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int. j. remote sensing, 1998 , vol. 19 , no. 1 , 65± 84
Fine-scale mapping of a grassland from digitized aerial photography:
an approach using image segmentation and discriminant analysis
A. LOBO*
Department of Ecology and Evolutionary Biology, Princeton University,
Princeton, New Jersey 08544-1003, U.S.A.
K. MOLONEY
353 Bessey Hall, Department of Botany, Iowa State University, Ames,
Iowa 50011-1020, U.S.A.
and N. CHIARIELLO
Department of Biological Sciences, Stanford University, Stanford,
California 94305, U.S.A.
( Received 2 July 1996; in ® nal form 10 June 1997 )
Conventional methods of classi® cation from remotely-sensed images
seldom discriminate accurately among the land cover categories that are relevant
in ecological applications. In the present study, we apply an image segmentation
technique to a high-spatial-resolution ( 13´5 cm), digitized, aerial, colour-infrared
photograph of an annual grassland and subsequently identify land cover categories
through ® eld inspection and linear canonical discriminant analysis of the image.
We show that per-segment statistics can be used to discriminate among four land
cover categoriesÐ bunch grasses, dense cover of annuals, sparse cover of annuals
and bare groundÐ while conventional per-pixel statistics produce low separabilities for the same categories. We also show that soil disturbances by pocket gophers
( T homomys bottae ) can be identi® ed and they are signi® cantly concentrated in
areas covered by bunch grasses at the time of image acquisition. We conclude
that image segmentation and linear canonical discriminant analysis of high spatial
resolution imagery provides an adequate tool for monitoring a grassland’s patch
dynamics at a scale and with a legend that are compatible with outputs of
spatially-explicit ecological models.
Abstract.
1.
Introduction
The spatial structure of ecosystems is a factor that strongly a€ ects ecosystem
dynamics ( Whittaker and Levin 1977, Borman and Likens 1979, Levin 1976, 1986,
1989, 1992, Wiens 1989) and biogeochemical cycling ( Pastor and Post 1988 ).
Landscapes, viewed as complex spatio-temporal mosaics, are the object of study of
the discipline landscape ecology, which emphasizes the relationships between pattern
and process ( Turner 1989, Turner and Gardner 1990).
The work we report here is part of a broader e€ ort to study the relationships
coupling pattern and process in an annual, serpentine grassland located at Jasper
Ridge, San Mateo County, California, USA ( Hobbs 1985, Hobbs and Hobbs 1987,
* Present address: Institut de Ciencias de la Tierra (CSIC), Lluõ s Sole Sabarõ s s/ n 08028,
Barcelona, Spain.
0143± 1161/98 $12.00
Ñ
1998 Taylor & Francis Ltd
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66
A. L obo et al.
Moloney et al . 1991, Hobbs and Mooney 1991, Moloney 1993, Wu and Levin 1994,
Moloney and Levin 1996). Remote sensing of grasslands has been conducted at a
regional (i.e., Tucker et al . 1985, Justice and Hiernaux 1986 ) and local scale, by both
remotely-sensed imagery ( i.e., Foran 1987, Curran and Williamson 1987, Williamson
and Eldridge 1993, Everitt et al . 1986, Friedl et al . 1994) and ® eld spectroradiometry
(i.e., Asrar et al . 1986, Huete and Jackson 1987, Gamon et al . 1993, Li et al . 1993,
Weiser et al . 1986). Ecologists have also been studying grasslands because of their
inherent spatial variability and patterning. This has generated a great deal of data
( Horn 1993 ) and has led to modeling to explore the ecological dynamics of grassland
systems (e.g., Pacala and Silander 1985 and 1990, Pacala 1986, Hobbs and Hobbs
1987, Co n and Lauenroth 1989, Moloney et al . 1991, 1992, Moloney and Levin
1996, Seligman and van Keulen 1989 and 1992 ).
The present study was designed to assess the quality of ecological information
that can be retrieved from an aerial image database. This database, containing a
series of high spatial resolution images obtained by low ¯ ying aircraft, has been
compiled for the Jasper Ridge grassland over a number of years. We are particularly
interested in developing a link between ground observations and spatially-explicit
modeling through the use of remotely-sensed imagery. The ® rst step in establishing
this link is to produce image-derived maps with ecologically meaningful legends and
high spatial accuracy. Once this is done we will use this information to help design
spatially-explicit simulation models of the Jasper Ridge grassland system that are
based on a detailed understanding of the spatial structure of that system. The imagederived maps will also provide us with a reference point for testing the validity of
model output. Our immediate objectives in this study were (i ) to characterize and
map the vegetation types that can be accurately retrieved from high-resolution
remotely-sensed images, and (ii ) to map the location of disturbances ( patches of bare
ground ) caused by gopher activity within the study area over a number of years, as
these disturbance are considered to be largely responsible for the ecological patterning
seen at Jasper Ridge ( Hobbs and Hobbs 1987, Hobbs and Mooney 1985, 1991,
Moloney et al . 1991, Moloney and Levin 1996).
