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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
T1 > T2 7 the threshold values
f (i j)= a value of source image wavelet
where
transformation
The above given thresholding is applied for two set of detailed
sub-images: | LHI,HLI,HHI which come from first
decomposition of the whole image and LH2,HL2,HH2 which
come from the second decomposition of the LL sub-image. This
thresholding respects the properties of sub-images: non-
directionality of the LL sub-image and the directionality of the
detailed sub-images. The results shown in figure ld is
a evidence that wavelet transformation with the proposed
thresholding is a useful method in de-noising.
Figure 1. The way from original to de-noised image
a = the original image
b = the decomposition into four sub-images (first level)
c = the result of the soft thresholding
d = the de-noised image
3. EDGE DETECTION USING LAPLACE OPERATOR
Edge detection is the process of extracting out locations of high
contrast in an image.
The most popular methods of this process use high-pass filters
of a specific size. The image convolution with a small filtering
mask approximates the first or second derivative of the image
intensity function. There are two detectors applied (Pitas,
2000):
* first order derivative — so called intensity gradient — i.e.
Roberts, Sobel - result is a vector,
* second order derivative - Laplace operator (laplacian) -
result is a scalar:
n 2
o. Q^o Q^o
&,)-7 9.78 (2)
ex^ y^
639
The intensity gradient is easy to perform but it gives very little
control over smoothing and edge localization. The Laplace
operator gives better results but it is very sensitive to noise,
more than the intensity gradient method. Therefore it is often
applied together with the Gaussian smoothing and they form so
called the Laplacian of Gaussian (LoG) operator. But the LoG
operator provides that the image intensity function operates in
the same way in any direction from each pixel. This is the
reason why both noise and detailed information are removed.
In this work the Laplace operator is used as the next step after
image de-noising.. The approximation of the equation (2) is
realized as a result of image convolution with the Laplace mask
and we obtain a laplassian image:
Ki, ]) * g, )* Lug G)
where = /(i, j) = laplasian image
gli, j) = the intensity value of de-noised image
)- 1954
J nusk zi -8 1
1 1 ]
4. THE EXECUTION OF ORTHORECTIFICATION
WITH A SPECIAL RESAMPLING
The orthorectification is the process of removing geometric
errors inherent within aerial and satellite images due to
a orientation of cameras and the influence on projection of
ground surfaces. In the indirect way of orthorectification for
the position on orthoimage the equivalent location in the source
image is calculated by using a projecting equations and by
applying a DEM and exterior orientation parameters of
a camera (Kraus, 1997). The procedure starts from ground
position (X,Y) and projects it towards to a coordinate system of
the source image and the position (x,y) is received. The source
image is a array where the position of pixels is represented
thrugh an integer row-columns coordinate system. Therefore
the orthorectification process comprises a digital resampling
procedure. This resampling relies on an assessment of the
intensity values of a group of pixels from source image to
assign a value to the position (x,y). Three algorithms of
resampling are normally employed in orthorectification
software packages: the nearest neighbor method uses the
intensity of one source pixel, the bicubic method interpolates a
new value from four pixels and the cubic convolution method -
from sixteen source pixels.
The Bilinear Interpolation and the Cubic Convolution often
produces similar results, however the Cubic Convolution
method generally produces a smoother output raster. But these
methods have the effect of a low-frequency convolution. Most
of the edges are smoothed, and some extremes of the data file
values are lost. Only the nearest neighbor method insures that
the extremes and subtleties of the data values are not lost. But
this method causes usually a stair-stepped effect around edges
(Erdas, 1999).
In the work described in this paper a special resampling method
was tested — see formula (4). The result is shown in the figure 2.
