International Journal of Remote Sensing
Vol. 30, No. 23, 10 December 2009, 6099–6119
Subpixel abundance estimates in mixture-tuned matched filtering
classifications of leafy spurge (Euphorbia esula L.)
J. J. MITCHELL*† and N. F. GLENN‡
†Department of Geosciences, Idaho State University – Idaho Falls, 1784 Science Center
Dr., Idaho Falls, ID 83492, USA
‡Department of Geosciences, Idaho State University – Boise, 322 E. Front St., Suite 240,
Boise, ID 83702, USA
Downloaded By: [Mitchell, Jessica J.] At: 22:45 4 December 2009
(Received 18 February 2008; in final form 8 February 2009)
Two demonstration sites in southeast Idaho, USA were used to extend remote
sensing of leafy spurge research to fine-scale detection for abundance mapping
using matched filtering (MF) scores. Linear regression analysis was used to quantify the relationship between MF estimates and calibrated ground estimates of
leafy spurge abundance. The two sites had r2 values of 0.46 and 0.64. Both the slope
of the regressions and the scaling behaviour of MF scores indicate that the
technique consistently underestimated true abundance (defined here as percentage
canopy cover) by roughly one-third. This underestimation may be influenced by
field estimation bias and algorithm confusion between target and background
signal. Further results indicate that MF exhibits linear scaling behaviour in six
locations containing dense, uniform infestations. At these locations, where canopy
cover was held relatively constant, high spatial resolution (3 m) estimates were not
significantly different from coarser spatial resolution estimates (up to 16 m). Given
the mathematically unconstrained nature of the estimation technique, MF is not a
straightforward method for estimating leafy spurge canopy cover.
1.
Introduction
Frequency, density, biomass and cover are metrics used to measure plant population
abundance in the field. Canopy cover is the proportion of ground occupied by a target
species when viewed from above; although subjective, it is a widely used field method
because it provides abundance information with comparatively low effort (Booth
et al. 2003). Canopy cover is also relatable to remotely sensed data collected with
nadir-viewing sensors. Ground measurements of canopy cover can be combined with
remote sensing imagery for invasive weed surveying. The use of remote sensing
technology to regularly estimate the abundance of specific invasive weed species at
the regional scale improves the ability to monitor populations, develop long-term
adaptive management strategies and understand invasion ecology dynamics (Johnson
1999, Parker Williams and Hunt 2002). Leafy spurge (Euphorbia esula L.) is an
invasive weed that is particularly expansive and damaging in the western US and
with which remote sensing has been successfully used both to map its presence (Everitt
et al. 1995, Anderson et al. 1999, O’Neill et al. 2000, Dudek et al. 2004, Parker
*Corresponding author. Email: [email protected]
International Journal of Remote Sensing
ISSN 0143-1161 print/ISSN 1366-5901 online # 2009 Taylor & Francis
http://www.tandf.co.uk/journals
DOI: 10.1080/01431160902810620
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J. J. Mitchell and N. F. Glenn
Williams and Hunt 2004, Glenn et al. 2005) and estimate its abundance (Parker
Williams and Hunt 2002).
Leafy spurge can form dense, uniform patches and during peak phenology it is
spectrally distinguishable from surrounding vegetation by its yellow–green flower
bracts using high-resolution aerial photography and hyperspectral sensors (Everitt
et al. 1995, Hunt et al. 2004). These authors attribute leafy spurge discrimination to
higher reflectance in the visible region (0.4–0.7 mm) and higher reflectance and different
signature profiles in the chlorophyll absorption region (0.55–0.69 mm). Given the
unique spectral characteristics of leafy spurge, studies have been conducted to estimate
canopy cover using image analysis software. Birdsall et al. (1995) obtained leafy spurge
cover estimates with the same level of precision as ocular estimates using 35 mm colour
photographs taken 1 m above the ground. Parker Williams and Hunt (2002) estimated
leafy spurge abundance using Airborne Visible Infrared Imaging Spectrometer
(AVIRIS) imagery (20 m pixels, 224 bands (0.4–2.5 mm)) and the classification
technique mixture-tuned matched filtering (MTMF). In their study, matched filtering
(MF) pixel scores, interpreted as estimates of subpixel target abundance from the
MTMF classification, were directly related to ocular ground estimates of canopy
cover with a correlation of r2 = 0.69. Mundt et al. (2007) also directly related
MF pixel scores to field estimates of leafy spurge canopy cover, but reported a weak
relationship (r2 = 0.32). Poor results were attributed to multiple field persons sampling
data, temporal variability in field data collection, and endmember variability (variance
in subpixel abundance estimates that is dependent on the selection of classification
endmembers; Roberts et al. 1993, Asner and Lobell 2000, Bateson et al. 2000).
