Remote Sensing of Environment 101 (2006) 82 – 94
www.elsevier.com/locate/rse
Enhanced detection of the coral Acropora cervicornis from satellite imagery
using a textural operator
Samuel J. Purkis a,*, Soe W. Myint b, Bernhard M. Riegl a
a
National Coral Reef Institute, Nova Southeastern University Oceanographic Center, 8000 N. Ocean Drive, Dania Beach, FL 33004, USA
b
Department of Geography, Arizona State University, Tempe, AZ 85287-0104, USA
Received 30 June 2005; received in revised form 17 November 2005; accepted 19 November 2005
Abstract
The strength of a texture-based classification lies in the fact that it detects spatial patterning as a function of spectral variation within a
particular facies class, as opposed to spectral consistency which drives standard probability-driven image classifiers. Following this premise, the
Moran’s I spatial autocorrelation metric was proven to return values which differed significantly for areas characterised by dense interlocking
thickets of the coral Acropora cervicornis versus areas populated by a sparse mixed coral assemblage dominated by Montastrea annularis. The
different behaviour of the metric was sufficient to facilitate spatial discrimination of the two assemblages using a supervised classifier with
accuracies that surpass the level of prediction offered by standard spectral-based methods. Discrimination was optimum when autocorrelation was
evaluated within a moving window with side-lengths ranging between circa. 30 – 70 m. The discrimination ability is postulated to be linked to
intrinsic differences in the spatial-patterning of the two assemblages at scales of tens of metres. The observed patterning can be further related to
the growth form and architecture of the differing coral assemblages. The study demonstrates the potential of using kernel-based autocorrelation
metrics in unison with satellite data and offers a pertinent tool for monitoring ecologically important coral assemblages that are statistically
indistinct using traditional spectral methods.
D 2005 Elsevier B.V. All rights reserved.
Keywords: IKONOS; Spatial autocorrelation; Coral reef; Texture; Acropora cervicornis
1. Introduction
The traditional method for analysis of earth observation data
in landscape-research is the classification of eco-types based on
pixels in the same land cover class being close in spectral
feature space (Burnett & Blaschke, 2003). Similarly in
traditional remote sensing of reefal areas, from-image statistics
are used to train a probability-driven classifier such that pixels
of similar optical properties are assigned to a common class.
The technique is effective in the majority of cases since
different benthic types frequently display separable optical
signatures (Hochberg et al., 2003a; Karpuzli et al., 2004;
Purkis, 2005; Purkis & Pasterkamp, 2004). However, the
probability-driven approach fails when the desired substrate
classes are spectrally inseparable, as is frequently the case
when observed with today’s multispectral satellite systems.
* Corresponding author. Tel.: +1 954 262 3647.
E-mail address: [email protected] (S.J. Purkis).
0034-4257/$ - see front matter D 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.rse.2005.11.009
While sensors such as IKONOS offer metre-scale satellite
imagery, they remain spectrally impoverished and as such are
not well adapted for coastal seabed mapping. Furthermore, due
to the multiple scattering of natural optical radiation an
effective path of a photon in seawater is rather large, insuring
high sensitivity of upwelling radiation to the content of
dissolved and suspended substances in water (Haltrin et al.,
2002). Consequently in optically shallow waters where the
majority of corals reside, separating the spectral contribution of
the seafloor from that of the water column is problematic and
further compromises the accuracy of benthic classification. The
contribution of the water column can be successfully modelled
and removed using a radiative transfer (RT) approach (e.g.
Deepak et al., 2005; Hedley & Mumby, 2003; Isoun et al.,
2003; Purkis, 2005; Riegl & Purkis, 2005). When confined to
multispectral satellite data, the RT strategy however is limited
by the fact that water depth throughout the area of interest must
be accurately constrained with a high spatial resolution, and as
such, the solution is largely precluded in areas lacking ancillary
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
83
under investigation is of particular importance as it likely
represents one of the largest remaining Caribbean populations
of the coral Acropora cervicornis, a species that is presently
listed as a candidate for the Endangered Species Act (Bruckner,
2002).
bathymetric data. For this reason several recent studies neglect
automated image classification in favour of expert visual
interpretation of satellite data and/or aerial photography
combined with semi-automated spectral or morphological
operators (e.g., Andréfouët & Guzman, 2005; Dı́az et al.,
2000; Franklin et al., 2003). While it is now clear that visual
interpretation can return accuracies comparable to, and in some
cases exceeding, those levied by probability driven classifiers,
there undoubtedly remains a niche for automated classification
in areas which are too extensive and therefore prohibitively
time consuming to manually digitise.
Autocorrelation denotes a method to study similarity/
dissimilarity of pixel values, a property that has the potential
to be substrate specific, providing that seabed patterning can be
used as a proxy for benthic cover. Positive autocorrelation
implies that proximate observations take on similar values,
while negative values indicate high variance over small spatial
scales. The use of wavelet transform algorithms in the
characterization of texture features in remotely sensed images
of terrestrial landscapes has been proven effective (Myint,
2003; Myint et al., 2004; Wang et al., 2004). Similarly, in the
shallow marine environment the use of texture-based algorithms for facies discrimination has been deemed to be of value
in coral habitats (Holden et al., 2001) and applied successfully
in the context of the detection of temporal change in reef
homogeneity (Dustan et al., 2001; LeDrew et al., 2004). This
experiment builds on the premise that important substrate types
may be spectrally similar but retain distinct autocorrelation
properties by virtue of a systematic variance in albedo at a
discrete spatial scale (e.g., Atkinson & Lewis, 2000; Holden et
al., 2001). In this respect, spatial autocorrelation is a possible
candidate for the separation of important substrate types when
more traditional optical-based techniques have failed. This
paper investigates whether the problem of optical inseparability
can be circumnavigated using the textural component of an
imaged landscape as a signal with which to discriminate
between branching and massive coral assemblages. The area
2. Methods
2.1. Study area
The island of Roatán (Fig. 1) is situated ¨55 km off the
south coast of mainland Honduras and has been the focus of
numerous studies of coral status (Deepak et al., 2005; Fonseca,
1997; Keck, 2000, 2004; Keck et al., 2005; Maeder et al.,
2002). Roatán is the largest of the Bay Islands with an area of
12,740 ha, and is surrounded by an extensive fringing reef
system. Like many of the Caribbean islands, Roatán is
undergoing rapid development to accommodate a surge in
tourism, with reef-based nature-tourism comprising the dominant market-share (e.g., Luttinger, 1997). In concert with the
rise in visitor numbers has been an increased exploitation of the
reef systems, combined with concurrent degradation of the
resource. Development has been particularly rapid on the north
coast of the island where the relative proximity of the shore to
deep water is attractive for recreational dive operators. The
Smith and Cordelia banks are part of a single bank-reef system
that rises out of deep water (> 150 m) ¨2 km off the end of the
airport’s landing strip, situated on the south-western tip of
Roatán. Lying on the windward side of the island, high winds,
rough seas, and strong currents render the reef-system
inaccessible for much of the year and therefore anthropogenic
impact is limited to a few local fishermen and dive operators.
