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% @(#)transfwave.hlq 19.1 (ESO-IPG) 02/25/03 13:34:20
%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%.COPYRIGHT (c) 1993 European Southern Observatory
%.IDENT transfwave.hlq
%.AUTHOR 06-APR-93, IPG/ESO
%.KEYWORDS MIDAS, help files,
%.PURPOSE On-line help file for the command: TRANSF/WAVE
%.VERSION 1.0 JS : Creation, 06-APR-93
%----------------------------------------------------------------
\se
SECTION./WAVE
\es\co
TRANSF/WAVE JS 06-APR-93
\oc\su
TRANSF/WAVE Name_File_Image Name_File_Wavelet Which_Algorithm Nbr_Scale
[Cut_Off_Frequency]
compute a wavelet transform
\us\pu
Purpose:
Computes the wavelet transform of an image
\up\sy
Syntax:
TRANSF/WAVE Name_File_Image Name_File_Wavelet
[Which_Algorithm] [Nbr_Scale] [Cut_Off_Frequency]
\ys\pa
Name_File_Image = Name of the image
\ap\pa
Name_File_Wavelet = Name of the file which contains the wavelet
transform
\ap\pa
Which_Algorithm = Algoritm number (1 to 8)\\
1: a trous algorithm with a linear scaling function; the
wavelet function is the difference betwwen two resolutions\\
2: a trous algorithm with a B3-spline scaling function; the
wavelet function is the difference betwwen two resolutions\\
3: algorithm using the Fourier transform: without any
reduction of the samples between two scales the Fourier
transform of the scaling function is a b3-spline the
wavelet function is the difference between two resolution\\
4: pyramidal algorithm in the direct space, with a linear
scaling function\\
5: pyramidal algorithm in the direct space, with a b3-spline
scaling function\\
6: algorithm using the Fourier transform:
with a reduction of the samples between two scales the
Fourier transform of the scaling function is a b3-spline the
wavelet function is the difference between two resolution\\
7: algorithm using the Fourier transform:
with a reduction of the samples between two scales
the Fourier transform of the scaling function is a b3-spline
the wavelet function is the difference between the square of
two resolutions\\
8: Mallat's Algorithm with biorthogonal filters.\\
\\
2 is the default value.
\ap\pa
Nbr_Scale = Number of scales of the wavelet transform.
3 is the default value.
\ap\pa
Cut_Off_Frequency = 0.1 ... 0.5; default 0.5. The Cut_Off_Frequency
is necessary for algorithms using the Fourier transform. In
other cases, it is ignored. This value defined the cut-off
frequency of the scaling function.
\ap\see
See also:
HEADER/WAVE, RECONS/WAVE, VISUAL/WAVE
\ees\no
Note:
For the first three algorithms, there is no reduction of the
number of samples. Then the size of the wavelet transform is
equal to that of the image multiplied by the scale number.
For the algorithms 4 to 7, the number of samples is equal to
(NxN + N/2xN/2 + N/4xN/4 + ...).
For the last algorithm, the wavelet transform size is equal
to the image's one.
\\
The last algorithm is the only one which is not isotropic.
\on\exs
Examples:
\ex
TRANSF/WAVE image1 wave_image1 5 4
Computes the wavelet transform of image1 with 4 scales by
the pyramidal algorithm in the direct space. The result
is saved in the file wave_image1.
\xe \sxe
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