CG - Center of Gravity

PURPOSE

Compute coordinates of center of gravity of an image/volume with respect to the SPIDER image/volume center (NX/2 + 1, NY/2 + 1, NZ/2 + 1). Also computes radius of gyration for volumes.

SEE ALSO

CG PH	[Center of Gravity - Phase approximation ||]
SH	[Shift - using bilinear/trilinear interpolation ||]

USAGE

.OPERATION: CG

   <or>
CG [x],[y],[z]

[This operation can take three or four optional register variables. On completion of operation, if these variables are present,
First variable receives: X Center of gravity.
Second variable receives: Y Center of gravity.
With volumes, third variable receives: Z Center of gravity.
With volumes, fourth variable receives: Radius of gyration.

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

.THRESHOLD: 0.23
[Only data above this threshold will be used in computation.
The COG determination is very poor with typical high noise particle images windowed from cryo-em micrographs without an appropriate threshold which is hard to determine apriori. Try 'CG PH' for such images but even these alternative central measures may have problems. ]

NOTES

1. The coordinates of the center of gravity are printed out and placed into the optional register variables appearing in the operation line.

2. The center of gravity is usually not meaningfull for typical high noise particle images windowed from cryo-em micrographs. Try CG PH' for such images.

3. For definition of the radius of gyration, see: International Tables of Crystallography, vol. III, p327.

4. COG Algorithm (1D analog): Sum product of all Pixel values by their position, Then divide by sum of all pixel values.

5. USAGE EXAMPLE: To shift an image to its center of gravity computed for a threshold of T=0.23, one could use the following operation sequence:
   
   CG [x],[y]
     PIC001
     .23
   
   SH
     PIC001
     SHI001
     -[x], -[y]
   

SUBROUTINES

CENGR3

CALLER

UTIL1