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

USAGE

.OPERATION: CG

   <or>
CG [x],[y],[z]

[This operation takes 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 high noise images without an appropriate threshold which is hard to determine apriori.]

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. Use 'CG SYM' or 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