## CC N - Cross Correlation - Normalized ||

(03/02/01)

PURPOSE

Computes the normalized cross-correlation function of two images/volumes by using the Fourier transform relationship. The dimensions of the pictures must correspond to each other.   Example.

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

USAGE

.OPERATION: CC N

.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: CCF001
[Enter name of the file which will contain the cross-correlation coefficients. It can be the same as the input file. In this case the input file will be replaced by the cross-correlation.]

NOTES

1. The input data must be real. This operation does NOT accept Fourier format files.

2. The cross-correlation data are normalized.

3. The origin of the CCF is at (NX/2 + 1, NY/2 + 1, NZ/2 + 1).

4. The CCF contains artifacts from wraparound overlaps implicit in the Fourier computation. However, the CCF 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. 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 pictures are just twice as large in each dimension as the original pictures.

5. The use of 'CC N' with identical input and reference files is equivalent to the 'AC' (Auto-Correlation) operation. The input sequence:
CC N
PIC001
PIC001
has the same effect as:
AC
PIC001

6. If the data cannot fit into the memory, use the 'FT' and 'MU M' commands to calculate the CCF:
FT
INPUT1
FOUR1

FT
INPUT2
FOUR2

MU M
FOUR1
FOUR2

FT
FOUR2
CCF12
WARNING: The origin of CCF12 calculated in this way is in (1,1,1).

SUBROUTINES

CCRS, FMRS_1, FMRS_2, FMRS_3, CCRD_2, CCRD_3

CALLER

CORR1