Initially described by Keck et al. (2005) it is clear that both
Smith and Cordelia banks are unique in the fact that they are
characterised by dense and well developed thickets of the
branching coral A. cervicornis, unrivalled in size as compared
to that presently observed in the wider Caribbean region. Prior
Roatán
Guanaja
0
4
17.5oN
Utila
Hog Is.
Mexico
Belize
Bay Islands
Gibson
Bight
Anthony's
Key
Roatán airport
Guatemala
12.5oN
Honduras
El Salvador
West
Bay
Smith
Ban
Nicaragua
STUDY
0 1 2 3 4 5
km
N
W
Cordelia
Shoal
AREA
E
S
Costa Rica
92.5oW
82.5oW
Fig. 1. Map of Central America detailing the location of the Smith and Cordelia coral banks in relation to the island of Roatán, Honduras, in the south-western
Caribbean Sea.
84
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
to the mid 1970s, the branching corals Acropora palmata and
A. cervicornis accounted for more than 30– 50% of the total
coral cover to a depth of 20 m in the Caribbean (Aronson et al.,
2002; Gardner et al., 2003; Goreau, 1959). By the early 1980s
the coral zonation pattern dominated by these coral species had
essentially disappeared on many, if not most, of the Caribbean’s reefs (Aronson & Precht, 2001; Bythell & Sheppard,
1993; Bruckner, 2002; Jackson, 1992), with the decline
attributed to a combination of white-band disease, temperature
stress, predation and hurricanes. Given the catastrophic
Caribbean-wide decline of A. cervicornis, the occurrence of
large and dense, mono-specific thickets of the species on the
Smith and Cordelia banks is relevant to the coral’s continued
persistence. It is plausible that this area represents one of the
largest remaining populations of A. cervicornis in the
Caribbean and thus maybe a critical spawning source of
propagules which could allow this species to repopulate reef
communities in the region.
Fieldwork was conducted over Smith and Cordelia banks
15 –25th October 2004 for the purpose of ground verification.
A total of 200 spot-checks were dived from a boat at semiregular intervals across the study area, without a priori
knowledge of substrate distribution. The position of each
check was constrained using a differentially corrected global
positioning system (dGPS) and substrate coverage was
recorded to the lowest possible taxonomic level at each site.
Substrate character of the seabed was estimated for each point
using a digital photograph of a 1 1 m quadrat, which was later
analysed using standard image processing routines to retrieve a
percentage estimate of benthic cover. The corals in the area
could be partitioned into two distinct assemblages (Fig. 2).
Hereafter termed the ‘‘dense acroporid assemblage’’, this
consisted of extensive dense interlocking thickets of live A.
cervicornis with occasional colonies of A. palmata and
Agaricia tenuifolia. Average coverage of A. cervicornis
exceeded 80% of the available substrate. A second grouping
was characterised by patchy cover dominated by M. annularis,
A. tenuifolia and occasional Porites porites, interleaved with
sandy hardgrounds and hereafter is referred to as the ‘‘sparse
mixed assemblage’’. Average coverage of live corals in this
assemblage was less than 50%. In addition to the two coral
dominated assemblages, three broad non-coral classes were
defined to encompass the remaining benthic diversity:
i) A rubble assemblage consisting of a rampart of semiconsolidated to consolidated coral rubble bound by
calcifying algae and perceived to be a storm deposit.
ii) A groove assemblage corresponding to grooves of
several metres in relief characterised by extensive
deposits of carbonate sand and semi-consolidated coral
rubble. Isolated and occasional sparse M. annularis and
Siderastrea siderea colonies. Live coral cover <1%.
iii) A hardground assemblage representing a class of very
sparse coral cover particularly dominant in deeper areas
and frequently associated with sloping sandy hardgrounds. Cover dominated by M. annularis carpets with
live coral cover < 5%.
2.2. Image processing
The IKONOS image used in the study was acquired 29th
December 2003 under favourable conditions with low water
turbidity and cloud cover. The data were purchased with full
11-bit radiometric resolution and were acquired with solar
azimuth and elevation angles of 153- and 45-, respectively.
The image was radiometrically calibrated using the coefficients of Peterson (2001) to retrieve at-sensor radiance. The
imagery was further corrected for atmospheric effects using
the Fast Line-of-Site Atmospheric Analysis of Spectral
Hypercubes (FLAASH) software package in ENVI (by
Research Systems Inc.). FLAASH incorporates MODTRAN4
radiative transfer code and in addition to atmospheric
absorption and scattering, models and corrects for adjacency
effects. FLASH output is scaled irradiance reflectance that
scales to irradiance reflectance in the case of Lambertian
surfaces. The image was moderately compromised by surface
effects in shallow areas where wave action accentuated sunglint to a degree where the seabed was partially obscured.
