An estimator of edge length and surface area in digitized 2D and 3D images

Existing estimators for edge length in 2D and surface area in 3D are applied to a binary representation of the object. The authors estimate length and area through volume measurements. Volume is measured without thresholding and does not introduce a sampling error. Edges are transformed into volumes by giving them a constant height after which they can be shifted perpendicular to the edge over a small distance. Subtraction of two images shifted in opposite direction produces a volume that is proportional to the edge length. To guarantee a constant edge height along the edge or across the surface to be measured the authors apply a `soft´ clipping operation to the linear region of the edge. For accurate and isotropic displacement of edges the authors introduce a continuous space equivalent to the discrete local minimum and maximum filters. These filters are sampling invariant and allow shifts in the subpixel region