Given the lack of studies focusing on the use of MF scores to estimate vegetation
abundance, this study builds upon previous MTMF classifications of leafy spurge
(Parker Williams and Hunt 2002, 2004, Dudek et al. 2004, Glenn et al. 2005) by
addressing the need to determine the reliability of MF for vegetation abundance
maps. The reliability of MF for vegetation abundance estimation is probably influenced by limitations inherent in the MTMF design and by non-linear mixing. We
anticipate inconsistencies in MF abundance estimations related to the extent to which
MF is a relative rather than an absolute estimation of abundance. The only instance in
which an MF pixel represents 100% abundance is the training pixel. It is unlikely that
the spectrum of another pixel will perfectly match the training pixel; therefore, all
other pixels will produce abundance estimations less than 100%, even if cover on the
ground is 100%. Okin et al. (2001) caution that the ability to hyperspectrally estimate
vegetation quantities such as cover, biomass and Leaf Area Index (LAI) in arid and
semiarid environments (typically less than 50% vegetation cover) with spectral mixture analysis has limited reliability when cover is below 30% or where there is little
spectral contrast between vegetation and surrounding background materials. One
ambiguity is the assumption that materials within a given pixel combine linearly; yet,
there is a non-linear mixing component, due in part to multiple scattering from
semiarid vegetation (e.g. brush) (Roberts et al. 1993, Borel and Gerstl 1994, Ray
and Murray 1996). It is presumed that nonlinear mixing contributes to differences
among MF abundance estimates at varying scales. Early research on the influence of
sensor spatial resolution on map accuracy suggests that there is a tradeoff between
fine-resolution imagery, which has greater spectral noise, and coarse-resolution imagery, which has more mixing or confusion between vegetation types (Markham and
Townsend 1981, Woodcock and Strahler 1987). We hypothesized that the relationship between MF score and ground cover estimates will strengthen as high-resolution
Matched filtering subpixel abundance estimates
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imagery (3 m · 3 m pixels) is resampled to coarser resolutions (9–16 m · 9–16 m
pixels) and spectral noise is averaged out over progressively larger areas. The extent to
which MF scores accurately estimate abundance and exhibit linear scaling behaviour
has implications for the use of remote sensing technologies to monitor abundance of
any target at multiple scales.
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2.
Technical background
Hyperspectral remote sensing instruments sample at near-continuous wavelength intervals. As such, linear spectral mixture analysis methods have been developed to exploit
the high dimensionality of the data to unmix pixels into component materials, where the
relative area (cover) occupied by each material represents abundance fractions that sum
to one (Roberts et al. 1993, Settle and Drake 1993, Okin et al. 2001, Aspinall et al. 2002).
Therefore, standard spatial-based, pure pixel classifications produce images where
pixels are assigned to classes, while mixed pixel classifications produce grey-scale
images with pixels representing the fraction of subpixel targets (Roberts et al. 1993,
Settle and Drake 1993, Heinz and Chang 2001, Keshava and Mustard 2002,
Chang 2003). MTMF is a mixed pixel classification in which a partial unmixing method
suppresses background noise and estimates the subpixel abundance of a single target
material. The MTMF method includes three main steps: (1) a minimum noise fraction
(MNF) transformation of apparent reflection data (Green et al. 1988), (2) matched
filtering for abundance estimation and (3) mixture tuning to identify infeasible or
false-positive pixels (Boardman 1998). In addition to leafy spurge detection, recent
studies have used the MTMF technique to map the distribution of blackberry (Dehaan
et al. 2007) and fine-scale ground cover components related to burn severity
(Robichaud et al. 2007).
MF is an orthogonal subspace projection (OSP) operator described by Harsanyi
and Chang (1994). The technique is a unique approach to spectral mixture modelling
in that it does not require knowledge of the spectral signatures of other component
materials (Boardman 1998). An MF score is calculated for each pixel by matching
MNF transformed input data to a spectrally pure endmember target spectra while
suppressing the background. More specifically, a matched filter vector (target spectrum in MNF space) is projected onto the inverse covariance of the MNF transformed
data and normalized to the magnitude of the target spectra such that the length of the
MF vector equates to target abundance estimations that range from 0 to 100%
(Mundt et al. 2007). Spectra that closely match the training spectrum will have a
score near one while background noise will have a score near zero. False positives are
common to MF solutions because the technique is not subject to the sum-to-one and
non-negative constraints inherent to spectral signals within bounded image pixels
(Boardman 1998). Consequently, the MT component of the MTMF classification is
used to reduce the number of false positives by considering noise variance and
estimating the probability of MF estimation error in each pixel (Mundt et al. 2007).
A correctly classified pixel should have a high MF score and a low infeasibility value.
3.
3.1
Methods
Data collection
Hyperspectral images were collected in the vicinity of Spencer (112 10¢ W, 44 21¢ N)
and Medicine Lodge (112 30¢ W, 44 19¢ N), Idaho, USA on 28 June 2006, an optimal
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Figure 1.
shown.
J. J. Mitchell and N. F. Glenn
Location of study area, with hyperspectral flightlines and ground reference samples
date for capturing leafy spurge in peak bloom (figure 1). Both sites are located just south
of the Continental Divide, in the Centennial Mountains of Clark County, within 20 km
of the town of Dubois. A HyMap sensor (operated by HyVista, Inc., Sydney, Australia)
mounted on an aircraft flying about 1000 m above the ground was used to obtain
calibrated radiance data in 126 near-contiguous spectral bands (0.45–2.48 mm) that
range in width from 15 mm in the visible and near-infrared to 20 mm in the shortwave
infrared (Kruse et al. 2000). Three overlapping flightlines totalling 3.5 km · 12.0 km
were situated lengthwise approximately 0.65 km south of the town of Spencer, north of
Stoddard Creek. Two additional flightlines (1.75 km · 10 km each) were located in the
Medicine Lodge area, of which the first was oriented parallel and the second perpendicular to the Medicine Lodge Creek drainage. Imagery acquired at the Spencer study site
has a spatial resolution of 3.2 m · 3.2 m and imagery acquired at the Medicine Lodge
study site has a spatial resolution of 3.3 m · 3.3 m.
