actual distances makes this approach more adaptable than the
attenuation model to the forest stand conditions that affect the
detection of trees (e.g. presence of under-canopy vegetation).
However, the parameterization of the detection function is
based on the distances actually measured in all plots within a
stand or strata, so this method would seem to be more appro-
priate for homogeneous stands. Unlike applications described
in Ducey
et al.
(2014) and Astrup
et al.
(2014), where the
inclusion of covariates in the models did not significantly
improve the estimates, we achieved the better performance
by incorporating
DBH
as covariate in the detection probability.
Sánchez-González
et al.
(2016) proposed an approach for es-
timating sampling probability which combines an instrument
bias correction based on the minimum window size allowed
by the process of image segmentation and an occlusion ef-
fect correction adapted to ForeStereo from that of Seidel and
Ammer (2014) using
TLS
data. The hemispherical photogram-
metric correction described here combines the instrument bias
correction proposed by Sánchez-González
et al.
(2016) with
an improved correction of the occlusion effect. This method
integrates the probability of no occlusion for the entire sam-
pling range calculated from the size and position of apparent
trees. Seidel and Ammer (2014) worked with circular plots of
2 m radius in dense poplar plantations and obtained correla-
tions of 0.9 between
BA
estimates from data captured with
TLS
and ground truth data; the estimate bias was reduced by
1.4% (from -9.8% to -8.4%) after correction. The
HPC
approach
reduced the bias of
BA
estimates in plots of 8 m radius from
-35% to -8% in structurally diverse forests (i.e. with irregular
distribution of tree sizes). Notwithstanding the differences in
stand structure and between
TLS
data and stereo-hemispherical
photos, the more significant improvement in our analysis may
be related to the integration of the instrument bias correction
and to an improved estimation of the area occluded. In the
estimation of the occlusion probability with stereo-hemispher-
ical photos, partial blockage hinders tree matching; therefore,
the occlusion angle is the sum of the coverage angles of the
occluded and shading trees (Ducey
et al.
2014).
Correspondence between the projections of a tree in both
stereo images captured with ForeStereo is necessary in order
to detect the tree. The probability of detection has therefore
to be computed as a product of the probability of no occlu-
sion in the left image, by the probability of no occlusion in
the right image conditional on being visible in the left. This
need for this correspondence may explain the underestima-
tion of
BA
and
N
in our analyses with the Poisson attenua-
tion model correction of occlusions. The distance-sampling
based approach relies on the distance distribution of apparent
ntrast, is not affected by the correspondence
an sampling with
TLS
typically overestimates
ince the occlusion probability is greater for
trahler
et al.
2008; Lovell
et al.
2011; Yao
et al.
2011; Seidel and Ammer 2014). We estimated the occlusion
probability as an integral over the range of detection for each
tree, and the relation between the covering angles of the target
Appendix 1
Figure A1. Example of instrument bias: T
marked with a red arrow cannot be detected due to
instrument bias because the pixel size is of similar
magnitude to the stem projection width.
Figure A2. Example of occlusion: The tree marked with an arrow in the right image is occluded by tree marked with a triangle
in the left image.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
July 2019
505
