IEEE Geoscience and Remote Sensing Magazine - June 2019 - 55

JUNE 2019

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

the hull and the original spectrum from a constant (100%
reflection). The choice of hull technique and the definition
of edges influence the obtained absorption feature parameters (Table 1). The hull quotient technique exaggerates the
depth of absorption features at wavelengths at which the
albedo is low. This is notable in the visible and short-wave
wavelength (>2-µm) ranges of infrared spectra. For example, the 2.2-µm absorption feature of kaolinite (Table 1) has a
49.7% depth with the hull quotient technique (experiment A)
and a 23.4% depth with the hull difference technique
(experiment B). The hull quotient technique is more commonly used in the literature (e.g., [44] and [45]), because
feature depths are considered to scale with the albedo in
more a multiplicative than an additive sense. An additional
advantage of the hull quotient is that it is safe to use even
if the input data set is not in absolute reflectance values.
We recommend using the hull quotient as the default continuum removal technique.

Reflectance

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1.5
Wavelength (µm)
(a)

2.5

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1.5
Wavelength (µm)
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1.1
Normalized Reflectance

spectrum, or hull quotient, because it is the ratio between
the spectrum and the hull [40]. In this way, the absorption
features are always between zero and one and can readily be subjected to further analysis. Alternatively, the hull
could also be subtracted from the spectra, which would be
relevant when using apparent absorbance spectra [21].
In IDL DISPEC, a convex hull technique is, therefore,
applied first to remove the continuum (Figure 3). For each
absorption feature in a continuum-removed spectrum, the
algorithm calculates the center wavelength position, depth,
area, and asymmetry. First, the minimum reflectance value
in a spectrum is identified. From this point, the slopes on
either side are analyzed to find the shoulders (edges) of the
feature. The shoulders are defined by the points where the
spectrum is touched by its convex hull. Alternatively, the
shoulders are where the slopes of the feature change from
negative to positive or vice versa (inflection points), for the
left and right shoulder, respectively. The wavelength range
occupied by a feature is subsequently masked for the feature-finding algorithm, and the process continues until the
entire spectrum has been analyzed.
Once all of the features have been found, the area, asymmetry, and depth of each are calculated. The depth is determined by the distance between the deepest point of the
absorption feature and the convex hull. The area of each
feature is integrated between the spectrum and the hull
from shoulder to shoulder. The asymmetry is calculated as
a normalized difference between the area left of the center
wavelength and the area to the center wavelength's right.
Of incomplete features at the extremes of a spectrum, only
the absorption wavelength is registered, and other parameters are ignored. Also ignored in IDL DISPEC are features
that exceed any absorption depth limits set by a user.
Choosing a different definition of an absorption feature's shoulders also has a pronounced influence on the
resulting parameters. Defining the shoulders as the points
where a spectrum touches its convex hull gives the full
depth of the feature; however, the measure may incorporate multiple absorption bands. On the other hand, using
inflection points as shoulders separates all absorption
bands completely but may, in turn, not produce the complete depth of a feature. The results of experiments A and
B in Table 1, which had "maximum value" as the shoulder
definition, show the 2.2-µm absorption feature of kaolinite
as a single feature. The result of experiment C, which had
"inflection points" as the shoulder definition, shows two
separate features centered at 2.162 and 2.208 µm. It is up
to a user to determine what information is most important
to analyze in a spectral data set. Limiting the wavelength
range in which the algorithm searches for features helps to
make a tradeoff between these two approaches.
Two convex hull techniques exist that can remove the
continuum from a spectrum: the hull difference and the
hull quotient algorithms [40]. The hull quotient is obtained
by dividing the original spectrum by the hull. The hull difference is calculated by subtracting the difference between

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FIGURE 3. The continuum removal technique for infrared reflectance spectra. (a) The continuum is made by fitting a convex hull
over the spectrum. (b) The hull quotient is obtained by dividing the
original spectrum by the hull, and the hull difference is obtained
by subtracting the difference between the hull and the original
spectrum from a constant (100% reflection).

IEEE Geoscience and Remote Sensing Magazine - June 2019

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2019