# Full text: Mapping without the sun

```5 BI-RESOLUTION METHOD
5.1 The principle of bi-resolution method
If we can acquire image couples of the same landscape in the
same or similar spectral band with two different spatial
resolutions, the higher resolution image can stands for the
landscape so that the ratio of the image spectra gives the lower
resolution sensor’s MTF. Its theory basis is that the MTF of
reference image is nearly 1 at the frequency of interest in low
spatial resolution image and therefore is negligible.
\ im ageL„„(u,vi
estMTF Low (u,v) =
image Kcf {u,v)\
_ |scenetu^MTF^u^)
(a)
| scene(u, v)| MTF Ref (u, v)
MTFlo W {u,v)
(b)
Ml'F Rtf (u,v)
= MTFuwiU’V)
Where v ) are spatial frequency coordinates in units of cycles
per pixel, MTF Low (u,v) - MTF Rc/ (u,v) are MTF of low spatial
resolution image and reference image respectively.
image lur (u,v) * s the spectra image of low spatial resolution
image, which is the multiplication of the observed scene
spectrum and MTF, image R (u, v) * s the spectra image of
reference image. Cancellation of term | iC g„ e ( U)V )| in equation
(a) leads to equation (b). Because MTFr ( wv )is nearly 1, the
ratio of the image spectra gives the lower resolution sensor
MTF.
5.2 Target deployment/selection standards for bi-resolution
method
There is no special requirement for bi-resolution MTF
estimation method targets. However, to get ideal result, it’s
better to choose an image contain a variety of features, such as
roads, shorelines, buildings, etc. that exhibit high spatial
frequency content.
Another requirement is that the spatial resolution difference
should be as much as possible to insure that the higher
resolution image can stands for the true landscape.
5.3 Data processing steps for bi-resolution method
This method starts with the image simulation with an initial
PSF, This PSF is to be sampled as the high resolution image.
Convolving the high resolution image with this PSF and
undersampling at the low resolution sampling rate yields an
image which is compared to the low resolution image through a
least square residual computation. The initial parameter value is
then modified in order to minimize this least square residual,
according to a classical least square minimization algorithm.
The iterative process will end when the relative residual change
between two iterations goes below a threshold level to be fixed
by the user. Then, the PSF can be treated as the PSF of low
resolution sensor. A Fourier Transform is applied to the PSF
and normalized to obtain corresponding MTF.
6 ANALYSIS AND COMPARISON
We have introduced the principle of several widely-used
on-orbit MTF estimation methods (including point source/array
method, knife-edge method; pulse method, and bi-resolution
method), their target deployment/selection standards, data
processing steps. Each method has its applicability and
limitations. We should choose the optimal method according
the spatial resolution of sensor and target condition.
1) For point source/array method, it is suitable for
high/moderate resolution sensor MTF estimation. We can
directly obtain 2-D PSF and MTF, but this method requires
deploying special targets and the cost is relatively high. This
method has been successfully applied to MTF estimation of
Landsat/TMN SPOT^ Quickbird.
2) The target for knife-edge method is relatively easy to
deploy or select. Very high SNR can be obtained leading to
accurate MTF estimation. But for low resolution sensors, it is
difficult to find a large enough target.
3) For low resolution sensors, pulse method is a good choice.
While good results can be obtained, limiting factors including
controlling background regions on either side of the pulse,
avoiding zero-crossing when designing the target, and directly
deriving the PSF.
4) Bi-resolution method requires acquiring image couples of
the same landscape in the same or similar spectral band with
two different spatial resolutions simultaneously. The data
processing of this method is relatively complex, and it is
sensitive to noise and aliasing.
7 EXAMPLE
In on-orbit MTF estimation module, knife-edge method and
pulse method is the .primary MTF estimation methods. There
we give an example of MTF estimation result of SPOT/Pan
image using knife-edge method and pulse method.
7.1 Knife-edge method target and result
The targets used for knife-edge method is runway in Dalian
airport. Three different targets are given in figure 4 and the
MTF estimation results are shown in figure5.
```

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