Semi-automated measurement of true chord length distributions and moments by video microscopy and image analysis

The distribution of the lengths of airspace chords in pulmonary parenchyma characterizes many architectural features of the alveoli and alveolar ducts. Laborious to obtain manually, the distributions and density functions may be acquired semi-automatically by video microscopy, digitization and image processing. The accuracy of the estimation is influenced by the microscopical methods and also by the techniques used (i) to convert the digitized greyscale picture to a two-valued image, (ii) to collect the chord lengths and (iii) to compensate for finite field widths. The last problem arises because some chords are completely visible within a field while others are only partially seen, since one of the two air-tissue boundaries lies outside the field of view. This error systematically biases the observed distribution. This paper contains solutions to hardware, software and analytic problems encountered while developing the capability to measure airspace chord length density functions semi-automatically. Formulas for estimating the true chord length density function from samples of observed chord lengths are presented. Also given are formulas for the estimation of the first and second moments of the true chord length distribution from the means of observed chord lengths. These techniques of image preparation and analysis should be suitable for characterizing particle, grain or cell size distributions, especially where many profiles fall partially outside the field of view.