## CN N - Convolution - Normalized ||

(09/27/06)

PURPOSE

Computes the normalized convolution product of two images/volumes by using the Fourier transform relationship. The dimensions of the pictures must correspond to each other.   Example.

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

USAGE

.OPERATION: CN N

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

.REFERENCE 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 the input file will be replaced by the convolution.]

NOTES

1. The input data must be real.

2. The convolution data are normalized.

3. The origin of the CNF is at (NX/2 + 1, NY/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=NY/2, L=NX/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

NORM3, FMRS_2, FMRS_2R, FFTMCF, FMRS_1, FMRS_3, FMRS_3R, CNRS_2, CNRS_3, CNRD_2, CNRD_3

CALLER

CORR1