Prior to further processing, the glint-removal algorithm of
Hochberg et al. (2003b) was employed to correct for the waveinduced specular reflection, which successfully delivered a
largely glint-free image (cf. inset Fig. 2). Areas of deep water
(circa. > 15 m) were masked using a spectral threshold and
were not processed further. Prior to textural analysis, the pixels
identified during ground-truthing to belong to each of the five
defined community-types were extracted and analysed for
spectral separability in the first three bands of the IKONOS
data (Fig. 3). The ground-truth data were subsequently
partitioned into two groups, the first was used for the purpose
of classifier training and the second, for accuracy assessment
of classification products.
2.3. Detection of spatial autocorrelation
A conventional univariate measure of spatial autocorrelation
is Moran’s (1950) I statistic which ranges between 1.0 and
+1.0 depending on the degree and direction of correlation
within the sample. Band 1 of the IKONOS data, centred at 480
nm is optimised for retrieval of benthic character because its
short wavelength affords a high degree of water column
penetration. For this reason, band 1 was targeted for textural
analysis using Moran’s I spatial autocorrelation index. Moran’s
I was calculated according to Myint et al. (2004) using the
formula:
XX
I ðd Þ ¼
i
S2
Cij Wij
j
XX
Wij
i
j
where Wij is the weight at distance d so that Wij = 1 if point j is
within distance d from point i; otherwise, Wij = 0; C ij are
deviations from the mean (i.e., C ij = (Z i Z̄) (Z j Z̄), where Z̄
is the mean brightness value in the local window. S 2 is the
mean of the major diagonal of C ij . Moran’s I varies from + 1.0
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
85
Fig. 2. True-colour IKONOS image of the Smith and Cordelia bank-reef system corrected for radiometric and atmospheric effects. Inset shows the image prior to
correction for surface effects (Hochberg et al., 2003b). Red dots indicate the position of ground-verification points and an overview of the spatial distribution of the
ecologically important (though optically inseparable) ‘‘dense acroporid’’ and ‘‘sparse mixed’’ coral assemblages is provided. For clarity not all observations are
graphed. The relative size of the 11 moving-window sizes with edge lengths spanning from 20 to 100 m within which the Moran’s I spatial autocorrelation index was
calculated is shown for comparison.
for perfect positive correlation (a clumped pattern) to 1.0 for
perfect negative correlation such as would be returned for a
checkerboard pattern, while values close to zero indicate no
autocorrelation (as would be returned by a random pattern of
pixel brightness) (Legendre & Legendre, 1998). A worked
example showing the step by step calculation of I for a 2 2
pixel kernel is given in Fig. 4.
A local window of variable size was moved throughout the
whole image and used to calculate Moran’s I index according
to Myint et al. (2004). By iteratively increasing the dimension
of the window, autocorrelation was assessed over a range of
spatial scales. The index was calculated for window sizes of
5 5 through 25 25 pixels, which equates to windows of
length 20 m through 100 m, with an increment of 8 m (i.e. 11
iterations in total). It should be noted that the window edgelength was always an odd number of pixels since the computed
autocorrelation value is assigned to the centre pixel of the local
moving window (e.g. Fig. 5). However, if the local window
size is w w and the autocorrelation value is assigned to the
centre of the local window (i.e. at [(w + 1) / 2]th pixel position)
and the window is moved throughout the image, we will lose
(w 1) / 2 pixels on the top, bottom, left, and right side of the
image. To combat this artefact we used mirror extension of
(w 1) / 2 pixels around the image prior to initiating the
86
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
Group mean ± 95% CI
IKONOS 2 (%)
4.5
sparse
mixed
corals
4.0
3.5
dense
acroporid corals
3.0
5.0
5.5
6.0
Local window
(e.g., w = 25)
moves throughout
the image
(first position)
rubble
groove assemblage
Mirror extension (w-1)/2
hardground assemblage
6.5 7.0 7.5
IKONOS 1 (%)
8.0
Moran's I assigned
at the centre pixel
[(w+1)/2]th position
8.5
9.0
Fig. 3. Bi-spectral plots between IKONOS bands 1 (blue) and 2 (green) for five
reef assemblages identified during ground-verification. Axes are remotesensing reflectance and the error bars represent the 95% confidence interval
(CI) around the mean in each band. The dense acroporid and sparse mixed
assemblages targeted by the study are clearly inseparable at the 95% CI.
Original
image
width
Mirror extension (w-1)/2
computation. The algorithm was designed to automatically
extend the boundary of the image with (w 1) / 2 pixels if the
selected window size is w. Hence, the size of the extended
image was (original image size + (window size 1)). Mirror
extension is to copy the second-last row or column and add
next-to-last row and column, respectively. Then, copy the thirdlast row and column and add the next to the second-last row
and column, respectively, and so on depending on the number
of rows and columns required for extension (Myint, in press). It
should be noted that this extension is executed only during the
computation process and the output image has the same
number of rows and columns as the original image. An
example illustrating the original image, extended image, local
moving window, and assignment of Moran’s I value in the
local window is presented in Fig. 5.
If significant positive autocorrelation exists, pixels with
similar optical characteristics can be inferred to be present
within the window. Conversely, if spatial autocorrelation is
weak or non-existent, adjacent pixels within the window have
dissimilar spectral values. Multiple window sizes were tested in
order to ascertain the optimum distance over which I should be
calculated in order to best capture the textural component of the
target benthic classes. With a handle on the optimum and
therefore most ecologically relevant window size for each
substrate type, the spatial patterning within the image could be
investigated to determine whether texture is indeed substrate
specific.
The discriminate ability of the raw textural transform
imagery was tested through classification using a supervised
Mahalanobis classifier trained using regions of interest of
known benthic cover extracted from the ground-truth data.
Σ ΣCijWij
I=
Z1
Z3
s 2 Σ ΣWij
i j
Z2
Z4
12
56
Z1
165
2
Local window
(last position)
Extended image
Fig. 5. An example showing image extension, moving window, and Moran’s I
index assignment procedure.
