CN - Convolution ||

PURPOSE

Computes the convolution product of two pictures by using the Fourier transform relationship. Operation 'CN' works for 2D as well as 3D input data. The dimensions of the pictures must correspond to each other. The dimensions need not be powers of two (see 'FT' for any restrictions).

SEE ALSO

CN N	[Convolution - Normalized ||]
CC	[Cross Correlation ||]
CC N	[Cross Correlation - Normalized ||]
AC	[Auto Correlation ||]
AC N	[Auto Correlation - Normalized ||]
CC C	[Cross Correlation Coefficient]
FT	[Fourier Transform ||]

USAGE

.OPERATION: CN

.INPUT FILE: PIC001
[Enter the name of the first picture.]

.REFER FILE: REF001
[Enter the name of the second picture, which is used as the reference.]

.OUTPUT FILE: CNF001
[Enter name of the file which will contain the convolution coefficients. It can be the same as the input file. In this case INPUT FILE will be replaced by the convolution.]

NOTES

1. The type of the input data can be real or Fourier in any mixed form.

2. The convolution data are not scaled.

3. The origin of the CNF is at (NSAM/2 + 1, NROW/2 + 1).

4. The convolution product contains artifacts from wrap-around overlaps implicit in the Fourier computation. However, the convolution product is artifact-free within
   -L <= K <= +L
   -M <= I <= +M
   if the pictures are surrounded by frames containing the average, where the frame width is M/2 and the frame height is L/2. The complete artifact-free convolution product is obtained for the widths M=NROW/2, L=NSAM/2. In this case, the padded pictures are just twice as large in each dimension as the original pictures.

5. Note that RC (Real Convolution) offers an alternative to Fourier computation of the convolution product. RC should be used if the width of the point spread function is small (.le. 15).

6. If the data cannot fit into the memory use the 'FT' and 'MU' commands to calculate the CNF:

    
                 FT 
                 INPUT1 
                 FOUR1 
                 FT 
                 INPUT2 
                 FOUR2 
                 MU 
                 FOUR1 
                 FOUR2 
                 FT 
                 FOUR2 
                 CNF12 
            

   Warning: The origin of CNF12 calculated in this way is in (1,1).

SUBROUTINES

FMRS_2, FMRS_2R, FFTMCF, FMRS_1, FMRS_3, FMRS_3R, CNRS_2, CNRS_3, CNRD_2, CNRD_3

CALLER

CORR1