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
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