## CN - Convolution ||

(09/10/96)

PURPOSE

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

 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] rc [Real Convolution ||] FT [Fourier Transform ||]

USAGE

.OPERATION: CN

.INPUT FILE: PIC001
[Enter the name of the first image/volume.]

.REFER FILE: REF001
[Enter the name of the second image/volume, 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 (NX/2 + 1, NY/2 + 1, NZ/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
&'nbsp;  -L <= K <= +L
&'nbsp;  -M <= I <= +M
if the image/volumes are surrounded by frames containing the average, where the frame width is M/2 and the frame height is L/2. This can be achieved by use of the 'PD' operation.
The complete artifact-free CCF is obtained for the widths M=NY/2, L=NX/2. In this case, the padded image/volumes are just twice as large in each dimension as

5. 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 image/volumes 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 image/volumes are just twice as large in each dimension as the original image/volumes.

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

7. 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 (1,1,1).

SUBROUTINES

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

CALLER

CORR1