A Method for Optimizing Height Threshold When
Computing Airborne Laser Scanning Metrics
Eric Bastos Gorgens, Ruben Valbuena, and Luiz Carlos Estraviz Rodriguez
Abstract
In airborne laser scanning (
ALS
), a reference height threshold
is employed for computation of height and density metrics,
which are used as auxiliary variables for predicting forest
attributes. Lacking consensus, practitioners employ different
criteria to define a height threshold, which is applied to all
the metrics collectively. In this paper, we propose a change of
paradigm in ALS metric computation: height thresholds must
be optimized for each metric individually, instead of applying
a single one for all them. We present an optimization method
based on the maximal information coefficient (MIC), which is
applied for each metric, one-by-one. Results showed how a bad
choice of height thresholds damages the predictive potential of
most metrics. While increasing thresholds strengthened height
metrics’ relationship to volume, it weakened for density met-
rics, and therefore choosing different thresholds makes sense.
Introduction
Forestry applications of airborne laser scanning (
ALS
) are rap-
idly moving from research to operational status (White
et al
.,
2013; Maltamo
et al
., 2014). The main approach for estimating
forest attributes from airborne laser scanning (
ALS
) datasets
is to find relationships between metrics derived from laser
returns and stand attributes measured in the field (Næsset,
1997).
ALS
metrics are statistics that summarize the informa-
tion available in cloud points assessed from a specific area
(e.g., a sample plot). A variety of modeling techniques can be
used to relate forest attributes to specific
ALS
-based metrics
(e.g., Hudak
et al
., 2008, Hyyppa
et al
., 2012, Valbuena
et
al
., 2013). This is known as the area-based method (Næsset,
2002), which has become the most widespread approach in
ALS
-assisted forest assessments.
After subtracting the elevation of each laser return by the
underlying terrain, the
ALS
returns that correspond to the geo-
referenced field plot are extracted and the metrics computed.
The most used
ALS
-metrics are: location and dispersion mea-
sures defined as
ALS
height metrics (mean, standard devia-
tion, percentiles, etc.) (Magnussen and Boudewyn, 1998); and
proportions among vertical strata referred to as canopy cover
metrics (sensu McGaughey, 2013), also known as density
metrics (sensu Næsset, 1997 and 2002; Korhonen
et al
.; 2011;
we use this term throughout this paper). Reference heights,
i.e., threshold heights, are commonly used during the com-
putation procedures for these
ALS
metrics. There is, however,
a lack of consensus about which, and why, reference heights
should be employed (Wulder
et al
., 2013), and the plethora of
different criteria and methods found in the literature makes
their use often unclear or misjudged across studies.
Reference heights shall be used for either (a) specifying
a lower bound for calculating height metrics, i.e., minimum
height (
MinH
), or (b) defining breaks to separate the cloud
into two or more vertical strata, i.e., height breaks (
HBreak
).
MinH
masks out
ALS
returns underneath the specified thresh-
old, as a step before the computation of height metrics. On the
other hand,
HBreak
is employed to calculate relative propor-
tions of returns backscattered from above the given reference
height, for the computation of density metrics. The
MinH
and
HBreak
may have the same value (e.g., Garcia
et al
., 2010;
Valbuena
et al
., 2013), or they can be set independently (e.g.,
Næsset, 2002; Hudak
et al
., 2008). Different authors apply a
variety of criteria to set these reference heights, using dissimi-
lar rationale and motivation for their use.
MinH
defines
ALS
returns not satisfying a certain criterion
established empirically by a given practitioner. Two types
of approaches for setting that criterion can be found in the
literature. The first type of criterion is to eliminate returns
backscattered from objects other than the vegetation, by
selecting a reference height value above which points are
classified as canopy returns. These may be returns backscat-
tered from boulders, stones, dead wood, and other elements
not considered relevant for the target forest attribute. Nilsson
(1996) introduced
MinH
= 2 m, a criterion which has become
perhaps one of the most common choice (Næsset, 2011; Mon-
taghi
et al
., 2013). There is, however, a wide range of other
values employed in the literature: 0.17 meters (Hudak
et al
.,
2006), 0.3 meters (Garcia
et al
., 2010), or 0.5 meters (Næs-
set and Bjerknes, 2001). A second type of scenario is set by
authors who use
MinH
to mask out returns backscattered from
trees not included within the sample information obtained in
the field, as it is common during the mensuration campaign to
omit trees under a certain practical limit. This other criterion
was followed by Zimble (2003) who adopted a
MinH
= 5.7 m,
calculated as the height of those trees which were unmeasured
because of being smaller than a merchantability limit. Bol-
landsås
et al
. (2008) used a similar criterion to choose a
MinH
= 3 m. Jensen
et al
(2006) and Næsset (2011) used a
MinH
=
1.3 m arguing that field measurements do not consider trees
below that height, which is a common approach in forest
mensuration. Valbuena
et al
. (2013) also followed a similar ra-
tionale when selecting a
MinH
= 0.1 m, arguing that their field
data included mensuration for all tree sizes and seedlings, and
therefore only ground hits are to be masked out in such case.
HBreaks
splits the cloud into two or several strata, in
order to calculate proportions among them, as canopy cover
or density metrics. As for
MinH
,
HBreaks
may be empirically
Eric Bastos Gorgens is with the Universidade Federal
dos Vales do Jequitinhonha e Mucuri. Rodovia MGT 367
- Km 583, number 5000, Alto da Jacuba. CEP 39100-000,
Diamantina, Brazil; and formerly with the University of São
Paulo, Av. Pádua Dias, 11.
Rúben Pueblas Valbuena is with the University of Cambridge.
Downing Street, Cambridge CB2 3EA, and formerly with the
University of Eastern Finland, P.O. Box 111 Joensuu, Finland.
Luiz Carlos Estraviz Rodriguez is with the University of São
Paulo. Av. Pádua Dias, 11, CEP 13418-900 Piracicaba, Brazil.
Photogrammetric Engineering & Remote Sensing
Vol. 83, No. 5, May 2017, pp. 343–350.
0099-1112/17/343–350
© 2017 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.83.5.343
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
May 2017
343
