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Equations: Spaceballs

Spaceballs for details about the probe or View/Print PDF

 

Length estimate

 

This equation eliminates the terms F2 (area-fraction) and F3 (thickness-fraction) used by Mouton et al. (equation 2, 2002) by including that information in v (volume sampled).
n : Number of sections used
Qi : Intersections counted
v : Volume (grid X * grid Y * section thickness)
a : Surface area of the sphere
ssf : Section sampling fraction
Variance due to noise
Qi : Intersections counted
Variance due to systematic random sampling
s2 : Variance due to noise
m : Smoothness class of sampled function
Total variance TotalVar = s2 + VARSRS
s2 : Variance due to noise
VARSRS : Variance due to systematic random sampling
Coefficient of error
TotalVar : Total variance
s2 : Variance due to noise

 

References

Gundersen, H.J.G., Vedel Jensen, E.B., Kieu, K., & Nielsen, J. (1999). The efficiency of systematic sampling in stereology—reconsidered. Journal of Microscopy, 193 (3), 199–211.

Gundersen, H. J. G., Jensen, E.B. (1987). The efficiency of systematic sampling in stereology and its prediction. Journal of Microscopy, 147 (3), 229–263.

Mouton, P. R., Gokhale, A.M., Ward, N.L., & West, M.J. (2002). Stereological length estimation using spherical probes. Journal of Microscopy, 206 (1), 54–64.

 

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