Cavalieri correction for overprojection

Good morning,

when doing Cavalieri analysis the results show volume and volume corrected for overprojection. I found the formula including correction factor k. What is this correction factor based on?

Thank you,

@KSchoenhoff If the sections through the region of interest are thick compared with the whole region of interest, the phenomenon of over-projection can cause data to be missed.

If we look at this 3-D region from the direction indicated by the arrow, we will not be able to appreciate the thinner part of the region on the right, because the thicker part on the left is visually projected and blocks us from seeing the region getting smaller on the right. What the correction does in the formula is take the biggest cross section and throw it away. The good news is we don’t need to worry about this if we make our sections, either physical or optical, thin enough to not experience great changes in cross-sectional area through-out the extent of the section. If you are working with thin optical or physical sections, you do not have to worry about over-projection. Here is a link to a more complete explanation: [see: Volume estimate and over-projection]

Hope this helps! Thank you

Thank you very much. So if understood correctly the overprotection is included when assessing Cavalieri volume estimates from 40µm thick sections. However, as multiple consecutive sections with a particular interval are sampled, over- and underestimation both occur, levelling to a balanced result.
In this particular case (40µm thick section, systematic randomly sampled), would it make sense to use the corrected volume for overprojection, even if the CE is relatively small? Would using the corrected volume for overprojection reduce the error even more?

Thank you,

@KSchoenhoff It is not the thickness of the physical section that matters when thinking about overprojection, it is thickness of the optical section. What magnification are you using when you do the point counting? If you are using for instance a 20X objective you will have something like five or ten microns that you can resolve in the Z direction. Is the cross section of the region likely to change much in that distance? If not then you don’t need to worry about overprojection and should not use the correction.

Thank you for the quick response.
The overview outline is done in 5X and the points are marked in 40X. So if I understand it correctly, that would be even less then 20X and I could actually check how many microns I can resolve in Z direction?!
Thanks a lot,

@KSchoenhoff If you are doing your point-marking at 40X that will be a thinner z-plane than 20X and as you point out, that would be even less reason to correct for over-projection.

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