Field sampling was initiated at the Spencer site on 16 June 2006, a few days prior to
full bloom, and continued during and shortly after peak phenology, ending 26 July
2006. A total of 56 circular plots (7.32 m radius, 168.25 m2), 43 with leafy spurge
present and 13 with leafy spurge absent, were sampled in Spencer. Validation samples
were collected in Medicine Lodge from 26 July to 13 August 2006, after peak
phenology. A total of 55 circular plots (7.32 m radius, 168.25 m2), 43 with leafy
spurge present and 12 with leafy spurge absent, were sampled in Medicine Lodge.
These validation plots were collected by way of roaming surveys of leafy spurge
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Matched filtering subpixel abundance estimates
6103
infestations that focused on capturing a uniformly distributed range of target abundance at sites representative of the ecological variability within the project areas
(although forested locations were excluded). A Trimble GeoXT (Sunnyvale, CA,
USA) model Global Positioning System (GPS) receiver was used to collect geographic
locations of plots (points) and infestation boundaries (polygons), which were then
differentially corrected using Trimble Pathfinder software. The majority of infestation boundaries were roughly mapped and the circular plots were used to collect
calibrated, continuous ocular estimates of leafy spurge percentage canopy cover
(see reference samples in figure 1).
Beyond North America Weed Management Association (NAWMA) mapping
standards were used as a guide for field data collection (Stohlgren et al. 2005). The
sample design used a 7.32 m radius circle (168.25 m2) with three transects extending
from the centre of the circle to the perimeter at 30 N, 150 N, and 270 N (figure 2).
Nine quadrats, each with an area of 1 m2, were positioned along the right sides of
transects, at intervals of 1.8, 3.7 and 5.5 m from the plot centre. The structure of the
sampling plot is a slightly modified version of the Beyond NAWMA plot in that nine
quadrats were used instead of three to improve the accuracy of abundance
estimations.
To calibrate ocular estimates of leafy spurge percentage canopy cover across a
continuous interval, estimates for the first five plots included an initial ocular estimate
at the plot scale, followed by estimates at each of the nine quadrats using a point frame
(Floyd and Anderson 1982) and a Daubenmire quadrat frame (Daubenmire 1959).
Figure 2.
Modified beyond NAWMA field data collection scheme (Stohlgren et al. 2005).
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6104
J. J. Mitchell and N. F. Glenn
Initial estimates at the plot scale for the five calibration plots were consistently closer
to the average quadrat estimations using a point frame (only one of the five calibration plots varied by more than 1%). However, estimations at the five calibration plots
using the Daubenmire quadrat were consistently about 20% lower than initial ocular
estimates at the plot scale. Although the point frame estimation technique was
designed for sagebrush steppe ecosystems and is regarded as a more objective method
than visual cover estimation (Bonham 1989), the Daubenmire frame was chosen for
its ease of use and speed to estimate cover at the quadrat scale. In addition, this
technique is more effective at locating rare species (Meese and Tomich 1992, Dethier
et al. 1993), which was a field data collection criterion in a simultaneous study. Efforts
to calibrate plot-scale and average quadrat-scale cover estimates proceeded with a
single observer initially estimating leafy spurge percentage canopy cover at the plot
scale, then estimating leafy spurge percentage canopy cover to the nearest percent at
each of the nine quadrats using the Daubenmire frame. Such cover estimates were
performed at plots with either high or low percentage leafy spurge cover before
moving on to plots with leafy spurge cover in the mid-range. Percentage canopy
cover estimations were similarly made for shrub, bare ground and rock. In the final
analysis, regression plots indicated that there was strong agreement between the
ocular cover estimation techniques at the plot and quadrat level for both leafy spurge
(r2 = 0.76) and shrub (r2 = 0.82). These regression plots suggest that field estimations
are less variable when estimating low and high percentage cover than when estimating
percentage canopy cover in the mid-range (20–60% canopy cover).
3.2
Field spectroscopy
To assess the spectral characteristics of leafy spurge abundance data at varying
percentage covers, a field spectroradiometer (Analytical Spectral Device (ASD),
Boulder, CO, USA) was used to measure the spectral signatures of leafy spurge at
three locations (34, 63 and 98% canopy cover) in the Spencer study area. The ASD
bare fibre (25 field of view) was held at waist height (0.91 m) such that a signature on
the ground was collected from a 0.44 m2 area on the ground. The instrument was
calibrated prior to measurements at each location using a white spectralon panel
(Labsphere, North Sutton, NH, USA). A series of 15 readings was collected for each
infestation and representative signatures were selected for comparison (figure 3).
These field measurements suggest that the magnitude of reflectance values is directly
related to the density of the infestation. The spectral signatures were collected 2 days
after image acquisition (30 June 2006), at the same time of day that the imagery was
acquired, and under similar atmospheric conditions. Errors with the ASD prevented
the collection of spectral data concurrent with image acquisition.
3.3
Image processing
The imagery was preprocessed by HyVista, using the HyCorr (Hyperspectral
Correction) algorithm for atmospheric correction and conversion of radiance to
reflectance data. MTMF classifications were applied to mosaiced apparent surface
reflectance images of the Spencer (3.2 m pixels) and Medicine Lodge (3.3 m pixels)
study sites. Potentially pure pixels that geographically coincided with areas of high
percentage leafy spurge cover on the ground (training areas) were selected as potential
endmembers for classifying the imagery. For each study site, the reflectance signatures of these potential endmembers were extracted and evaluated relative to one
Matched filtering subpixel abundance estimates
6105
5000
98% leafy spurge cover
Reflectance (x10,000)
4000
63% leafy spurge cover
34% leafy spurge cover
3000
2000
0
0.35
0.55
0.75
0.95
1.15
1.35
1.56
1.76
2.05
2.25
2.45
Wavelength (µm)
Figure 3. Field spectroradiometer measurements of leafy spurge at locations with 34, 63 and
98% cover. Atmospheric windows of noise excluded for clarity.
another (figure 4) and relative to reflectance signatures from the field spectroscopy
measurements (figure 3). Previous work has documented that the selection of different
potential endmembers for hyperspectral MTMF classifications of leafy spurge can
result in significant variance in accuracy performance (Glenn et al. 2005, Mundt et al.
