Unbiased estimation of curve length in 3‐D using vertical slices

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Abstract
SUMMARY: An efficient sampling procedure is presented for estimation of total line length per unit volume Lv. It involves the following steps: (1) choose a vertical axis in the specimen, and cut the specimen to obtain VUR vertical slices of constant thickness Δ such that parallel planes of the slices contain the vertical direction; (2) observe the projected image of a vertical slice using transmission microscopy such that beam direction is perpendicular to the slice; (3) count the number of intersections of the projected images of the lineal features of interest with cycloid‐shaped test lines whose minor axis is perpendicular to the vertical axis. The expected value of the number of intersections per unit length prj is related to Lv as follows:Thus, Lv can be estimated from the measurements performed on the projected images of VUR vertical slices.

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