## CC H - Cross Correlation - Phase ||

(07/29/11)

PURPOSE

Computes the phase cross-correlation function of two images/volumes using the Fourier transform relationship. The dimensions of the two images/volumes must be the same. WARNING: This operation is expected to fail if there are Fourier coefficients of zero!   Example.

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

USAGE

.OPERATION: CC H

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

.REFERENCE FILE: REF001
[Enter the name of the second image/volume, which is used as the reference.]

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

NOTES

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

2. The cross-correlation data are not scaled. (If values are very, very large then maybe you should reduce the FMAX of the input files first?)

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 images 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 phase correlation is calculated as follows in FORTRAN:
```
CTEMP  = X(I,J) * CONJG(Y(I,J)) * CMPLX(COS(ARG),SIN(ARG))
O(I,J) = CTEMP / (SQRT(REAL(CTEMP)**2 + AIMAG(CTEMP)**2))
```

6. While using phase correlation beware of artifacts that may appear from harmonics with small amplitude - near zero harmonics have phase undefined. Noise can become a serious problem, even making the result completely useless.

SUBROUTINES

FMRS_2, FMRS_2R, FMRS_1, FMRS_3, FMRS_3R, CCRS_2, CCRD_2, CCRS_PH_3, CCRD_3

CALLER

CORR1