2007). Furthermore, Mundt et al. (2007) found that the mean of user-guided
6000
5000
Reflectance (x10,000)
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1000
4000
3000
2000
1000
0
0.45
0.75
1.03
1.32
1.68
2.12
2.47
Wavelength (µm)
Figure 4. Spectral signatures of potential leafy spurge endmember pixels. Pixels selected for
use in the final Spencer and Medicine Lodge classifications are depicted in dashed and solid
bold, respectively.
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J. J. Mitchell and N. F. Glenn
(a)
40
Infeasibility value
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endmember pixels with high percentage leafy spurge cover performed better than (1)
extreme or variant n-dimensional visualizer (ND-V) endmember pixels and (2) the
mean of all ND-V endmember pixels. Therefore, in our study, we selected a userguided endmember pixel with high percentage target cover and an average spectral
signature from each study site for use in the MTMF classification algorithm. The first
89 MNF bands of each study site mosaic were defined as input for the MTMF
classifications, along with the chosen endmember for each study site (see spectral
signatures in figure 4). Use of the first 89 bands was thought to be a good tradeoff
between introducing noise associated with higher bands and gaining information by
using more MNF bands for mapping than for deriving endmembers.
The MTMF classifications produced an MF band for each of the Spencer and
Medicine Lodge study sites, where pixel values represent the relative degree of match
with the training spectrum (figure 5). Thresholding of resultant infeasibility and MF
images (figure 5(a)) was performed by interactively selecting scatterplot values
30
20
10
–0.2
0.0
0.2
0.4
MF score
0.6
0.8
1.0
(b)
metres
Figure 5. (a) Scatterplot of infeasibility values versus MF scores. (b) Scatterplot values
calculated over a training area within the image.
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Matched filtering subpixel abundance estimates
6107
calculated over training areas within the images (figure 5(b)). Classified presence/
absence maps were produced for the Spencer and Medicine Lodge study sites with
overall accuracies of 67% and 85%, respectively. Errors of commission were favoured
over errors of omission for weed management purposes. The classified leafy spurge
maps generated for Spencer and Medicine Lodge were used to identify three locations
at each study site known to contain large (greater than a 16 m · 16 m pixel), uniform
infestations of leafy spurge. These locations correspond to plots 6 and 10 in Spencer
(see MF study locations in figure 6(a)) and plots 54, 75 and 85 in Medicine Lodge
(see MF study locations in figure 6(b)). Once these locations were identified, the
Spencer and Medicine Lodge reflectance mosaics were spatially resized by factors of
three and five times the original pixel resolution. The pixels were resized using a
square-wave pixel aggregation approach whereby pixels that contribute to the output
pixel are spectrally averaged (nine contributing pixels for the 9 m scale imagery and
25 contributing pixels for the 16 m scale imagery). MTMF classifications were also
applied to these resampled mosaics using endmembers spectrally similar to, and in the
geographic vicinity of, the original classification endmembers. These MTMF classifications produced four additional MF images: two MF images of the Spencer site at
three and five times the original spatial resolution (9.6 m and 16.0 m pixels), and two
MF images of the Medicine Lodge site at three and five times the original spatial
resolution (9.9 m and 16.5 m pixels).
3.4
MF score analysis
Linear regression analysis was used to quantify the relationship between ocular
canopy cover estimates and MF abundance estimates of leafy spurge in Spencer and
Medicine Lodge at the original 3 m pixel scale and at pixel aggregated 9 m and 16 m
scales. Linear regressions at all scales used a mean MF score calculated from both the
pixel containing the centre of the circular field plot (168.25 m2) and the nine surrounding MF pixels. To test whether linear regression was appropriate to use for the data
analysis, modality was assessed with histograms, homoscedasticity was investigated
by plotting residuals versus predicted values and qualitatively assessing the regression
plots, and error normality was tested using the Shapiro–Wilk test. A non-parametric
test, the Mann–Kendall, was also used to test for the presence of upward trends in MF
scores across increasing ground cover intervals. The Mann–Kendall is a rank-based
trend test that is applied to vector data, often time series (Mann 1945). For the
purposes of this dataset, ground cover was treated as time and MF scores were treated
as a series.
To explore the relationship between spatial scaling and MF score behaviour,
sampling units with dimensions of one, three and five times the original pixel sizes
(3.3 m in Spencer and 3.2 m in Medicine Lodge) were located within six locations
containing large, uniform infestations of leafy spurge (three in Spencer and three in
Medicine Lodge). The large, uniform infestations contained field plots and were
considered necessary to control for the influence of mixing from non-target reflectance and scaling issues; that is, varying ratios of sample support size (field sample size
of 168.25 m2) to prediction support size (successively coarser MF score pixel sizes).
The sampling units were arranged within selected infestations such that successively
coarser MF pixels fell in a nested arrangement. The nested arrangement was selected
to optimize comparison of original and pixel-aggregated MF values across spatial
scales. At all six locations, comparisons were made between pixel-aggregated
J. J. Mitchell and N. F. Glenn
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6108
Figure 6. Matched filtering abundance image from the MTMF classifications overlaid on
hyperspectral imagery of the (a) Spencer and (b) Medicine Lodge study sites. Darker pixels
represent higher abundance estimates.