Classifications were completed for each window size over
Cordelia and Smith banks and accuracy statistics were generated
against one hundred ground-verification points that had not been
used for classifier training. We subsequently used a combination
of two spectral and a single textural transform bands to generate
optical – textural layer composites (e.g. Wang et al., 2004). The
blue and green spectral bands were retained in all cases because
they offer the highest degree of penetration into the water
column. For all window sizes the textural bands were layered
with the blue and green bands and classified into 5 classes using
the Mahalanobis algorithm. Both the atmospherically corrected
visible bands and the textural data were normalised to values
spanning zero and one, so as to ensure that both data types were
assigned equal weighting in the classification. Following each
classification, the accuracy of the resulting thematic map was
assessed against the ground-verification data. For comparison
between classifications we used the producer’s accuracy which
as a measure of omission error, indicates how well training set
pixels of a cover type are classified. Next, considering that the
Cij=(Zi - Z)(Zj - Z)
Wij(adjacency)
i j
Original image length
Z1
Z2
Z3
Z4
0
1
1
0
Z1 2186 -4967 129 2653
s2 = Σ (Zi - Z)2/n
Z2 -496711289 -292 -6030
s2 =2186+11289+8+3221/4=4176
Z3 129 -292
Σ ΣCijWij = (0
Z2
1
0
0
1
Z3
1
0
0
1
Z1
Σ ΣWij = 8
i j
Z2
Z3
8
Z4
156
i
2186)+(1 -4967)+(1 129)+.....= -21425
i j
Z = (12+165+56+2)/4=59
Z4
0
1
1
0
Z4 2653 -6030 156 3221
I = -0.64
Fig. 4. A worked example for the calculation of Moran’s I autocorrelation statistic for a 2 2 pixel kernel.
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
raw image was compromised by surface effects (wave induced
glint) the degree to which Moran’s I was sensitive to these
artefacts was assessed. The comparison is important because
imagery of remote reef areas is often scarce and therefore suboptimal data is more commonly utilised as compared to
terrestrial studies. Lastly, a test was implemented to ascertain
whether the textural data showed evidence of stability in areas of
variable depth. If this was the case, textural analysis would hold
a distinct advantage over traditional optical classifiers which are
impeded when depth effects are not corrected for (e.g. Purkis &
Pasterkamp, 2004).
3. Results
Through analysis of the spectral signature of the groundtruthed pixels, the dense acroporid and sparse mixed assemblages were shown to overlap significantly (Fig. 3) resulting in a
consistently low-level of classification accuracy (Fig. 8c—
producer’s accuracy <60% in both cases). The objective of
autocorrelation characterisation is to identify spatial structure
that is unique to a particular facies type. Ideally differences in
spatial structure would allow separation of patches that are
indistinguishable in conventional spectral space. In this case,
the ecologically important dense acroporid and M. annularis
dominated sparse classes are spectrally inseparable and proof
that they could be identified texturally would be relevant to
future detection of A. cervicornis using IKONOS. The
separability of the two target substrate assemblages on the
basis of the Moran’s I autocorrelation index (Fig. 6) varies with
dense acroporid assemblage
sparse mixed assemblage
20 m
Group mean ± 95% CI
52 m
separable
window size (m)
36 m
68 m
84 m
100 m
-1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0
Moran's I autocorrelation
Fig. 6. Window size ( y-axis) versus Moran’s I index (x-axis) showing the
statistical separability of the dense acroporid (black dots) and sparse mixed
(white dots) coral assemblages on the basis of autocorrelation. The error bars
represent the 95% confidence interval around the mean and gray bars clarify
whether the CI’s of the two assemblages overlap. The broken vertical line
represents a Moran’s I value of zero and positive values indicate degrees of
positive autocorrelation and negative values, degrees of negative autocorrelation. For window sizes of 36, 52 and 68 m the two assemblages are statistically
distinct.
87
window size. At a window size of 20 m, both the dense
acroporid and mixed corals assemblages return strong negative
values of I and are inseparable at the 95% confidence interval.
With a window size of 36 m, the acroporid assemblage is
characterised by negative values but the sparse mixed coral
assemblage displays a pronounced departure to positive
autocorrelation with the result that the two classes are distinct
and statistically separable. The assemblages remain distinct
until a window size of 68 m, beyond which both the acroporid
and mixed sparse coral classes return values of I close to zero
(broken vertical line Fig. 6), indicating spatial randomness in
the patterning of pixel values. As the values of autocorrelation
converge towards zero for the larger window sizes, the
assemblages become inseparable at the 95% confidence
interval. Contour plots of the spatial distribution of Moran’s I
(Fig. 7) further reveal differences in the performance of the
index with varying window size. As identified in Fig. 6,
increasing window size returns a shift from negative to positive
values of Moran’s I. At 20 m extent, the majority of the bank is
characterised by values of negative autocorrelation interspersed
with discrete zones of local-strong positive autocorrelation. A
predominance of negative values persists for window sizes up to
52 m at which point the index is ubiquitously positive and still
punctuated with limited areas of high correlation (Moran’s
I å 1). At the smaller window sizes, the negative departure of
the index is to be expected as pixel heterogeneity at scales of 3
to 5 pixels (12 – 20 m) is clearly evident in the true-colour image
of the area (Fig. 2). At larger spatial scales, pixel variation is
clearly more homogeneous and correspondingly values of
positive autocorrelation are returned for larger window sizes.
Regardless of window size the zones characterised by high
autocorrelation values are located in areas occupied by sand
fields infilling the larger groove systems on the deeper portion
of the bank (cf. Fig. 2). Conversely, negative values are
preferentially situated in areas of high rugosity which during
ground-truth were shown to be characterised by live coral cover.
The findings show that irrespective of window size, sand-filled
groove structures are distinct from optically more complex areas
in terms of their textural component, but this is also the case for
a standard classification of a true-colour image (Fig. 3).
