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 [f],[con],[dif],[dis]

[This operation takes up to 4 optional register variables. On completion of the operation,
First variable receives: Optimum scaling factor.
Second variable receives: Offset between 2 volumes.
Third variable receives: Mean relative error.
Fourth variable receives: Discrepancy.]

.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: THREEDDIF001
[Enter file name for difference. Enter "*" if no difference volume is desired.]

NOTES

1. Error formulas:
   Mean relative error: E = SUM |F*V2-V1-CON| / SUM |V1-AV1|
   Discrepancy: E = SQRT [SUM |(F*V2-V1-CON)**2| / SUM |(V1-AV1)**2|]
   Where:
   V1,V2 = Voxel values of volume 1 and volume 2.
   F = Optimum scaling factor.
   CON = Offset between the two volumes.
   AV1 = Average voxel under mask in volume 1
   

2. For more details about the error measures see :
   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