MF pixel values and original 3 m scale MF pixel value means. For example, single
abundance estimates from 9.6 m · 9.6 m pixels were compared to the means of 3 · 3
arrays of 3.2 m pixels and single abundance estimates from 16.0 m pixels were
compared to the means of 5 · 5 arrays of 3.2 m pixels. It should be noted that nested
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Matched filtering subpixel abundance estimates
Figure 6.
(Continued.)
pixel arrangements of three overlapping image scales (3, 9 and 16 m) results in nested
sampling units that do not occur continuously throughout a conceptually composite
image. Consequently, while four of the nested sampling units intersected their respective field plots, a fifth sampling unit was located approximately 3.5 m from a field plot
and a sixth sampling unit was located approximately 7.5 m from a field plot.
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4.
J. J. Mitchell and N. F. Glenn
Results
Exploratory data analysis indicated a tendency towards bimodality for leafy spurge
cover and MF scores at all scales in both Spencer and Medicine Lodge. However,
when absence samples were excluded, bimodality was not found in the leafy spurge
cover and MF score data. Thus, two datasets were retained for the regression analysis:
one dataset containing both presence and absence samples and one dataset containing
only presence samples. All of the plots of residuals versus predicted values exhibited a
funnel shape, indicative of non-constant variance (plots not shown). Transformations
(including 1/y, gamma, and log) to stabilize variance were unsuccessful. Thus, homoscedasticity could not be confirmed. The results of the Shapiro–Wilk test (table 1)
indicate a rejection of the null hypothesis that the residuals have a normal distribution. However, exclusion of the absence samples in the Shapiro–Wilk test did increase
the normality of the residuals at the 3 m scale in Medicine Lodge (table 1).
Furthermore, qualitative inspection of the regression plots (figure 7) indicates that
the data behave linearly.
Based on these results, the relationship between ground cover and MF estimates of
leafy spurge was further tested with a non-parametric trend analysis, where slope
estimates near zero indicate no trend. In all cases the Mann–Kendall p-value was
0.000 and the null hypothesis of no significant upward trend in the data was rejected.
The slope estimates from these tests using the Medicine Lodge data were 0.238, 0.324
and 0.248 at the 3, 9 and 16 m scales, respectively. The slope estimates using the
Spencer data were 0.307, 0.251 and 0.224 at the 3, 9 and 16 m scales, respectively.
In the regression plots at the 3 m scale there was strong agreement in Spencer and
fair agreement in Medicine Lodge between field estimates and MF estimates of leafy
spurge abundance (figure 7). A regression analysis that included both presence and
absence reference samples collected at the Spencer site produced an r2 value of 0.63
(n = 51). When absence reference samples were excluded, the agreement still remained
strong (r2 value of 0.63; n = 38). A regression analysis that included both presence and
absence reference samples collected at the Medicine Lodge site produced an r2 value
of 0.46 (n = 55). When absence reference samples were excluded at Medicine Lodge,
the agreement decreased to an r2 value of 0.36 (n = 43). The exclusion of absence
samples consistently yielded slightly lower r2 values at all scales (figure 7). When
Table 1. Shapiro–Wilk normality test results of the residuals from linear regressions of MF
abundance estimates versus leafy spurge ground cover at the 95% confidence interval in the
Spencer and Medicine Lodge study sites.
Presence and absence reference samples
Spencer
3.2 m
9.6 m
16.0 m
Medicine Lodge
3.3 m
9.9 m
16.5 m
Presence reference samples
Test statistic
p-value
Test statistic
p-value
0.897
0.818
0.763
0.000
0.000
0.000
0.905
0.840
0.787
0.004
0.000
0.000
0.951
0.839
0.814
0.024
0.000
0.000
0.967
0.874
0.849
0.240*
0.000
0.000
*In this case the null hypothesis of normality is accepted.
Matched filtering subpixel abundance estimates
6111
(a)
Spencer 3 m scale (presence & absence samples)
Spencer 3 m scale (presence samples)
1.000
1.000
0.800
y = 0.35x – 0.04
2
R = 0.63
0.600
MF Score
0.600
MF Score
0.800
y = 0.32x – 0.02
R2 = 0.64
0.400
0.200
0.400
0.200
0.000
0.000
0.00
0.20
0.40
0.60
0.80
0.00
1.00
0.20
1.00
1.000
0.800
0.800
y = 0.28x – 0.02
2
R = 0.57
y = 0.31 – 0.04
R2 = 0.56
0.600
MF Score
0.600
MF Score
0.80
Spencer 9 m scale (presence samples)
Spencer 9 m scale (presence & absence samples)
1.000
0.400
0.200
0.400
0.200
0.000
0.000
0.00
0.20
0.40
0.60
0.80
1.00
0.00
0.20
0.40
0.60
0.80
1.00
–0.200
–0.200
Leafy Spurge Cover (%)
Leafy Spurge Cover (%)
Spencer 16 m scale (presence & absence samples)
Spencer 16 m scale (presence samples)
1.000
1.000
0.800
0.800
y = 0.28x – 0.02
R2 = 0.47
y = 0.31x – 0.04
2
R = 0.45
0.600
MF Score
0.600
MF Score
0.60
Leafy Spurge Cover (%)
Leafy Spurge Cover (%)
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0.40
–0.200
–0.200
0.400
0.400
0.200
0.200
0.000
0.000
0.00
0.20
0.40
0.60
0.80
0.00
1.00
0.20
0.40
0.60
0.80
1.00
–0.200
–0.200
Leafy Spurge Cover (%)
Leafy Spurge Cover (%)
Figure 7. Linear regression plots of MF scores versus leafy spurge cover for the (a) Spencer
and (b) Medicine Lodge study sites.