The results from the supervised classification of single band
Moran’s I data (Fig. 8a) reveal that window sizes spanning 28–
60 m return highest accuracy in the discrimination of the
acroporid and mixed coral classes. The outcome therefore
supports the statistical analysis (Fig. 6) which correspondingly
showed that at the 95% confidence interval these two classes
were only separable between the same window sizes. Highest
accuracy is attained using a window size of 36 m, where coral
dominated areas visited during ground-verification were
correctly identified with accuracies of 90% and 72% for A.
cervicornis and M. annularis, respectively. For window sizes
exceeding 60 m, the producer’s accuracy falls to levels of
approximately 60% for the two classes.
The three non-coral classes (Fig. 8b) similarly show a
varying level of prediction accuracy with increasing window
size. Reacting in a similar manner, the groove and rubble
assemblages show maximum accuracy (> 70%) for window
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S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
-ve autocorrelation
+ve autocorrelation
0.2
0.4
0.6
0.8 1.0
52 m
window size (m)
-1.0 -0.8 -0.6 -0.4 -0.2 0
20 m
36 m
68 m
84 m
100
92
84
76
68
60
52
44
36
28
20
100 m
Fig. 7. Contour plots of the spatial distribution of Moran’s I over the Cordelia shoal calculated using a window size from 20 to 100 m (only 6 plots are presented and
Smith Bank is excluded for brevity). Differing window sizes return zones of discrete local positive and negative autocorrelation. Increasing window size results in a
shift towards higher Moran’s I values and therefore positive autocorrelation. Areas of depth >15 m have been masked and excluded from analysis.
sizes of 20– 60 m, followed by an incremental decrease in
accuracy for window sizes up to 100 m. The pattern is similar to
that of the two coral assemblages and is to be expected
considering that the groove systems are associated with coral
dominated spurs and therefore react on a comparable spatial
scale. In contrast, the hardground assemblage is predicted poorly
(accuracy <55%) using a window of size 20 – 44 m, yet accuracy
increases rapidly for window sizes > 44 m, attaining accuracies
> 70% for all window sizes up until 100 m. The finding is
consistent with the assumption that the hardground assemblage
is consistently found in deeper waters than the spatially limited
spur and groove system and is typically expansive, operating
over scales of hundreds as opposed to tens of metres.
A hybrid classification was tested by combining the
Moran’s I textural image with the blue and green spectral
bands to form a layered texture – optical composite (Fig. 8c) for
the detection of the two target coral classes. The composite
imagery was normalised between zero and unity and again
classified using the Mahalanobis algorithm. The accuracy
returned from the composite data was less variable than when
only Moran’s I was considered, such that the producer’s
accuracy exceeded 50% in all cases apart from the very largest
window sizes. As with the single-band classifications the
highest accuracy was found for window sizes 28 – 60 m but the
prediction of M. annularis dominated areas was marginally
higher when the spectral data were included in the composite.
For the majority of window sizes the composite classifications
perform better than when only three spectral bands are
considered (horizontal grey lines, Fig. 8c), indicating that the
textural data is a positive addition to the classification process.
For all window sizes exceeding 84 m, this is not the case for
the mixed M. annularis class where the composites return
lower producer’s accuracies than the spectral classification. For
identification of A. cervicornis thickets, prediction remains
slightly higher than that offered spectrally, but becomes suboptimal when the window size reaches 100 m. The results
suggest that the larger window sizes introduce noise that is
detrimental to the identification of the target coral classes.
For classifications conducted using 3 spectral bands and 3
band spectral-textural composites, derived from imagery that
had not been corrected for surface-effects (Fig. 2, inset),
accuracy was sub-optimal for all window sizes and therefore is
not presented. For aquatic remote sensing, examples of scene
specific noise characteristics include atmospheric variability,
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
a
100
5
7
9
window size (pixels)
11 13 15 17 19
b
21
23
25
100
70
60
50
40
Moran's I
30
20
separable 95% CI
sparse mixed
assemblage
10
9
window size (pixels)
11 13 15 17 19
28
36
7
9
c
5
44
52 60 68 76
window size (m)
window size (pixels)
11 13 15 17 19
84
92 100
21
23
21
23
25
hardground assemblage
80
70
groove
assemblage
60
50
40
Moran's I
30
rubble
assemblage
20
10
0
20
100
7
90
dense acroporid
assemblage
80
producer's accuracy (%)
producer's accuracy (%)
90
5
89
0
20
28
36
44
52 60 68 76
window size (m)
84
92 100
25
producer's accuracy (%)
90
dense acroporid
assemblage
80
70
acroporid spectral
60
sparse mixed spectral
50
Moran's I
green
blue
40
30
20
separable 95% CI
sparse mixed
assemblage
10
0
20
28
36
44
52 60 68 76
window size (m)
84
92 100
Fig. 8. Window size (x-axis) versus prediction accuracy ( y-axis) of the spatial extent five benthic classes using a supervised classification. (a) is the result of a singleband supervised classifier operated upon the Moran’s I autocorrelation output by window size for the dense acroporid and sparse mixed coral assemblages. Similarly,
(b) is the classification accuracy for the remaining three non-coral classes. (c) Is the result of a multiband classification where the Moran’s I autocorrelation output
has been stacked to form a 3-band composite in unison with the green and blue IKONOS spectral bands. The horizontal gray lines are the classification accuracy for
each assemblage when the classifier is driven solely using the spectral bands of the IKONOS without Moran’s I textural information. In both cases, the textural
classification outperforms the optical classification for window sizes >30 m and <90 m. The vertical broken lines indicate the intervals between which the two coral
assemblages are separable at the 95% CI (Fig. 6).
effects from the air –water interface such as swell, wave and
wavelet-induced reflections, and refractions of diffuse and
direct sunlight (Brando & Dekker, 2003; Wettle et al., 2004). In
this study, sun-glint arising from specular reflection off faceted
wave fields strongly skewed the Moran’s I index, masking
substrate-specific patterns and forcing a global-shift to negative
autocorrelation values (by virtue of increased heterogeneity of
pixel values). For this reason, robust correction of surface
effects would seem a critical precursor to textural analysis. As
confirmed by this study and that of LeDrew et al. (2004), this is
unlikely to limit the usefulness of the technique because the
algorithm offered by Hochberg et al. (2003b) was shown in
both cases to be capable of retrieving an image that in its raw
state seemed largely compromised by surface effects.
