Estimation of individual tree volume by importance sampling and antithetic variates from the cylindrical shells integral

1992 ◽  
Vol 22 (3) ◽  
pp. 326-335 ◽  
Author(s):  
Thomas B. Lynch ◽  
Shen-Then Chang ◽  
John P. Chandler
Keyword(s):  
Importance Sampling ◽  
Cylindrical Shells ◽  
Volume Estimation ◽  
Volume Integral ◽  
Volume Estimate ◽  
Cross Sectional ◽  
Individual Tree ◽  
Solid Of Revolution ◽  
Antithetic Variates ◽  
Tree Stem

A method of estimating individual tree volume by importance sampling is developed that is based on the cylindrical shells volume integral. The cylindrical shells volume integral conceptualizes a tree stem as being a solid of revolution comprising a collection of thin cylinders. Previous applications of importance sampling to individual tree volume estimation have been based on the method of slices integral, in which the tree stem is viewed as a solid of revolution comprising a collection of thin disks. Both approaches provide unbiased estimates of individual tree volume for any monotonic tree taper, if it can be assumed that the tree is circular in cross section. An advantage of the cylindrical shells approach is that total tree height need not be measured to accomplish the estimation process, as would be required when using importance sampling estimators based on the method of slices integral. Tree volume estimation via importance sampling based on the cylindrical shells integral requires measurement of stump cross-sectional area, which is usually more easily obtained than total or merchantable height measurements. Both approaches require one or more upper stem diameter measurements. Computer simulation shows that use of antithetic variates with importance sampling reduces the variance of the volume estimate significantly when a paraboloid is used as a proxy taper function.

Variance reduction in Ueno's method and cylinder sampling for forest volume estimation

1995 ◽  
Vol 25 (11) ◽  
pp. 1783-1794 ◽  
Author(s):  
Thomas B. Lynch
Keyword(s):  
Computer Simulation ◽  
Variance Reduction ◽  
Volume Estimation ◽  
Critical Height ◽  
Volume Estimate ◽  
Individual Tree ◽  
Stand Volume ◽  
Reduction Techniques ◽  
Antithetic Variates ◽  
Volume Equation

Three basic techniques are proposed for reducing the variance of the stand volume estimate provided by cylinder sampling and Ueno's method. Ueno's method is based on critical height sampling but does not require measurement of critical heights. Instead, a count of trees whose critical heights are less than randomly generated heights is used to estimate stand volume. Cylinder sampling selects sample trees for which randomly generated heights fall within cylinders formed by tree heights and point sampling plot sizes. The methods proposed here for variance reduction in cylinder sampling and Ueno's method are antithetic variates, importance sampling, and control variates. Cylinder sampling without variance reduction was the most efficient of 12 methods compared in computer simulation that used estimated measurement times. However, cylinder sampling requires knowledge of a combined variable individual tree volume equation. Of the three variance reduction techniques applied to Ueno's method, antithetic variates performed best in computer simulation.

scholarly journals Accuracy of common stem volume formulae using terrestrial photogrammetric point clouds: a case study with savanna trees in Benin

2021 ◽  
Author(s):  
Hospice A. Akpo ◽  
Gilbert Atindogbé ◽  
Maxwell C. Obiakara ◽  
Arios B. Adjinanoukon ◽  
Madaï Gbedolo ◽  
...  
Keyword(s):  
Point Clouds ◽  
Stem Volume ◽  
Individual Tree ◽  
Volume Calculation ◽  
Tropical Regions ◽  
Solid Of Revolution ◽  
Taper Function ◽  
Geometric Solids ◽  
Traditional Approaches ◽  
Tree Stem

AbstractRecent applications of digital photogrammetry in forestry have highlighted its utility as a viable mensuration technique. However, in tropical regions little research has been done on the accuracy of this approach for stem volume calculation. In this study, the performance of Structure from Motion photogrammetry for estimating individual tree stem volume in relation to traditional approaches was evaluated. We selected 30 trees from five savanna species growing at the periphery of the W National Park in northern Benin and measured their circumferences at different heights using traditional tape and clinometer. Stem volumes of sample trees were estimated from the measured circumferences using nine volumetric formulae for solids of revolution, including cylinder, cone, paraboloid, neiloid and their respective fustrums. Each tree was photographed and stem volume determined using a taper function derived from tri-dimensional stem models. This reference volume was compared with the results of formulaic estimations. Tree stem profiles were further decomposed into different portions, approximately corresponding to the stump, butt logs and logs, and the suitability of each solid of revolution was assessed for simulating the resulting shapes. Stem volumes calculated using the fustrums of paraboloid and neiloid formulae were the closest to reference volumes with a bias and root mean square error of 8.0% and 24.4%, respectively. Stems closely resembled fustrums of a paraboloid and a neiloid. Individual stem portions assumed different solids as follows: fustrums of paraboloid and neiloid were more prevalent from the stump to breast height, while a paraboloid closely matched stem shapes beyond this point. Therefore, a more accurate stem volumetric estimate was attained when stems were considered as a composite of at least three geometric solids.

