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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
It has been shown (Mallat, 1998) that fast implementation of
(12) can be achieved when s is an integer power of 2 by
filtering alternatively through a low-pass filter (L) and a high-
pass filter (H).
Then, the external energy at scale s is defined as the negative
of the modulus of wavelet transform at scale s
Wi yy (13)
"image
SE = rf +
The above definition. of external energy together with the
continuation method in the wavelet domain represents a
generalized version of the gradient-based — scale-space
continuation method.
We employ this wavelet- based snake model in our experiments
on satellite images. The flow chart of utilized model is shown
in Figure 1.
snake shake snake
final snake Æ calculation |< calculation «calculation |<<— initial snake
wavelet wavelet wavelet
modulus modulus modulus
f d I
H H H ;
lowpass lowpass lowpass i
A i wavelet
i decomposition
Original L 1 L i
- b :
Image I > lowpass lowpass 4 lowpass i
* pe scale
fine coarse
Figure 1. Flow chart of the wavelet-based active contour model
4. TESTS AND RESULTS
The wavelet-based active contour model has been tested on
satellite images to determine different features and detect linear
characteristics. This model has been applied on SAR images
first, and then on high resolution images.
In this paper we present tests carried out on a SAR image of
Italy aimed at the detection of the coastline.
Coastline detection is generally based on the comparison with
existing cartography, which is relative to temporarily distant
periods and it would therefore demand a repeated updating not
realistically feasible.
The use of satellite images represents, potentially, a faster and
flexible alternative. In particular, these images allow to cover
wide scales, at unprecedented uniform accuracy levels.
Edge detection in SAR images is made difficult by the presence
of speckle, and std. methods developed for optical images are
generally applied only after a process of speckle reduction.
The wavelet-based active contour model combine wavelet
decomposition (Dohono, 1995) and edge detection in a single
procedure.
With reference to the flow chart in Figure 1, the first operation
consists in filtering through a low-pass filter and a high-pass
filter the original image. We shall refer as an illustration to the
SAR image acquired by the ERS-2 Satellite on 25 June 1995 of
gulf of Salerno (Italy).
Figure 2. Original image
After the low-pass and high-pass filters are applied, the results
arc displayed in the following figures, which refer to three
different scales of increasing accuracy
SEES ; PY
ARE
SG
Figure 3. Low-pass and high-pass filters applied to the original
image at three different scales of increasing accuracy.
We next calculate the wavelet modulus by using (13) at all
scales. At each step, the snake is obtained. The resulting curve
is used as an initial guess for the snake at the next finer scale.
The process is repeated until the finest scale available in the
original image is reached .
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