**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). using phase approximation. Example.

**SEE ALSO****CG**[Center of Gravity] **CENT PH**[Center image/volume using phase approximation] **SH**[Shift - using bilinear/trilinear interpolation ||]

**USAGE**- .OPERATION: CG PH [x],[y],[xr],[yr]

- or:

CG PH [x],[y],[z],[xr],[yr],[zr]

[For images this operation can return up to four optional register variables:

Variable Example Receives First [x] Integer approximation of X center of gravity Second [y] Integer approximation of Y center of gravity Third [xr] Sub-pixel X center of gravity Fourth [yr] Sub-pixel Y center of gravity [For volumes this operation can return up to six optional register variables:

Variable Example Receives First [x] Integer approximation of X center of gravity Second [y] Integer approximation of X center of gravity Third [z] Integer approximation of Z center of gravity Fourth [xr] Sub-pixel X center of gravity Fifth [yr] Sub-pixel Y center of gravity Sixth [zr] Sub-pixel Z center of gravity .INPUT FILE: FIL001

[Enter name of image/volume.]

**NOTES**

- To place the center of gravity at the origin one has to
use the 'SH' operation and reverse the signs of the
shifts.
- Implemented by P. Penczek.
- This operation only works for images where the object is
bright (white) on a dark background.
- This operation sometimes reports incorrect center (at the
upper left corner) for dumbbell shaped objects. The
error is sporadic even given the same input file. The
implementor states: 'The code is correct. The operation is
not foolproof; it sometimes fails'.
- The estimation of center of gravity in this algorithm is based
on phase approximation as following:

i) The projections of image densities onto X and Y axes are computed.

ii) First order 1D Fourier Transforms of each projection are computed.

iii) The maxima of first order harmonics on X and Y axes are taken as the coordinates of center.

Beware - negative images can generate systematic artifactual shift equal to half-size of image. Dumbbell-shaped objects also produce the same artifact.

**SUBROUTINES**- FINDCENT, CENT_3PH, CENT_PH

**CALLER**- UTIL1

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