ocular field estimates of leafy spurge canopy cover were related to MF abundance
scores for resized pixels, agreement declined, with successively larger pixel sizes in
Spencer (9.6 m2, r2 = 0.57; 16 m2, r2 = 0.47; figure 7(a)) and Medicine Lodge (9.6 m2,
r2 = 0.46; 16 m2, r2 = 0.42; figure 7(b)). The slopes of all regressions indicate that the
MF scores are underestimating field estimates of leafy spurge cover (considered here
as true abundance). The underestimation is roughly one-third. At both sites, r2 values
were greater than previous results reported by Mundt et al. (2007) and were similar to
results reported by Parker Williams and Hunt (2002).
Analyses of MF scores at different scales also indicated that MF estimates consistently underestimated true abundance (table 2). One test location in Spencer
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J. J. Mitchell and N. F. Glenn
(b)
Medicine Lodge 3 m scale
(presence & absence samples)
1.000
0.800
y = 0.29x – 0.05
R2 = 0.36
0.600
MF Score
MF Score
0.800
y = 0.25x – 0.03
2
R = 0.46
0.600
Medicine Lodge 3 m scale
(presence samples)
1.000
0.400
0.200
0.400
0.200
0.000
0.000
0.00
0.20
0.40
0.60
0.80
1.00
0.00
–0.200
0.20
Medicine Lodge 9 m scale
(presence & absence samples)
1.000
0.800
0.800
1.00
y = 0.41x – 0.06
R2 = 0.34
0.600
MF Score
MF Score
0.80
Medicine Lodge 9 m scale
(presence samples)
1.000
y = 0.37x – 0.03
R2 = 0.46
0.600
0.400
0.400
0.200
0.200
0.000
0.000
0.00
0.20
0.40
0.60
0.80
1.00
0.00
0.20
0.40
0.60
0.80
1.00
–0.200
–0.200
Leafy Spurge Cover (%)
Leafy Spurge Cover (%)
Medicine Lodge 16 m scale
(presence & absence samples)
1.000
0.800
Medicine Lodge 16 m scale
(presence samples)
1.000
0.800
y = 0.31x – 0.02
R2 = 0.42
y = 0.34x – 0.05
R2 = 0.30
0.600
MF Score
0.600
MF Score
0.60
Leafy Spurge Cover (%)
Leafy Spurge Cover (%)
Downloaded By: [Mitchell, Jessica J.] At: 22:45 4 December 2009
0.40
–0.200
0.400
0.200
0.400
0.200
0.000
0.000
0.00
0.20
0.40
0.60
0.80
1.00
–0.200
0.00
0.20
0.40
0.60
0.80
1.00
–0.200
Leafy Spurge Cover (%)
Leafy Spurge Cover (%)
Figure 7.
(Continued.)
intersected plot 6, where leafy spurge cover was estimated at 94% (table 2). The
corresponding MF abundance score was estimated at 0.599 (59.9%) using a single
pixel. When MF abundance estimations were calculated for this test location using
reclassified images spectrally aggregated at three and five times the original pixel
resolution, the estimates were 0.568 and 0.639, respectively. The additional two test
locations selected in Spencer were associated with plot 10, where leafy spurge cover
was estimated at 93% (table 2). One test location was approximately 9.0 m from plot
10 (10a) while the other test location intersected plot 10 (10b). The corresponding MF
abundance scores for the test locations 10a and 10b were estimated at 0.220 and 0.160,
respectively, using a single pixel. When MF abundance estimations were calculated
for the test locations 10a and 10b using reclassified images spectrally aggregated at
5 · (16.0 m)
0.315
3 · (9.6 m)
0.244
25 pixels
0.374
5 · (16.5 m)
0.478
9 pixels
0.266
3 · (9.9 m)
0.491
Test location 75 (intersects plot 75)
Plot 75 leafy spurge cover = 96%
25 pixels
1 pixel
0.245
0.098
the original pixel resolution
5 · (16.5 m)
1 · (3.3 m)
0.246
0.098
Test location 85 (intersects plot 85)
(Plot 85 leafy spurge cover = 85%)
3.3 m MF score pixel values
1 pixel
9 pixels
Mean 0.168
0.222
MF score pixel values resampled at 3 · and 5 ·
1 · (3.3 m)
3 · (9.9 m)
Value 0.168
0.215
Medicine Lodge
25 pixels
0.282
9 pixels
0.235
Test location 10b (intersects plot 10)
Plot 10 leafy spurge cover = 93%
25 pixels
1 pixel
0.345
0.160
the original pixel resolution
5 · (16.0 m)
1 · (3.2 m)
0.420
0.160
Test location 10a (approximately 3.5 m from plot 10)
Plot 10 leafy spurge cover = 93%
3.2 m MF score pixel values
1 pixel
9 pixels
Mean 0.220
0.322
MF score pixel values resampled at 3 · and 5 ·
1 · (3.2 m)
3 · (9.6 m)
Value 0.220
0.348
Spencer
3 · (9.6 m)
0.639
9 pixels
0.525
5 · (16.0 m)
0.816
25 pixels
0.559
1 · (3.3 m)
0.479
1 pixel
0.479
3 · (9.9 m)
0.549
9 pixels
0.426
5 · (16.5 m)
1.000
25 pixels
0.489
Test location 54 (intersects plot 54)
Plot 54 leafy spurge cover = 96%
1 · (3.2 m)
0.599
1 pixel
0.599
Test location 6 (intersects plot 6)
Plot 6 leafy spurge cover = 94%
Table 2. MF scaling behaviour. Scores averaged over 3 · 3 pixel areas and 5 · 5 pixel areas are compared to scores derived from reclassified images
degraded to 3 · and 5 · the original pixel resolution.
