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DR ERR - Density Reference - Error between two volumes

(8/25/97)

PURPOSE

Calculates the mean relative error and the discepancy between two volumes. A scaling factor and additive constant is determined to scale the first volume such that the errors are minimized.

SEE ALSO

DR [Density reference]
DR DIFF [Density reference - error & difference between 2 volumes]

USAGE

.OPERATION: DR ERR

.FIRST FILE: 3DR004
[Enter name of 3-D file]

.SECOND FILE: 3DR005
[Enter name of second 3-D file]

NOTES

  1. Error formulas:

  2. Mean relative error: E=SUM |A*DIJ2-DIJ1-CONST| / SUM |DIJ1-D|

  3. Discrepancy: E=SQRT [ SUM ((A*DIJ2-DIJ1)**2)/ SUM ((DIJ-D)**2)]

  4. DIJ1,DIJ2 voxel values of volume 1 and volume 2
    An optimum scaling factor.
    CONST offset between the two volumes.

  5. For more details about the error measures see e.g.: Colsher J.G. Iterative Three-dimensional Image Reconstruction from Tomographic Projections, Computer Graph. & Image Proc. 6, (1977) 513-537.

  6. Herman G.T. Two Direct Methods for reconstructing pictures from their projections: A comparative study. Computer Graph. & Image Proc. 1,(1972) 123-144

SUBROUTINES

COMP3D

CALLER

VTIL2

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