Integration of Magnitude and Shape Related Features in Hyperspectral Mixture Analysis to Monitor Weeds In Citrus Orchards.

Abstract

Traditionally, Spectral Mixture Analysis (SMA) fails to fully account for highly similar ground components or endmembers. The high similarity between weed and crop spectra therefore hampers the implementation of SMA for steering weed control management practices. To address this problem, the current study presents an alternative SMA technique, referred to as Integrated Spectral Mixture Analysis (iSMA). iSMA combines both magnitude (~reflectance) and shape (~derivatives) related features in an automated waveband selection protocol and allows for an optimal separation between weed and crops, irrespective of the scenario considered. Compared to traditional approaches iSMA significantly improved weed cover fraction estimations (~17% increase). Analysis was performed on different simulated mixed pixel spectra sets compiled from in situ measured weed, Citrus canopy and soil spectra.

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THE INTEGRATION OF MAGNITUDE AND SHAPE RELATED FEATURES IN HYPERSPECTRAL
MIXTURE ANALYSIS TO MONITOR WEEDS IN CITRUS ORCHARDS

B. Somers*1, K. Cools1, S. Delalieux1, W. W. Verstraeten1, J. Verbesselt2,S. Lhermitte1 & P. Coppin1

1 Dept. of Biosystems, M3-BIORES, Katholieke Universiteit Leuven,
Celestijnenlaan 200E, BE-3000 Leuven, Belgium
2CSIRO Forest Biosciences, Private Bag 10,
Clayton South, VIC 3169, Australia

* corresponding author; email: ben.somers@biw.kuleuven

1.
INTRODUCTION

In an agricultural context hyperspectral mixture analysis (SMA) potentially bears the ability to map the spatial distribution of weeds and as
such allows for a site specific application of herbicides [1]. The high similarity in spectral characteristics between weeds and crops,
however, leads to sub-optimal classification accuracies when conventional approaches are considered [2, 3]. The current study presents an
alternative SMA technique to address this problem. In an integrated approach original and derivative reflectance features are considered
simultaneously in a single analysis. As such, a perfect description of both the magnitude and shape of ground component spectra becomes
feasible. Subsequently, an automated waveband selection protocol tracks the spectral features that display the lowest spectral similarity.
The selected subset, which maximizes the inter-class variability while minimizing the intra-class variability, is incorporated in a mixture
analysis resulting in increased sub-pixel fraction estimate accuracy. The algorithm is validated both for simulated and in situ measured
mixtures of weed canopy, Citrus tree canopy and bare soil spectra.

2.
THEORETICAL BACKGROUND

2.1.
Linear Spectral Mixture Analysis (SMA)
In linear spectral mixture analysis the observed spectrum r for any given pixel in the scene is expressed as:
?
=
j
ε+= Mfr
with
1
1
=
m
jf
and
10
≤≤
jf
(1)
M is a matrix of which each column corresponds to the spectral signal of a specific ground cover class (endmember) and f is a column
vector [f1,…,fm]T that denotes the sub-pixel cover fractions occupied by each of the m endmembers. The portion of the spectrum that cannot
be modeled is expressed as a residual term, ?. Sub-pixel endmember fractions for the corresponding vector f are obtained by minimizing
=?
=
next equation considering the constraints of Eq. (1):
²²
1
rMff
n
i
i
−=ε
(2)
In a conventional SMA approach, image-wide endmember spectra are defined. The accuracy of sub-pixel fraction estimates therefore
decreases linearly with both the variability within and the similarity among endmember classes [3].

2.2.
Derivative Spectral Mixture Analysis (DSMA)
Derivative endmember spectra are used to emphasize endmember specific diagnostic absorption features, while reducing differences in the
spectral magnitudes [4]. The linear mixture model (1) is rewritten as:
?
=
j
ε
λλ
λ
+×=
n
n
n
n
d
Md
f
d
rd
)(
with
1
1
=
m
jf
and
10
≤≤
jf
(3)
n
n
d
rd
λ
λ)(
is the nth derivative of the spectrum at wavelength ? of the mixed pixel,
n
n
d
Md
λ
is the nth derivative of the endmember matrix M.

