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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
for enhancing the spatial details but also keeping the spectral
fidelity of the IRMSS image.
2. METHOD PRINCIPLE
Generally, each pixel in a lower resolution image is in
correspondence with some given numbers of pixels (called as
sub-pixels) in a higher resolution image after precise
registration. Data fusion is to decompose each pixel in a lower
resolution image into a group of sub-pixels and to predict their
values, which can not be observed in the lower resolution image.
The ideal situation is that the predicting values for these sub-
pixels are the same as their real observation data. In this case,
not only the spatial details are enhanced, but also the spectral
fidelity is preserved. However, this is only ideal, and it is
impossible in application.
Based on remote sensing theory, the average value of these sub-
pixels real observation data is equal to their correspondent pixel
brightness value in a lower resolution image. Therefore, cach
pixel brightness value in the lower resolution image should be
equal to the average value of its co-registered sub-pixel values
in the new fusion image, i.e., the spectral energy is unchanged
after data fusion processing. In this case, the fidelity to the
image spectral properties will not be destroyed to some extent.
In fact, the spectral energy is unchanged at least within a single
original pixel of the lower resolution image. According to this
kind of signature, a new method, termed as Preserving Spectral
Fidelity method (named as PSF for simplicity), can be used for
data fusion to enhance the spatial details of a lower spatial
resolution image without destroying its spectral fidelity.
3. ALGORITHM
Based on the analysis as above, each pixel in a lower resolution
image is in correspondence with some given numbers of pixels
in a higher resolution image after precise registration. Firstly,
for each pixel in a low resolution image, the average value of
its correspondent sub-pixels values in a high resolution image is
computed; secondly, calculate the difference between the pixel
brightness value in the low resolution image and its average
value, generally, Each pixel in the low resolution image will
have a correspondent average value in the high resolution
image and have a given difference; then, add the difference to
every sub-pixel value in the high resolution image. This
procedure is applied to every pixel to produce a new image,
Which will have similar spatial details to the high resolution
image, since it is derived from the high resolution image; at the
same time, it still keeps its original spectral fidelity of the low
resolution image, because the spectral energy is unchanged
within one pixel of the low resolution image.
The operation procedures are as the following:
(1). To compute the average value of a group of sub-pixel
values in a higher resolution image. Considering the spatial
resolution of CCD images(19.5m) and IRMSS images (78m),
one pixel in an IRMSS image is in correspondence with 4x4
sub-pixels in a CCD image. Set CCD and IRMSS digital image
functions as DN, and DN, respectively. For any pixel at (x, y)
M an IRMSS image, its correspondent average value
a NUS . p^
DN, (x, y) in a CCD image is computed as the following:
911
Y DN (Ax e Ay j) (1)
iz0. jz0
BN ys
4x
Here: xy=0,1.23,...
Each pixel in the IRMSS image will have a group of co-
registered sub-pixels and have a correspondent average value in
the CCD image.
(2). To calculate the difference between the pixel brightness
value in the IRMSS image and its correspondent average value
in the CCD image.
Every pixel in the IRMSS image will have a given difference,
so that the difference is a variable of pixel position (x, y),
fx, y) :
f Gy) * DN (x, y) - DN, (x, y) (2)
(3). To add the difference to every sub-pixel value in the CCD
image and to produce a new pixel brightness value
DN (4x +i4y+ J):
DN, (4x +i4y + j) = DN, (4x +idy + J) - f(x, y) (3)
Equation (3) is a mathematic model of preserving spectral
fidelity method for data fusion. Each pixel in an IRMSS image
will have a group of co-registered sub-pixels in a CCD image,
this procedure is applied to each pixel in the IRMSS image and
further to every sub-pixels in the CCD image to produce a new
image.
Since the new image is derived from the CCD image, obviously
it has the similar spatial information to the CCD image. At the
same time, the new image keeps the spectral energy unchanged
within one pixel of the IRMSS image, so that the new image
has the similar spectral information to the IRMSS image and
the spectral fidelity is preserved. It is easy to prove the spectral
energy unchanged within one pixel of an IRMSS image after
data fusion processing.
From Equation (3), compute the average value for a group of 4
x4 sub-pixels, which are co-registered with one pixel in an
IRMSS image.
p oS (4)
DN, (x, y) = > DN, (Ax íAy * J) Ut
X^ i20. j-0
i.e.,
1 1=3,j=3 : 5 ^ 5
DN, (x, v) = pn > (DN, (4x +idy+ j)+ f(x.) ©)
X
i-0.;-0
Combine equations (1) and (2):