4. Discussion
Investigation into separability (Fig. 6) and classification
accuracy (Fig. 8) clarifies that window size influences the
degree to which the textural operator can be used to
discriminate between areas occupied by dense acroporid coral
forms and the more sparse mixed assemblage. The result is
logical under the assumption that autocorrelation should
remain constant once sufficient pixels are included within the
window to summarise the textural component of the facies in
question. When the window size reaches a point where it is
large enough to straddle a class boundary, a mixed signal will
be returned and discrimination ability will rapidly decrease. For
this reason and as indicated by the prediction accuracy of the
non-reefal classes (Fig. 8b), the optimum window size for
separation is likely to be substrate specific because different
benthic classes are typically characterised by unique patchsizes and geometry. This was clearly demonstrated to be the
case in the Arabian Gulf (Purkis et al., 2005), where different
benthic cover types were shown to display different patch-size
distributions as well as unique patch-boundary patterning. It is
also clear that since window size is critical to class separation,
then the appropriate size for the target substrate must be known
90
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
a priori if textural analysis is to be of value. This is a
conceivable limitation to the technique and requires further
investigation into whether spatial patterning is site-specific by
class, else if global rules can be derived (i.e. valid for several
reef or facies types). The step is beyond the scope of this paper
but should be addressed in the future.
In light of the fact that the optimum size of the moving
window was derived to lie between 28 and 60 m for the
identification of A. cervicornis and M. annularis, subsequent
classification could be tuned to operate on data created using
these window sizes. The synergy of spectral and textural
bands into a composite dataset did not serve to elevate the
accuracy with which the facies could be identified. The
addition of spectral data is therefore superfluous, especially if
the optimum kernel size for the target benthos has already
been determined analytically else through field measurement
of substrate patterning. Indeed, prediction of A. cervicornis
with accuracies greater than 80% (as returned from singleband textural data) is sufficient for ecological analysis (e.g.
Purkis & Riegl, 2005) and surpasses the capability reported
for spectral-based classifiers used on IKONOS in comparable
reef settings (Andréfouët et al., 2003; Maeder et al., 2002;
Purkis, 2005).
With knowledge that Moran’s I is a useful statistic with
which to identify branching versus massive coral assemblages,
it is worthwhile postulating which mechanisms facilitate the
separation. To detect the different spatial expression of the two
coral assemblages at colony level would require a pixel of finer
resolution that the 4 metres offered by IKONOS, let alone the
smallest textural window employed in this analysis (20 m).
Indeed, it is clear from the literature that coral growth forms are
only separable at pixel sizes of centimetre to metre scale (i.e. at
a spatial scale commensurate with the size of individual coral
colonies) as offered by modern airborne platforms (e.g.
Mumby et al., 2004). Clearly it is the textural expression of
multiple colonies (i.e. the assemblage) that the Moran’s I index
encodes and is significantly different ( p = 0.05) between the
areas dominated by branching (dense acroporid assemblage)
and massive (sparse mixed) corals.
At assemblage-scale (i.e. tens of metres), spatial patterning
is dependent on the growth form of the target coral since
different structures order and space themselves with respect to
their life cycle. A. cervicornis is possibly the fastest growing of
all corals (linear growth rates can exceed 100 mm/year, Lewis
et al., 1968; Shinn, 1976) and the species is able to rapidly
monopolise available substrate to form a climax-community
consisting of a dense inter-locking branching framework (e.g.
Purkis & Riegl, 2005). Conversely, massive coral species such
as M. annularis exhibit linear growth rates of only ¨6– 10 mm/
year (e.g. Dodge et al., 1974). By virtue of its slow growth, M.
annularis corals tend to form more isolated colonies interspersed with areas of bare substrate. This facilitates the
settlement and growth of slower growing species, such as P.
porites in the case of the sparse mixed coral assemblage. At
scales of metres to hundreds of metres, the intrinsic spatial
patterning of the assemblage dominated by A. cervicornis and
that dominated by M. annularis is likely to be different.
In the case of the Smith and Cordelia bank system, the
sparse mixed assemblage contains coral colonies (mostly M.
annularis) interspersed with sandy low-relief hardgrounds.
Being heterogeneous, this assemblage should return lower
autocorrelation values than the dense interlocking growth form
of the acroporid assemblage. However, this is clearly not the
case (Fig. 6) as the acroporid assemblage is distinct in returning
negative values of Moran’s I, indicating a departure from
spatial randomness towards organised heterogeneity. Although
this result may be counterintuitive, the patterning of the dense
acroporid assemblage at scales of tens of metres is punctuated
by discrete areas of collapsed A. cervicornis framework, likely
caused by storm events. Such breaks in the otherwise
homogeneous live interlocking framework is a plausible
mechanism for the departure to negative autocorrelation and
may explain why the assemblage differs texturally from the
sparse mixed coral assemblage. In the latter case, heterogeneity
arises by virtue of sand sheets interleaving between individual
coral colonies which promotes ordered heterogeneity at metrescale, as opposed to tens of metres in the case of the acroporid
framework. It should be noted that dense-interlocking acroprid
frameworks can persist for many years after the corals have
died because the structure is sufficiently robust to retain the
carbonate skeleton in life-position (e.g. Purkis & Riegl, 2005).
Moran’s I is likely to also be able to detect the spatial
patterning associated with dead skeletons, but unlikely to be
capable of separating live from dead without additional spectral
information.
