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Horvitz-Thompson-like stand density estimation is a method for estimating the stand density from tree crown objects extracted from airborne laser scanning data through individual tree detection. The estimator is based on stochastic geometry and mathematical morphology of the (planar) set formed by the detected tree crowns. This set is used to approximate the detection probabilities of trees. These probabilities are then used to calculate the estimate. The method includes a tuning parameter, which needs to be known to apply the method. We present a refinement of the method to allow more general detection conditions than those of previous papers. We also present and discuss the methods for estimating the tuning parameter of the estimator using a functional k-nearest neighbors method. We test the model fitting and prediction in two spatially separate data sets and examine the plot-level accuracy of estimation. The estimator produced a 13% lower RMSE (root-mean-square error) than the benchmark method in an external validation data set. We also analyze the effects of similarity and dissimilarity of training and validation data on the results. Key words: segmentation, stochastic geometry, detectability, nearest neighbor, forest inventory. L'estimation de type Horvitz-Thompson de la densite de peuplement est une methode d'estimation de la densite de peuplement a partir d'objets qui sont des couronnes d'arbres obtenues par detection d'arbres individuels a partir de donnees de balayage laser aeroporte. L'estimateur est base sur la geometrie stochastique et la morphologie mathematique de l'ensemble (planaire) forme par les couronnes d'arbres detectees. Cet ensemble est utilise pour approximer les probabilites de detection des arbres. Ces probabilites sont ensuite utilisees pour calculer l'estimation. La methode comprend un parametre d'ajustement qui doit etre connu pour pouvoir l'appliquer. Nous presentons un raffinement de la methode afin de permettre des conditions plus generales de detection que celles des articles precedents. Nous presentons et discutons des methodes d'estimation du parametre d'ajustement de l'estimateur en utilisant la methode fonctionnelle des k plus proches voisins. Nous testons l'ajustement et la prediction du modele pour deux ensembles de donnees spatialement distincts et nous examinons la precision de l'estimation a l'echelle de la parcelle. L'estimateur a produit une REQM (racine de l'erreur quadratique moyenne) 13% inferieure a celle de la methode de reference pour un ensemble de donnees de validation externe. Nous analysons egalement les effets de la similitude et de la dissemblance des donnees d'entrainement et de validation sur les resultats. [Traduit par la Redaction] Mots-cles : segmentation, geometrie stochastique, detectabilite, plus proche voisin, inventaire forestier., 1. Introduction Volume and biomass related attributes are usually of primary interest in remote-sensing-based forest inventories. If these quantities are estimated at tree level, scaling them to area level requires [...]

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. Key words: stand density estimation, individual tree detection, stochastic geometry, detectability, germ-grain models. Les methodes de detection d'arbres individuels ne detectent pas les petits arbres caches sous les gros arbres. C'est un probleme pour les inventaires forestiers realises par teledetection qui mene, par exemple, a une forte sous-estimation de la densite des peuplements. Nous avons mis au point de nouvelles methodes pour formuler la probabilite de detecter les arbres individuels--la detectabilite--fondees sur la geometrie stochastique, et nous les avons utilisees pour obtenir des estimateurs de la densite des peuplements. Nous assumons qu'un arbre demeure non detecte si le point central de sa cime se situe dans un ensemble erosif forme par la cime des plus gros arbres. Ces estimateurs permettent qu'un arbre soit considere comme non detecte meme si une portion de sa cime est visible, en tenant compte de possibles differences de precision entre les donnees de teledetection et les algorithmes de detection. Le comportement de ces estimateurs a ete quantifie a l'aide de 36 placettes de terrain et compare a un estimateur propose anterieurement. Le meilleur estimateur en fonction des donnees utilisees, qui permet que des arbres soient consideres comme non detectes lorsque 40 % ou plus du rayon de leur cime est cache, se comporte bien comparativement a l'estimateur forme directement a partir du nombre d'arbres detectes a l'aide d'un algorithme. Il a reduit de 54 % l'erreur quadratique moyenne et a considerablement deplace la moyenne des erreurs des donnees de modelisation vers zero. De petites variations du rayon de la cime qui peut etre visible ne semblent pas avoir d'impact sur l'exactitude des estimations. La generalisation des resultats fera l'objet de recherches ulterieures. [Traduit par la Redaction] Mots-cles : estimation de la densite des peuplements, detection des arbres individuels, geometrie stochastique, detectabilite, modeles germes-grains., Introduction Individual tree detection (ITD) is one of the basic techniques to derive information from aerial remote sensing data (Vauhkonen et al. 2014a). In ITD, algorithms are developed for detecting [...]

In circular plot sampling, trees within a given distance from the sample plot location constitute a sample, which is used to infer characteristics of interest for the forest area. If the sample is collected using a technical device located at the sampling point, eg, a terrestrial laser scanner, all trees of the sample plot cannot be observed because they hide behind each other. We propose a Horvitz‐Thompson–like estimator with distance‐based detection probabilities derived from stochastic geometry for estimation of population totals such as stem density and basal area in such situation. We show that our estimator is unbiased for Poisson forests and give estimates of variance and approximate confidence intervals for the estimator, unlike any previous methods. We compare the estimator to two previously published benchmark methods. The comparison is done through a simulation study where several plots are simulated either from field measured data or different marked point processes. The simulations show that the estimator produces lower or comparable error values than the other methods. In the sample plots based on the field measured data, the bias is relatively small—relative mean of errors for stem density, for example, varying from 0.3% to 2.2%, depending on the detection condition. The empirical coverage probabilities of the approximate confidence intervals are either similar to the nominal levels or conservative in these sample plots. [ABSTRACT FROM AUTHOR]