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J. J. Mitchell and N. F. Glenn
three and five times the original pixel resolution, the estimates were 0.348 and 0.244,
respectively, at the 9 m scale and 0.420 and 0.315, respectively, at the 16 m scale. One
test location in Medicine Lodge intersected plot 85, where leafy spurge cover was
estimated at 85% (table 2). The corresponding MF abundance score was estimated at
0.361 using a single pixel. When MF abundance estimations were calculated for this
location using reclassified images spectrally aggregated at three times and five times
the original pixel size, the 9 m estimate was 0.215 and the 16 m estimate was 0.246.
Two additional test locations in Medicine Lodge intersected plots 75 and 54, where
leafy spurge cover was estimated at 96%. The corresponding MF abundance scores
for the test locations intersecting these plots (75 and 54) were estimated at 0.098 and
0.479, respectively, using a single pixel. When MF abundance estimations were
calculated for test locations in the vicinity of plots 75 and 54 using reclassified images
spectrally aggregated at three and five times the original pixel resolution, the 9 m
estimates were 0.491 and 0.549, respectively. The 16 m resized estimates for the test
locations associated with plots 75 and 54 were 0.478 and 1.000, respectively.
Two-sample t-tests were used to statistically compare MF pixel values from the six
study locations at the 3 m and 9 m scale, the 3 m and 16 m scale and the 9 m and 16 m
scale. In all cases there was no statistically significant difference in pixel values
between scales (table 3). Paired t-tests were used to statistically compare averaged
MF pixel scores to aggregated MF pixels scores (table 3). Scores were paired by
location and there was no statistically significant difference between the averaged and
the aggregated scores at both the 9 m and the 16 m scale.
5.
Discussion and conclusions
The lack of homoscedasticity from the plots of residuals versus predicted values
indicate that the non-constant variance is a function of leafy spurge cover. Such
non-constant variance could be related to the relative ability to ocularly estimate
leafy spurge cover at different densities (i.e. it may be easier to estimate low and high
cover and more difficult to estimate moderate cover). The lack of homoscedasticity
could also be related to inherent heterogenic differences in spatial distribution patterns at various percentage covers. Although the regression plots exhibited linear
characteristics, lack of homoscedasticity and normal error distributions rendered the
resultant r2 values debatable. Mann–Kendall non-parametric trend test results were
Table 3. Student’s t-test results for comparing MF score differences across scales and for
comparing averaged MF pixel scores to aggregated MF pixels scores, paired by location
(95% confidence interval); n = 6.
p-value
Samples
3 m and 9 m pixel scale
3 m and 16 m pixel scale
9 m and 16 m pixel scale
Pairs
Nine MF pixel values averaged over 3 · 3 pixel area vs. a single aggregated MF
pixel value at the 9 m scale
Twenty-five MF pixel values averaged over 5 · 5 pixel area vs. a single aggregated
MF pixel value at the 16 m scale
0.483
0.201
0.393
0.074
0.099
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6115
consistent with the linear regression results for the presence only data sets in that both
tests provided evidence of a weak to moderate relationship between ground cover and
MF estimates of leafy spurge cover.
Comparative results indicate that the MF score consistently underestimated true
leafy spurge canopy cover. Underestimations are likely to be influenced by field
methods for estimating canopy cover, scaling between field estimates and pixel sizes,
limitations inherent to MTMF techniques and by the MTMF classification’s ability to
separate leafy spurge from background spectra. The MF scores were directly related to
ocular cover estimates at the plot scale. While these plot scale estimates were calibrated
and strongly agreed with the average quadrat estimation method (r2 = 0.76), canopy
cover may have been overestimated in the field, thus accounting for the underestimation of MF scores. Although locations of dense, uniform infestations were selected to
reduce the influence of scaling on the relationship between field and MF estimates of
target abundance, we recognize that the scale of the field plots of leafy spurge cover do
not match the original and resized pixel scales. Specifically, the field estimates were
not made at each incremental pixel size (9, 81 and 256 m2) but were made over a scale of
168 m2. While all six of the field plots were dense, uniform, and at least 256 m2 in area,
overprediction of leafy spurge could have occurred in the field by assuming percentage
cover was homogeneous across these plots. For example, within plot 85 (85% cover),
mixing of other materials may have occurred nonlinearly across the plot. Similarly, we
assume that the plot scale cover estimations could be extrapolated to the larger infested
areas (at least 256 m2). Furthermore, in the cases of plots 10a and 85, the results may be
biased because of the geographical separation between the field plots and the spatially
aggregated MF scores. While field notes indicate that leafy spurge encompassed areas
where MF scores were calculated, our field plots were not ideally situated for the nested
arrangement. A related factor in mismatching between field and image plots is georeferencing. Based on comparisons to GPS data, the Spencer mosaic had a mean
locational error of 0.813 m and the Medicine Lodge mosaic had a mean locational
error of 3.39 m. We suggest that the 168 m2 circular plot is a good size for estimating
leafy spurge percentage cover at the 3–9 m scale. This suggestion is primarily based on
the strong relationship between MF scores and all abundance measurements at the 3–9
pixel scale (table 1).