Effects of measurement error on Monte Carlo integration estimators of tree volume: critical height sampling and vertical Monte Carlo methods

2015 ◽  
Vol 45 (4) ◽  
pp. 463-470 ◽  
Author(s):  
Thomas B. Lynch
Keyword(s):  
Monte Carlo ◽  
Measurement Error ◽  
Sampling Error ◽  
Monte Carlo Integration ◽  
Critical Height ◽  
Volume Estimate ◽  
Cross Sectional ◽  
Individual Tree ◽  
Control Variate ◽  
Multiplicative Measurement Error

The effects of measurement error on Monte Carlo (MC) integration estimators of individual-tree volume that sample upper-stem heights at randomly selected cross-sectional areas (termed vertical methods) were studied. These methods included critical height sampling (on an individual-tree basis), vertical importance sampling (VIS), and vertical control variate sampling (VCS). These estimators were unbiased in the presence of two error models: additive measurement error with mean zero and multiplicative measurement error with mean one. Exact mathematical expressions were derived for the variances of VIS and VCS that include additive components for sampling error and measurement error, which together comprise total variance. Previous studies of sampling error for MC integration estimators of tree volume were combined with estimates of upper-stem measurement error obtained from the mensurational literature to compute typical estimates of total standard errors for VIS and VCS. Through examples, it is shown that measurement error can substantially increase the total root mean square error of the volume estimate, especially for small trees.

An antithetic variate to facilitate upper-stem height measurements for critical height sampling with importance sampling

2013 ◽  
Vol 43 (12) ◽  
pp. 1151-1161 ◽  
Author(s):  
Thomas B. Lynch ◽  
Jeffrey H. Gove
Keyword(s):  
Importance Sampling ◽  
Basal Area ◽  
Cross Sectional Area ◽  
Sample Point ◽  
Sectional Area ◽  
Critical Height ◽  
Cross Sectional ◽  
Individual Tree ◽  
Sample Tree ◽  
The Cross

Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the “antithetic variate” associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 − b/B), where b is the cross-sectional area at “borderline” condition and B is the tree’s basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias.

scholarly journals Right ventricular ejection fraction as predictor of outcome in acute heart failure using RV ellipsoid model: A retrospective analysis of a prospective cross-sectional study

2021 ◽  
Vol 10 ◽  
pp. 204800402110027
Author(s):  
Eshan Ashcroft ◽  
Otar Lazariashvili ◽  
Jonathan Belsey ◽  
Max Berrill ◽  
Pankaj Sharma ◽  
...  
Keyword(s):  
Heart Failure ◽  
Ejection Fraction ◽  
Right Ventricular ◽  
Retrospective Analysis ◽  
Cross Sectional Study ◽  
Volume Estimation ◽  
Sectional Study ◽  
Cross Sectional ◽  
Ventricular Ejection Fraction ◽  
Rv Function

Objectives The right ventricular (RV) function is an important prognostic factor in acute and chronic heart failure (HF). Echocardiography is an essential imaging modality with established parameters for RV function which are useful and easy to perform. However, these fail to reflect global RV volumes due to reliability on one acoustic window. It is therefore attractive to calculate RV volumes and ejection fraction (RVEF/E) using an ellipsoid geometric model which has been validated against MRI in healthy adults but not in the HF patients. Design This is a retrospective analysis of a prospective cross-sectional study enrolling 418 consecutive patients with symptoms of HF according to a predefined study protocol. All patients underwent echocardiographic assessment of RV function using Tricuspid Annular Plane Systolic Excursion (TAPSE) and RV fractional area change (RVFAC) and RVEF/E. Setting Single centre study with multiple locations for acute in-patients including high dependency units. Participants Patients with acute or exacerbation of chronic HF older than 18 y.o. Main outcome measures Ability of RVEF/E to predict patient outcomes compared with two established parameters of RV function over two-year follow-up period. Primary outcome measure was all-cause mortality. Results RVEF/E is equal to TAPSE & RVFAC in predicting outcome (p ≤ 0.01 vs p ≤ 0.01) and provides additional benefit of RV volume estimation based on standard 2D echo measurements. Conclusions In this study we have shown that RVEF/E derived from ellipsoid model is not inferior to well established measures of RV function as a prognostic indicator of outcome in the acute HF.