Conventional methods based on the multi-variate classi® cation of per-pixel spectral properties (e.g., Mather 1987) are insu cient to resolve the terrain categories
that are often needed for ecological research. This is particularly true when they are
applied to high-resolution aerial imagery, due mainly to the variability of re¯ ectance
found within most natural cover types as they appear in the imagery. In this paper
we apply a technique for processing high-resolution imagery based on image segmentation and linear canonical discriminant analysis, and show that its results are
superior to those produced by conventional pixel-based processing.
2.
Study site
Our study site was located in the Jasper Ridge Biological Preserve of Stanford
University. Jasper Ridge is a low lying ridge (maximum elevation of 189 m) situated
in the foothills of the Santa Cruz Mountains on the San Francisco Peninsula of
California. The climate is Mediterranean with an average annual rainfall of 500 mm
and very little or no precipitation from May to September. The crest of the ridge is
bisected by serpentine soils, which are distinct from adjacent soils in being shallow,
nutrient-poor, and high in some heavy metals ( Walker 1954, McNaughton 1968,
Hobbs and Mooney 1991 ). The serpentine soils support a grassland that is dominated
by a diverse array of native annual forbs, but also includes perennial forbs, bunch
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Image segmentation and discriminant analysis for mapping a grassland
67
grasses, and annual grasses, most of which are also native, with plant densities that
2
can exceed 25 000 plants mÕ ( Huenneke et al . 1990). Similar grasslands occur on
serpentine soils throughout west-central California and are considered remnants of
native grassland that once also occurred on more fertile soils (Murphy and Ehrlich
1989 ). The activity of pocket gophers (T homomys bottae ) creates disturbances that
are considered to be a major factor in the spatial patterning and dynamics of the
grassland ( Hobbs and Hobbs 1987, Hobbs and Mooney 1985, 1991, Moloney
et al . 1991 ).
3.
M ethods
In developing a land cover map of the Jasper Ridge grassland, we chose to use
the ® nest scale available from the existing digital imagery as the basic unit of analysis.
This was done for two reasons: ® rst, spatially-explicit ecological models are generally
developed using a bottom-up approach, in which the output at one given scale is
predicted from the interaction of processes de® ned at a smaller scale, hence requiring
information at relatively ® ne scales. Second, we were interested in exploring the
limits of our ability to resolve information in complex scenes using our image
processing methods. Because of these considerations, the smallest unit (grain) of
analysis was the smallest unit of observation that we could resolve in digitizing the
high spatial resolution images available for the grassland. The total area studied
(extent ) was the largest area we could practically sample in the ® eld with the spatial
accuracy necessary for making comparisons between ® eld data and the vegetation
map constructed through image analysis.
Per-pixel processing often produces inadequate results for the analysis of spatial
pattern of ecological communities, particularly when working with high resolution
imagery. Image texture (that is, within-object pixel variability) is a fundamental
variable for discriminating di€ erent natural cover types. The variance of a given
object is not only a consequence of the random variation of the sensor’s response,
but is also an intrinsic characteristic of the object itself. Objects are not characterized
by a uniform re¯ ectance value, but rather by a distribution of values that typically
are spatially autocorrelated ( Ramstein and Ra € y 1989). The variation of tone or
repetition of visual patterns across a surface creates the impression of roughness or
smoothness ( Irons and Petersen 1981 ).
The importance of texture is even greater for images obtained by low ¯ ying
aircraft than for most satellite imagery as a consequence of the higher spatial
resolution. Although a number of texture measurements have been successfully used
(i.e., Haralick et al . 1973, Weszka et al . 1976, Irons and Petersen 1981, see Marceau
1989 for a review), an important di culty in the e€ ective use of texture is that texture
is not de® ned at the pixel level but is a characteristic of groups or clusters of pixels.
Identifying appropriate regions of pixels for quantifying texture is not a trivial
problem. Early attempts at quantifying texture within images were done by computing ® rst-order and second-order statistics from slicing rectangular windows (Haralick
et al . 1973, Weszka et al . 1976, Davis et al . 1979, Davis et al . 1981). In such an
approach new textural channels are generated with the results from the statistical
analyses. These channels are subsequently added as new data layers for the multivariate classi® cation of the image ( Hsu 1978, Irons and Petersen 1981, Marceau
et al . 1990 ). Unfortunately textural channels have the same drawback as any ® lter
based on moving windows: when the window is fully contained within an object or
landscape unit, the textural statistics retrieved from the window are relevant, but
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68
A. L obo et al.
when the window straddles the boundaries of two or more objects its statistics tend
to be poor at discrimination. This is analogous to the blurring e€ ect caused by a
moving mean ® lter. Because of this problem, our approach has been to divide the
image into segments or homogeneous regions which are subsequently identi® ed. In
other words, a `per-segment’ classi® cation of the image is used instead of the more
conventional `per-pixel’ classi® cation. Such a per-segment approach was suggested
in the early days of the application of statistical pattern recognition to the analysis
of remotely-sensed digital imagery ( Kettig and Landgrebe 1976, Landgrebe 1980)
but, compared to per-pixel procedures, has been used very rarely since, probably
because of its complexity ( Sali and Wolfson 1992, Woodcock and Harvard 1992,
Ryherd and Woodcock 1996). However, an analogous per-® eld approach has often
been employed in agricultural applications, where computerized databases sometimes
provide the boundaries of crop ® elds (Megier et al . 1984, Jansen and van Amsterdam
1991, Pedley and Curran 1991 and Jansen and Molenaar 1995). In this cases, the
per-® eld approach has exhibited better performance relative to the more commonly
used per-pixel approaches.
