Stereological estimation of tubular length

Very efficient and unbiased principles exist for estimating the total three-dimensional (3D), two-dimensional and zero-dimensional amounts of arbitrary structure in 3D space. The total one-dimensional length of real structure, in the ordinary sense, is an abstraction from the point of view of integral geometry. All stereological estimators of 'tubular length' are thus approximations. In addition, they are riddled by biases due to several types of artificial edges and other practical problems. This paper discusses several of these and proposes practical solutions of minimal biases.