scholarly journals Predicting Growing Stock Volume of Eucalyptus Plantations Using 3-D Point Clouds Derived from UAV Imagery and ALS Data

Forests ◽  
2019 ◽  
Vol 10 (10) ◽  
pp. 905 ◽  
Author(s):  
Guerra-Hernández ◽  
Cosenza ◽  
Cardil ◽  
Silva ◽  
Botequim ◽  
...  
Keyword(s):  
Laser Scanning ◽  
Basal Area ◽  
Remote Sensing Data ◽  
Tree Height ◽  
Point Clouds ◽  
Volume Estimation ◽  
P Value ◽  
Test Statistic ◽  
Individual Tree ◽  
Significant Difference

Estimating forest inventory variables is important in monitoring forest resources and mitigating climate change. In this respect, forest managers require flexible, non-destructive methods for estimating volume and biomass. High-resolution and low-cost remote sensing data are increasingly available to measure three-dimensional (3D) canopy structure and to model forest structural attributes. The main objective of this study was to evaluate and compare the individual tree volume estimates derived from high-density point clouds obtained from airborne laser scanning (ALS) and digital aerial photogrammetry (DAP) in Eucalyptus spp. plantations. Object-based image analysis (OBIA) techniques were applied for individual tree crown (ITC) delineation. The ITC algorithm applied correctly detected and delineated 199 trees from ALS-derived data, while 192 trees were correctly identified using DAP-based point clouds acquired from Unmanned Aerial Vehicles (UAV), representing accuracy levels of respectively 62% and 60%. Addressing volume modelling, non-linear regression fit based on individual tree height and individual crown area derived from the ITC provided the following results: Model Efficiency (Mef) = 0.43 and 0.46, Root Mean Square Error (RMSE) = 0.030 m3 and 0.026 m3, rRMSE = 20.31% and 19.97%, and an approximately unbiased results (0.025 m3 and 0.0004 m3) using DAP and ALS-based estimations, respectively. No significant difference was found between the observed value (field data) and volume estimation from ALS and DAP (p-value from t-test statistic = 0.99 and 0.98, respectively). The proposed approaches could also be used to estimate basal area or biomass stocks in Eucalyptus spp. plantations.

Individual tree merchantable volume to total volume ratios based on geometric solids

1989 ◽  
Vol 19 (5) ◽  
pp. 679-683 ◽  
Author(s):  
James D. Newberry ◽  
Harold E. Burkhart ◽  
Ralph L. Amateis
Keyword(s):  
Loblolly Pine ◽  
Volume Ratio ◽  
Individual Tree ◽  
Ratio Data ◽  
Geometric Solids ◽  
Two Parameter ◽  
Tree Stem

Individual tree volume ratio equations were developed on the basis of the volume formulas of certain geometric solids. Two parameter-free and two parameterized models were formulated, based on different basal diameters. The parameter-free models should be useful when few individual tree volume ratio data exist for a given species or for a particular population of trees. The parameterized models are appropriate, of course, to those situations where volume ratio data exist. The parameter-free models performed as well as the parameterized models in the upper half of the tree stem for the loblolly pine data used for comparison. The parameterized models performed well all along the tree stem.

