Transformation of a grid of quadrats to cope with perspective artifacts

Abstract

The direct superimposition of a standard test grid of congruent quadrats onto an image bearing a population of particles exhibiting perspective artifacts, tends to increase the variance of the population size estimator, because the quadrat contents become unbalanced. If the quadrats are transformed according to the same projection mechanism affecting the particles, however, then the variance is restored into moderate values. Our purpose was to provide exact, easily programmable equations for the relevant transform.