Stand density estimators based on individual tree detection and stochastic geometry

Individual tree detection methods leave smaller trees hiding below larger trees undetected. This is a problem for remote sensing forest inventories, leading, for example, to severe underestimation of stand density. We develop new methods of formulating the probability of detecting individual trees — the detectability — based on stochastic geometry and use them to derive estimators of stand density. We assume that a tree remains undetected if the centre point of the crown falls within an erosion set based on the larger tree crowns. These estimators allow the tree to be undetected even if a portion of its crown would be visible, taking into account possible differences in the accuracy of remote sensing data and detection algorithms. The behaviour of these estimators is quantified using 36 field plots and compared with a previously proposed estimator. The best estimator according to the data used, allowing trees to be undetected when 40% or more of crown radius is hidden, performs well compared with the estimator formed directly from the number of algorithmically detected trees. It produces a 54% reduction in the root mean square error and shifts the mean of errors notably towards zero in the modelling data. Small variations in allowed visible crown radius do not seem to impact the accuracy of the estimates. Generalization of the results remains as a topic of future research.