DR DIFF - Density Reference - Error & Difference between two volumes

PURPOSE

Calculates the mean relative error and the discrepancy between two volumes within an (optional) mask. A scaling factor and additive constant is determined to scale the second volume such that the errors are minimized. Optionally volume 1 is subtracted from the scaled volume 2 and the results stored in an output volume. (operation includes all functions of 'DR ERR')

SEE ALSO

DR ERR

[Density Reference - Error between two volumes]

USAGE

.OPERATION: DR DIFF

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

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

.MASK FILE: MASK001
[Enter name of mask file or "*" if no mask is to be applied]

If a mask was specified :

.APPLY MASK TO BOTH, SCALING AND DIFFERENCE/ERROR? (Y/N): Y
[Specify if the mask should be applied only in the step of scaling the two volumes (answer: N) or, besides during scaling also during the error calculation and difference volume calculation (answer: Y) ]

.OUTPUT DIFFERENCE FILE: THREEDDIFFERENCE001
[Enter file name for difference. Enter "*" if no difference volume is desired.]

NOTES

1. Error formulas:
   Mean relative error: E=SUM |A*DIJ2-DIJ1-CONST| / SUM |DIJ1-D|
   Discrepancy: E=SQRT [ SUM ((A*DIJ2-DIJ1)**2)/ SUM ((DIJ-D)**2)]
   DIJ1,DIJ2 voxel values of volume 1 and volume 2.
   An optimum scaling factor.
   CONST offset between the two volumes.
   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.
   Herman G.T. Two Direct Methods for reconstructing pictures from their projections: A comparative study. Computer Graph. & Image Proc. 1,(1972) 123-144

SUBROUTINES

COMP3DMAD

CALLER

VTIL2