This variability or tendency towards underestimation is, in part, inherent to the
MTMF technique because it was developed with the idea of estimating subpixel
abundance by measuring the similarity between spectra from image pixels and a single
‘pure’ training spectrum. In the regression analysis, evidence of linearity and high r2
values suggest that MF is, at minimum, providing relative measures of abundance.
However, the range in MF scores near 100% canopy cover is large (approximately
0.020–1.000; see figure 7). In another example, table 2 compares the MF values of 3 m
pixels located in dense infestations near 100%. Ideally, these MF values should all be
close to 1.000 but in fact they range in value from 0.098 to 0.599. The degree of
underestimation most probably depends on subtle spectral variation in leafy spurge
and the amount of spectral contrast between the target and the background. Pixels
relatable to target cover near 100% on the ground will be less than 100% because the
spectra will not perfectly match the training pixel spectrum.
We also suspect that the MTMF classifications were mistaking some leafy spurge as
background, thereby underestimating target abundance. For example, low contrast will
be associated with a larger underestimation of the abundance. Continued research in
this area is needed and should explore the extent to which the magnitude of
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J. J. Mitchell and N. F. Glenn
underestimation is a function of scene content. Although we found it more difficult to
separate target pixels from background pixels during the hyperspectral classification of
leafy spurge at the Spencer site (the overall classification accuracy was 67% for Spencer
and 85% for Medicine Lodge), there was better linear regression agreement at the
Spencer site. Better agreement may be attributed to wider ranges in MF score pixel
values, which provided better spreads for regression analyses. In both Spencer and
Medicine Lodge, the strongest regression relationships occurred at the 3 m pixel scale.
By contrast, the highest abundance estimates tended to occur at coarser scales, whether
estimates were calculated by averaging pixels or extracting scores from spatially
aggregated images. Mann–Kendall slope estimate results indicated the strongest trend
occurred at the 3 m scale in Spencer, but at the 9 m scale in Medicine Lodge. Overall, our
hypothesis that the relationship between MF score and ground cover estimates would
increase as noise is averaged out over coarser spatial resolutions cannot be completely
dismissed given inconclusive statistical results and the fact that the highest MF scores
consistently occurred at the 16 m scale for the six high-cover test locations (table 2).
It is difficult to isolate linear MF behaviour from nonlinear MF behaviour because
the distribution of MF scores within an image has a mean of zero and is normalized to
the range of target spectra. In general, if an attribute behaves linearly, then as the
support size increases the mean will remain the same while variance decreases and the
symmetry of the distribution increases (Isaaks and Srivastava 1989). The implication
is that adjustment factors can be calculated to integrate linear attribute data with data
collected at different spatial resolutions. While we cannot directly test MF score
behaviour in such a manner, significance testing across scales and between pixelaggregated and pixel-averaged MF estimates suggests there is a linear component to
the MF estimation at the six test locations. Nonlinear mixing is likely to have a greater
influence on MF estimations in other, less ideal environments. Unfortunately, quantifying nonlinearity or even verifying its presence is not a simple process for experimental field data such as ours. Additional studies using simulated laboratory data
would be better suited for determining the extent to which the MF score is a composite
measurement that exhibits nonlinear scaling behaviour.
Coincidently, it may not be appropriate to relate MF abundance estimates to
vegetation abundance estimates. Unconstrained linear spectral mixture analysis methods do not necessarily reflect true material abundance fractions and should be interpreted for detection, discrimination and classification, not quantification (Heinz and
Chang 2001). Therefore, MF, as a mathematically unconstrained linear spectral
mixture analysis method, generates scores that should only be interpreted as the likelihood that a target is contained within a given pixel. While the MTMF classification
technique may perform well at detecting the presence of a material, it may not be
equally appropriate for estimating the abundance of materials. Future research should
focus on the use of constrained linear spectral analysis methods to remotely estimate
vegetation abundance (e.g. fully constrained least squares, Heinz and Chang 2001).
Furthermore, because robust ground reference datasets of canopy cover are timely and
costly (e.g. in this study, the number of replicates (n = 6) for testing the resized pixels
versus averaging pixels was not sufficient for definitive conclusions), it would be more
efficient to first test candidate methods under simulated conditions where known
fractions of materials are mixed prior to analysis. When testing a candidate method
in the field, we recommend selecting a demonstration site with a large number of
widespread, uniform infestations and a field sample design where the scale at which
cover is estimated in the field directly corresponds to the scale of resized pixels.
Matched filtering subpixel abundance estimates
6117
Acknowledgements
We thank the anonymous reviewers who helped to strengthen the merit of this paper.
This research was funded by USDA Natural Resources Conservation Service
Conservation Innovation Grant No. 68-0211-6-124, Pacific Northwest Regional
Collaboratory, as part of a Pacific Northwest National Laboratory project funded
by NASA through Grant No. AGRNNX06AD43G, and NOAA OAR ESRL/
Physical Sciences Division (PSD) Grant No. NA04OAR4600161. Field data collection was made possible through the generous advice and assistance of Jeffrey
Pettingill and staff at Bonneville County Weed and Pest Control, Shane Jacobson
(US Forest Service, Dubois, Idaho), Keith Bramwell (Continental Divide
Cooperative Weed Management Area), and Tom Stohlgren (USGS Fort Collins
Science Center).
Downloaded By: [Mitchell, Jessica J.] At: 22:45 4 December 2009
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