Cavalieri Estimator formulas
Area associated with a point (Ap)
- g2: Grid area
Volume associated with a point (VP)
- m: Section evaluation interval
: Mean section cut thickness
Estimated volume (
)
- Ap: Area associated with a point
- m’: Section evaluation interval
: Mean section cut thickness- Pi: Points counted on grid
Estimated volume corrected for over-projection ([v])
- t: Section cut thickness
- k: Correction factor
- g: Grid size
- a’: Projected area
Coefficient of error (CE)
- TotalVar: Total variance of the estimated volume
- n: Number of sections
- Pi: Points counted on grid
Variance of systematic random sampling (VARSRS)
, 
- m: Smoothness class of sampled function
- s2: Variance due to noise
- n: Number of sections
: Shape factor
R e f e r e n c e s
García-Fiñana, M., Cruz-Orive, L.M., Mackay, C.E., Pakkenberg, B. & Roberts, N. (2003). Comparison of MR imaging against physical sectioning to estimate the volume of human cerebral compartments. Neuroimage, 18 (2), 505–516.
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.
Howard, C. V., & Reed, M.G. (2005). Unbiased Stereology, Three-Dimensional Measurement in Microscopy (Chapter 3). New York: Garland Science/BIOS Scientific Publishers.