Merchantable timber volume estimation using cross-sectional photogrammetric and densitometric methods

1984 ◽  
Vol 14 (6) ◽  
pp. 803-810 ◽  
Author(s):  
Gordon A. Maclean ◽  
George L. Martin
Keyword(s):  
Volume Estimation ◽  
Aerial Photographs ◽  
Volume Data ◽  
High Precision Measurement ◽  
Cross Sectional ◽  
Timber Volume ◽  
Film Density ◽  
Density Values ◽  
Independent Variable ◽  
Profile Area

A procedure is described for estimating timber volume from high-precision measurement of the cross-sectional area of a canopy profile on medium-scale vertical aerial photographs. Timber volume data were obtained from 75 data points in a study area containing several forest types, and canopy profile areas were measured with a stereoplotter at the corresponding points on the aerial photographs. Film density values were also measured along each profile using a scanning microdensitometer. Canopy profile area was found to be independent of the direction of the profile relative to the flight line of the photography. The relation between timber volume and profile area was found to be highly significant, semilogarithmic, and species dependent, with regression R2 values ranging from 0.67 to 0.79. The area under a curve obtained by plotting film density values is not sufficiently correlated with timber volume to be a significant independent variable, either alone or with profile area. However, film density information was found to be of significant value in correcting the profile areas for canopy microopenings too small to be measured with a stereoplotter. With the area of microopenings included as a separate independent variable, regression R2 values range from 0.82 to 0.88.

Leaf area – sapwood cross-sectional area relationships in repressed stands of lodgepole pine

1987 ◽  
Vol 17 (3) ◽  
pp. 205-209 ◽  
Author(s):  
M. G. Keane ◽  
G. F. Weetman
Keyword(s):  
Hydraulic Conductivity ◽  
Leaf Area ◽  
Wood Density ◽  
Lodgepole Pine ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Density Profiles ◽  
Individual Tree ◽  
Individual Trees

To better understand the phenomenon of growth "stagnation" in high-density lodgepole pine (Pinuscontorta Dougl. ex Loud.), leaf area and its relationship with sapwood cross-sectional area were examined on both an individual tree and stand basis. Leaf areas of individual trees in a 22-year-old stand varied from 30.8 m2 (dominants in stands of low stocking) to 0.05 m2 (suppressed trees in stands of high stocking). Leaf area indices ranged from 13.4 to 2.3 m2 m−2 between low and high stocking levels, respectively. Over the same stocking range, the ratio of leaf area to sapwood cross-sectional area was reduced from 0.3 to 0.15 m2 cm−2. Intraring wood density profiles showed that ovendry density increased from 0.52 to 0.7 g cm−3 and the proportion of early wood decreased over a stocking level range of 6500–109 000 trees/ha. A reduction in hydraulic conductivity in the stems of stagnant trees, suggested by the greater proportion of narrow-diameter tracheids present, may lead to a greater resistance to water transport within the boles of trees from stagnant stands, leading to low leaf areas.

scholarly journals Very High Density Point Clouds from UAV Laser Scanning for Automatic Tree Stem Detection and Direct Diameter Measurement

2020 ◽  
Vol 12 (8) ◽  
pp. 1236 ◽  
Author(s):  
Karel Kuželka ◽  
Martin Slavík ◽  
Peter Surový
Keyword(s):  
Cross Sections ◽  
Hough Transform ◽  
Laser Scanning ◽  
Point Clouds ◽  
Mean Bias Error ◽  
Bias Error ◽  
Least Trimmed Squares ◽  
Remotely Sensed Data ◽  
Individual Tree ◽  
Tree Stem

Three-dimensional light detection and ranging (LiDAR) point clouds acquired from unmanned aerial vehicles (UAVs) represent a relatively new type of remotely sensed data. Point cloud density of thousands of points per square meter with survey-grade accuracy makes the UAV laser scanning (ULS) a very suitable tool for detailed mapping of forest environment. We used RIEGL VUX-SYS to scan forest stands of Norway spruce and Scots pine, the two most important economic species of central European forests, and evaluated the suitability of point clouds for individual tree stem detection and stem diameter estimation in a fully automated workflow. We segmented tree stems based on point densities in voxels in subcanopy space and applied three methods of robust circle fitting to fit cross-sections along the stems: (1) Hough transform; (2) random sample consensus (RANSAC); and (3) robust least trimmed squares (RLTS). We detected correctly 99% and 100% of all trees in research plots for spruce and pine, respectively, and were able to estimate diameters for 99% of spruces and 98% of pines with mean bias error of −0.1 cm (−1%) and RMSE of 6.0 cm (19%), using the best performing method, RTLS. Hough transform was not able to fit perimeters in unfiltered and often incomplete point representations of cross-sections. In general, RLTS performed slightly better than RANSAC, having both higher stem detection success rate and lower error in diameter estimation. Better performance of RLTS was more pronounced in complicated situations, such as incomplete and noisy point structures, while for high-quality point representations, RANSAC provided slightly better results.

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