coefficient between
BA
estimated from ForeStereo data and
field measurements (0.83).
Discussion and Conclusions
Estimation of forest stand variables from sample data cap-
tured using ForeStereo requires precise knowledge of the
sources of error associated with sampling schemes, image
processing, and estimation methods. This work analyzed the
performance of different methods for estimating sampling
probability. Working with a single point sampling design the
probability of sampling a tree depends on two factors: the
relationship between the distance range of detection and the
tree size, and the probability of being occluded by another
tree. In addition, in order to attain unbiased estimations, the
locations of the plot centres should be selected randomly or
on a regular grid, but not prevailing open locations within the
plot. The displacement of the device to a distance of 0.5 m
from the nearest tree is necessary as the variability of tex-
tures within the stem associated with the macro-acquisition
of images hampers stem segmentation. Due to the wide field
of view of the fish eye lens, the size of the features projected
decreases rapidly at 0.5 m and the occlusion effect is reduced
substantially. However, this displacement is small when com-
pared with the tree spacing and should not cause a noticeable
bias. The relationship between the distance range of detection
and the tree size is defined by the image resolution and by the
algorithms used in the segmentation process. The probability
of occlusion has to be inferred from the actual distribution of
the apparent trees. Employing ForeStereo data from a forest
inventory, we tested and compared three approaches for
estimating the sampling probability and calculating plot level
variables: Relaskop-based sampling and correction of occlu-
sions with Poisson attenuation model, distance-sampling
based correction for instrument bias and occlusions, and the
proposed
HPC
, which combines the segmentation based cor-
rection for instrument bias method (Sanchez-González
et al.
2016) and a new correction of occlusions effect calculating
the shadowed area, based on the Seidel and Ammer (2014)
method. The three approaches incorporate some kind of
correction for instrument bias and occlusion of trees, and all
three led to an improvement in the raw estimates; reducing
the estimate bias and increasing the correlation with ground
truth data.
Each method for estimating sampling probability is sup-
ported by different assumptions, and the suitability of one or
other method depends on the forest structure and on the char-
acteristics of the
PS
technology employed. For example, the
approach consisting of Relaskop-based sampling and correc-
tion of occlusions with Poisson attenuation model (Strahler
et
al.
2008) depends on the
DBH
of the apparent trees and on the
basal area factor selected and assumes a Poisson distribution
of tree distances from the sensor. For an accurate determina-
tion of the effective tree diameter
D
E
, this method may require
calibration (e.g. with traditionally measured plots). Ducey
et
al.
(2014) and Astrup
et al.
(2014) proposed a distance-sam-
pling based approach relying on the actual distribution of the
apparent tree distances. Under this approach, the assumptions
are implicit in the model selected for probability of detec-
tion (e.g. Half-Normal or Hazard-Rate functions). Employing
Figure 11. Basal area (BA) estimates from ForeStereo vs BA derived from field data and regression line of linear models
in plots of 8 m (empty triangles and dashed line) and 9.8 m radius (filled squares and dash-dot line). A: uncorrected, B:
Relaskop-based sampling and Poisson attenuation model, C: distance-sampling with Hazard-Rate function, D: distance
sampling with Hazard-Rate function and
DBH
as covariate, E: distance sampling with Half-Normal function and
DBH
as
covariate, F: hemispherical photogrammetric correction.
504
July 2019
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
