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