CG PH - Center of Gravity - Phase approximation ||

(5/04/13)

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

  1. To place the center of gravity at the origin one has to use the 'SH' operation and reverse the signs of the shifts.

  2. Implemented by P. Penczek.

  3. This operation only works for images where the object is bright (white) on a dark background.

  4. 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'.

  5. 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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