UNBIASED VOLUME ESTIMATION WITH COAXIAL SECTIONS - AN APPLICATION TO THE HUMAN BLADDER

A problem of current medical interest is how to estimate the volume of an object from coaxial sections. Such images can be produced in ultra sound scanning, when the planar scan sections all emanate from a commo n axis. Two unbiased volume estimators for this sampling regime, previ ously published without derivation, are derived and presented here in some detail. The estimators are based on an ancient theorem of Pappus of Alexandria (c. AD 320). One of the estimators was used to estimate the volume of urine in the bladder of six human volunteers. The case e xample was attractive because the corresponding volumes could be voide d and directly measured after the scanning session. thus confirming th e unbiasedness of the estimator used. Sample size guidelines are also given.