The strategy of classification adopted in this study is a
Fsensor-down_ approach, whereby autocorrelation and classification statistics are derived entirely from the image. Consequently, the results are inherently tied to the scene analysed and
not relevant to imagery acquired at a later date and/or with a
different sensor, even if environmental conditions are comparable. As with spectral data, I values could be incorporated into
a Freef-up_ strategy (e.g. Purkis, 2005) and a spatial library tied
to community types (i.e. analogous to a spectral library) could
be populated. Using this library a classifier could be driven by
the generic spatial properties of the benthos as opposed to the
scene-specific variables used in this study. Such an approach is
beyond the scope of this paper, but worthy of consideration for
future work.
As outlined at the beginning of this essay, depth related
filtering of electromagnetic energy serves to decrease the
intensity of water leaving radiation to a level that can preclude
the discrimination of optically similar substrates from orbit
(e.g. Lubin et al., 2001). Attenuation also reduces the dynamic
range of pixel values at depth as compared to shallow water
areas, precluding the comparison of absolute autocorrelation
values between depth zones. Correction for depth effects is best
achieved with knowledge of bathymetry over the entire area of
study (e.g., Deepak et al., 2005; Purkis, 2005), else using
hyperspectral data sets (e.g., Mumby et al., 2004). The strength
of a texture-based classification lies in the fact that it detects
spatial patterning as a function of spectral variation within a
particular facies class, as opposed to spectral consistency which
drives standard probability-driven classifiers. It is a lack of
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
spectral consistency that inhibits accurate identification of
constant substrate type over depth gradients. Without correction for depth effects, a substrate patch colonising sloping or
complex topography is therefore split into multiple, spectrally
different classes, which do not mirror the actual distribution of
the ecotype.
For this study we lacked an independent constraint on
bathymetry. The analysis showed that the ability of the
Moran’s I index to discriminate between the target assemblages
was not compromised by a lack of depth correction (there was
no correlation evident between the depth of the groundverification sites and their accuracy of prediction). Moran’s I
therefore appears to hold promise as a largely depth-invariant
index of spatial coverage. The study therefore supports
LeDrew et al. (2004) who correspondingly report that textural
algorithms are relatively uncoupled from depth changes. The
mechanism with which this is achieved is likely to be related to
the fact that while submergence serves to inflict a relative
reduction of seabed albedo, the absolute pattern of inter-pixel
variation particular to a given class is preserved. However, with
seafloor depth and water column optical properties relatively
consistent across the scene presented in this study, it is not
possible to be definitive as to the depth dependence of the
index.
To ascertain the true depth dependence of I to depth
variation, a test was carried out on a 500 500 m section of
imagery which contained significant variation in water depth
associated with spurs and grooves, had extensive areal
coverage of the five defined benthic cover types and contained
a high concentration of both ground-verification data and depth
soundings (Fig. 2 subset). Without an independent constraint
on bathymetry, analysis of the imagery had to this point been
conducted without correction for radiative transfer effects.
However, this is obviously not the case for all potential studies
and thus it is implicit to examine the sensitivity of the index to
radiative transfer effects if the results are to hold meaning in a
more global context.
As an initial test, the overall accuracy of a standard optical
classification was compared to that returned by a Moran’s I
textural transform using a window size of 36 m (deemed most
appropriate for detection of the majority of classes). The
imagery had been corrected for glint and atmospheric
influence, but radiative transfer effects were not tackled,
therefore pixel values were at the level of remote sensing
reflectance just above the water/air boundary (R rs(z =a )).
Secondly, and following the empirical procedure of Stumpf
et al. (2003), a bathymetric digital elevation model (DEM) was
derived for the 500 m2 test area. The coefficients of the
derivation were tuned manually against 17 in situ soundings
and the output predication varied with an RMS error of 0.4 m
to known water depths. Using the empirically derived DEM as
input, a radiative transfer solution (Purkis 2005; Purkis &
Pasterkamp, 2004) was used to retrieve substrate reflectance
(R b) which is the reflectance of the seabed without the
influence of the water column. The resulting image (perceived
to be largely free of water column effects) was analysed using
both the optically and texturally driven classifier. Lastly, in
91
order to quantify the influence of variable bathymetry, water
column effects were implicitly Fforward_ modelled back into
the imagery by inverting the model of Purkis & Pasterkamp
(2004) ((1)), but using a synthetic DEM constructed by adding
the water depth model derived following Stumpf et al. to a
synthetic depth ramp varying from 0 to 6 m across the diameter
of the test image (Fig. 9). The result of this exercise was the
addition of the optical effect of an artificial depth gradient
across the study site, rendering pixel values in units of
modelled remote sensing reflectance just above the water/air
boundary (R rs(modelled)).
RrsðmodelledÞ ¼ 0:54 Rb e2kz þ 1 e2kz Rw :
ð1Þ
As for the inverse model, the attenuation coefficient (k) of
the water body was set to that of Jerlov water type 1 and the
reflectance of optically deep water (R w) was set to values
experimentally determined in a comparable setting (Purkis,
2005). Water depth is denoted by z and a factor of 0.54 (Morel
& Prieur, 1977) was applied to compensate for refraction at the
water/air boundary. As before, the resulting image was
analysed using both the optically and texturally driven
classifier.
For the initial test case where the imagery was processed
solely for glint and atmospheric effects (R rs(z =a)) (Fig. 9), the
optical and textural classification both yield similar overall
accuracies of 58% and 61% for optical and textural,
respectively. Upon processing for depth effects and the
retrieval of substrate reflectance (R b), the accuracy of the
optical classification increases markedly (79%) while the
textural classifier only increases by 1% to an overall accuracy
of 62% for the five benthic classes. Working on spectral
consistency within the 5 classes, the optical classification
benefits from the correction of depth effects and therefore
returns a higher accuracy. In contrast, the textural character of
the seabed is largely unaltered by the correction for radiative
transfer effects since the increase in reflectance for the pixel
values is relative and therefore uncoupled from the output I
value. The difference in behaviour of the two approaches is
most stark when the imagery processed using the modelled
depth ramp is considered. Here, the optical classification
becomes unreliable (overall accuracy = 31%) while the texturally based classifier returns only a slightly lower accuracy
(52%) than observed in the previous two scenarios. The optical
classification is understandably compromised as the imposition
of the depth gradient greatly affects the spectral consistency of
pixels of a similar class across the image, therefore preventing
reliable assignment of pixels to classes during classification.
