The Euler number and the connectivity of an arbitrary object is define
d, and it is illustrated why the connectivity of an n-dimensional obje
ct cannot be estimated in an ( n - 1 ) dimensional section. The disect
or-principle for 3-D counting of the Euler-events is illustrated in ca
ncellous bone. The correct handling for unbiased counting of events at
artificial edges is outlined. A nomogram for predicting the precision
of an estimate is provided.