Improving Cavalieri volume estimation based on non-equidistant planar sections: The trapezoidal estimator

The Cavalieri estimator allows one to infer the volume of an object from area measurements in equidistant planar sections. It is known that applying this estimator in the non-equidistant case may inflate the coefficient of error considerably. We therefore consider a newly introduced variant, the trapezoidal estimator, and make it available to practitioners. Its typical variance behaviour for natural objects is comparable to the equidistant case. We state this unbiased estimator, describe variance estimates and explain how the latter can be simplified under rather general but realistic models for the gaps between sections. Simulations and an application to a synthetic area function based on parietal lobes of 18 monkeys illustrate the new methods.