The modelled depth ramp similarly alters the textural
component of the imagery, yet the output autocorrelation
image still contains sufficient textural difference between the
five benthic classes to facilitate an acceptable classification.
Assuming a constant seabed albedo of 40% R b across the 500
m diameter of the image and by forward modelling a 6 m
depth gradient onto it (as for the third case of Fig. 9), the added
water column creates a 5% absolute variance in R rs(z=a) across
the 36 m diameter of the Moran’s I kernel used for the test.
92
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
Fig. 9. Upper frame is the overall classification accuracy for a 500 500 m subset of imagery used to test the sensitivity of the Moran’s I index to variable
bathymetry under three different levels of processing for radiative transfer effects (lower frames). Left bottom depicts analysis of imagery following correction of
radiometric and atmospheric effects only, rendering pixel vales in units of remote sensing reflectance just above the water/air boundary (R rs(z=a)) . Middle represents
imagery further corrected for water column effects and in units of substrate reflectance (R b). Right depicts left but with the addition of a modelled depth gradient
across the image subset. On the left of the frame, water depth is equivalent to actual +6 m, which decreases linearly to actual +0 m on the right. The purpose in
adding the gradient is to accentuate the effect of variable bathymetry across the scene. Pixel values are modelled remote sensing reflectance just above the water/air
boundary (R rs(modelled)). In all cases, image subsets are gray-scale representations of IKONOS band 1, draped over actual bathymetry as derived empirically and tuned
with field depth soundings. Vertical exaggeration is 15. The position of the subset in the greater study area is shown in Fig. 2.
The 5% variance in above surface reflectance caused by the
synthetic bathymetric variation is less than the within-class
textural variation caused by heterogeneity of seafloor albedo
and/or heterogeneous surface and water column effects.
However, if the kernel size is increased to 76 m, the variance
in above surface reflectance attributed to the depth gradient
exceeds 20% across the kernel (by virtue of the increased
disparity in water depth across the kernel) and introduces
variance of a magnitude great enough to disrupt any substrate
specific autocorrelation response. Therefore, providing that the
assigned Moran’s I kernel is significantly smaller than the
scale of bathymetric variation within the scene, the textural
operator is relatively uncoupled from depth changes and not
compromised to the same degree as standard optical classifiers.
However, the test also highlights the fact that if the kernel size
and the spatial scale of bathymetric change are of a similar
magnitude, the textural approach, as for the optical, is similarly
compromised by varying depth. This imposes an important
limitation to the use of texture as a tool for benthic
classification and user’s must be aware that although a textural
approach may outperform standard optical techniques in cases
where radiative transfer effects cannot be tackled, the scale of
bathymetric variation within the scene must be considered. An
added complication is that as proven earlier in the paper, the
optimum kernel size must relate to the intrinsic scale of
patterning of the target benthos, which may be incompatible
with the size of kernel required to minimise depth effects. In
saying this, the textural approach in certain situations would
seem to be a powerful tool if used in conjunction with
knowledge of the scale of variation of the components
influencing seabed albedo.
Spatial autocorrelation also has potential to classify benthic
character in non-spectral raster datasets such as marine
topographic LIDAR (Light Detection and Ranging), such as
demonstrated by Brock et al. (2001, 2004) who used seabed
rugosity as a habitat proxy. Fractal metrics have also been used
as a measure of spatial dependency in satellite data and used to
drive classification in terrestrial habitats (e.g., Emerson et al.,
1999; Jaggi et al., 1993; Myint, 2003). Purkis et al. (2005)
showed that coral facies in the Arabian Gulf displayed
substrate-specific fractal properties and postulated that this
could be explored for habitat differentiation. As such, this
manuscript is seen as a precursor to the exploration of a fractal
based classifier for coral dominated habitats. As for Moran’s I,
the fractal dimension can be assessed through a moving kernel
of varying size (e.g., Myint, 2003).
In summary, Moran’s I was shown to have the potential to
differentiate two ecologically important coral assemblages
within an IKONOS image that could not be separated using
a standard spectral-based classifier. Furthermore, sensitivity
analysis showed the textural algorithm to be relatively
uncoupled, and therefore insensitive to bathymetry, providing
that the scale of depth variation is dissimilar to that of the
heterogeneity of the targeted benthic classes. The finding
highlights the potential of textural operators for coral monitoring when applied at ecologically meaningful spatial scales. We
S.J. Purkis et al. / Remote Sensing of Environment 101 (2006) 82 – 94
postulate that different coral growth forms at sub-metre scale
promote assemblage-specific patterning properties that can be
detected at the scale of metres to decametres. A priori
knowledge of the intrinsic geometry of the target coral
assemblage and length scale of bathymetric variation is
valuable in tuning the textural algorithm with respect to the
selection of the optimum local-window size employed during
computation.
Acknowledgements
The authors are grateful for the expert guidance of J. Keck
during fieldwork and the hospitality offered by the management and staff of Anthony’s Key resort and Roatán Institute for
Marine Sciences. The help of V. Richards during groundverification is acknowledged. We would also like to thank E.J.
Hochberg for use of the Matlab toolbox de-glint v.1.1. and
for his excellent remarks during the review process. We are
further indebted to two anonymous reviewers for their
insightful comments. The autocorrelation algorithm development in this research was supported by a NASA EPSCoR grant
received through the Oklahoma Space Grant Consortium. This
is NCRI contribution 76.
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