2.3.
Integrated Spectral Mixture Analysis (iSMA)
Original reflectance spectra (~ magnitude) and derivative spectra (~ shape) both provide independent and new information on the spectral
characteristics of ground components. We therefore propose to integrate both in one analysis. This integrated mixing model has the same
form as the reflectance/derivative mixing models of Eqs. (1) & (3) with the distinction that the least square regression estimator will rely on
both the equations of (1) and (3) to estimate f. A weighted least square regression approach is used to equalize the contribution of the
derivative and original reflectance features. This is necessary because
²
1
,derivative
ε
?
=
i
n
i
is relatively small compared to
²
1
e, reflectanc
ε
?
=
i
n
i

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which implies that the least square estimator is mainly determined by the original reflectance features if no weighting operation is
performed. Secondly, stable spectral features (i.e., least sensitive to spectral variability) are automatically selected for use in the mixture
analysis based on a minimum InStability Index (ISI) criterion [2]. ISI is defined as the ratio of the spectral variability within (i.e., the sum
of the one-sided 95% confidence interval per endmember class) and the spectral variability among the endmember classes that are present
within the mixture (i.e., average Euclidean distance between the class means). The selected set of stable spectral features can be composed
of both original and/or derivative (1st and 2nd order) reflectance values.

3.
VALIDATION

The performance of iSMA to map the spatial distribution of weed patches in Citrus orchards was evaluated. Simulated [5, 6] and in situ
measured mixtures of weed canopy, tree canopy and bare soil spectra were analyzed. In situ measurements were performed using a full-
range (350-2500 nm) spectroradiometer (ASD, Boulder, CO). The abundance error (?f) and the coefficient of determination (R²) between
the estimated and real (i.e., ground truth) endmember fractions were used to assess classification accuracy [6].

4.
RESULTS

Table 1: The performance of the SMA, DSMA and iSMA for different scenarios
?f
Endmembers description
R² Intercept Slope
mixtures of1: sim. in situ sim. in situ sim. in situ sim. in situ
Citrus sinensis & Lolium sp.
SMA
DSMA*
0.26 0.29 0.19 0.10 0.22 0.27 0.59 0.48

0.07 0.09 0.74 0.63 0.07 0.12 0.91 0.77

iSMA 0.06 0.08 0.87 0.75 0.06 0.09 0.91 0.86
Citrus sinensis, Echium sp.
SMA
DSMA*
0.14 0.11 0.51 0.32 0.07 0.23 0.80 0.61
& bare soil
0.05 0.09 0.88 0.67 0.00 0.05 0.97 0.80

iSMA
SMA
DSMA*
0.03
0.26
0.07
0.28
0.90
0.21
0.73
0.13
0.01
0.17
0.04
0.21
0.97
0.53
0.88
0.49
Citrus retuculata, Plantago sp.
& bare soil
0.06 0.08 0.86 0.76 0.02 0.07 0.95 0.83

iSMA 0.04 0.06 0.88 0.79 0.02 0.05 0.95 0.86
1 A shade endmember is included in all mixtures; *Results are shown for the first derivatives only

5.
DISCUSSION & CONCLUSIONS

The iSMA approach, which combines both shape and magnitude related spectral features in an automated waveband selection protocol,
allows for optimal weed patch monitoring in Citrus orchards. Both for the simulated and in situ measured mixtures iSMA performed better
than traditional mixture analysis approaches (Table 1). The sub-optimal accuracy achieved for in situ measured pixels is assigned to
nonlinear mixing caused by multiple photon scattering [7]. Currently an attempt is made to improve the accuracy by modeling the
nonlinear interactions. As iSMA is insensitive to changing scenarios (Table 1), the algorithm provides a powerful tool as a dynamic weed
development monitoring technique. Moreover, the iSMA approach is relevant in any other ecosystem or application domain in which
highly similar endmembers need to be separated (e.g., urban environments [8]). Future research should, however, validate this statement.

6.
REFERENCES

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extent and spectral characteristics of crops”, Photogrammetric Eng. & Remote Sens., in press.
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[8] Song; C., “Spectral mixture analysis for subpixel vegetation fractions in the urban environment: how to incorporate endmember
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