
i = i-J;
Fig. 7.4. The multi-scale registration procedure used in the experiment
7: Hua-mei Chen, Pramod K. Varshney
Table 7.1. Image pyramid constructed from digital aerial photograph
Level
Image size
Resolution Scaling
[pixel x pixel]
(m)
factor
0
4000x4000
0.1508
0.0222
2000x2000
0.3016
0.0444
2
1000xlOOO
0.6032
0.0887
3
500x500
1.2064
0.1774
4
250x250
2.4128
0.3548
5
125x125
4.8256
0.7096
image pyramid (Burt and Adelson 1983; Burt 1984; Toet 1992). Here we used
Haar wavelet decomposition to accomplish this task because of its simplicity.
For the experiment, an image pyramid of 6 levels (level 0 ~ level 5, level
o is the original resolution) was constructed. Table 7.1 lists the image size
and corresponding spatial resolution at each level. To apply the multi-scale
optimization strategy, we start with the registration of the HyMap image and
the aerial photograph at levelS. The aerial photograph at level 5 is served
as the floating image because of the reason mentioned previously. We denote
the transformation parameter set obtained at this level (i. e. scale, rotation, xdisplacement (in pixel), y-displacement (in pixel)) as [55, rs, dxs, dys], then the
parameter set [55/2, rs, dxs, dys] is used as the initial search point to optimize
the MI similarity measure between the HyMap image (reference image) and
the aerial photograph at level 4 (floating image). The reason for doubling the
scaling factor is that the resolution of the digital aerial photograph is doubled
when we move from levelS to level 4, as a result, the scaling factor between
the photograph at level 4 and the HyMap image is decreased by the same
factor 2. The above procedure is repeated until the digital aerial photograph at
level 0 (original resolution) is reached. Figure 7.4 summarizes the multi-scale
optimization procedure stated above.
In Fig. 7.4, {Fdf:Ol forms an image pyramid of L levels and the image at
each level is used in consecutive iterations, from i = L - 1 to i = 0, as the
~
ng
Floati
Image Fi
L
-'" ...
~
renee
Refe
image R
Maximization of MI
[SOi_I,'ili_l.dxOi_I,dYOi_l]
. .
using any local optimizer
= [Si 12, r"dx"dYi I
with initial search point [Si' lj,dxi,dYi]
[SOirOi,dxoi,dyo, ]
i = i-J;
Fig. 7.4. The multi-scale registration procedure used in the experiment