AbstractExisting estimators for edge length in2Dand surface area in3Dare applied to a binary representation of the object. In this paper we estimate length and surface area through grey‐volume measurements. Volume is measured without thresholding and does not introduce a sampling error. Object boundaries are carefully transformed into volumes using bandlimited operations.We give two methods: GC and GCL. The GC method measures the length of an isophote. The GCL method measures the length of the Laplacian zerocrossing line. The GC estimator is biased because the isophote position is shifted towards smaller radii due to both analogue and digital low‐pass filtering. The GCL estimator contains a compensating mechanism and yields unbiased results for both the edge position and the length.Extension of both methods to3Dimages is straightforward. The3DGC area bias is scale independent. The3DGCL method yields unbiased edge position. For3Dobjects without tunnels or enclosed cavities the3DGCL area bias amounts to a constant correction per object and an unbiased estimator can still be construc