A number of approaches to image segmentation have been developed (i.e., Kettig
and Landgrebe 1976, Landgrebe 1980, Fu and Mui 1980, Haralick and Shapiro
1985, Cross et al . 1988, Benie and Thomson 1992). In the present study we have
employed a segmentation algorithmÐ the Iterative Mutually-Optimum Region
Merging ( IMORM) segmentation algorithm ( Lobo 1997 )Ð to de® ne regions in an
image of the Jasper Ridge grassland. Once the regions were identi® ed we then
classi® ed them using Linear Canonical Discriminant Analysis ( LCDA) .
Image and GIS processing and statistical analysis were performed with
GRASS 4´0 ( U.S. Army Corps of Engineers 1991 ) and S-PLUS (Statistical Sciences
1993 ), for which some speci® c functions in the S-PLUS language were written by
the ® rst author.
3.1. Image digitization and optimizatio n
We used aerial Colour Infrared (CIR) photographs, which were acquired each
Spring from 1988 to 1992, to develop the land cover map of the serpentine grassland
at Jasper Ridge. The 1991 photograph had to be removed from the study due to its
poor acquisition quality. Dates of the ¯ ights ( 29 March 1988, 10 April 1989, 9 April
1990 and 24 April 1992) were set to be coincident with the period of maximum green
biomass.
We digitized an area of 24 mm by 36 mm from each 240 mm by 240 mm colour
diapositive obtained from the CIR negatives. The digitizing process and subsequent
colour enhancement by linear stretching of the histogram rendered a trispectral
digital image coded in 24 bits. The digitized area was located in the NW region of
the grassland and included a 30 m by 30 m experimental plot that was being intensively studied on the ground. For the 1992 acquisition the plot was marked at the
corners and at several internal points by stakes that were covered with white discs
at the date of image acquisition. This allowed identi® cation of the plot both on the
ground and in the photographs.
The 1992 image was used as a basic reference. After de® ning an arbitrary system
of coordinates for the stakes, the image was georecti® ed by ® tting two ® rst-order
polynomials to pairs of coordinates on the ground and in the image. Once the image
was recti® ed, the resolution was 135 mm on the ground per pixel.
The 1988± 1990 images were coregistered to the 1992 image by identifying
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Image segmentation and discriminant analysis for mapping a grassland
69
corresponding points and applying a ® tted ® rst-order polynomial. The 1988± 1990
images were then colour corrected to the 1992 image by histogram matching. The
region intersected by all four recti® ed digital CIR images became the area of study,
covering a 41´85 m by 50´09 m region that included the aforementioned 30 m by 30 m
experimental plot.
3.2. Segmentation
The ® rst step that we applied in developing the land cover map of the Jasper
Ridge serpentine grassland was to segment the image into homogeneous ( but not
uniform) regions of pixels. There are two advantages to segmenting an image in this
way: ® rst, it drastically reduces the size of the data matrix in the classi® cation process
as segments are fewer than pixels. This makes it possible to save the data as a multivariate table and to apply a wider range of multi-variate techniques that are commonly available in software packages designed for the analysis of remotely-sensed
imagery. The second advantage is that a segmented image allows the use of imagederived local statistics for groups of pixels organized into segments and thus allows
a consideration of within-object grey-level variability.
The segmentation method that we used here, IMORM, was applied to the digital
images after an Edge Preserving Smoothing (EPS, Nagao and Matsuyama 1980).
The EPS algorithm is an iterative local mean ® lter in the direction of minimum
variance within a neighbourhood of a prede® ned radius. EPS yields a facet image.
Each facet is a small region within which, as a result of the EPS, all pixels have
converged to the same local mean. We ran EPS on the ® rst Principal Component
( PC-1) of the digitized CIR image. ( PC-1 accounted for 76´0 per cent of the total
variance of the image.) EPS was run with a radius of three pixels and stopped when
there was a change of less than 0´1 per cent between consecutive iterations. Facets
resulting from EPS were each labelled with a unique integer and a multi-variate
data matrix of per-facet variables was built by using this labelled facet image as a
template over the PC images. Each row of the per-facet multivariate data matrix
recorded the following variables for one facet: facet label, number of pixels in the
facet, and the mean and standard deviation of the facet in each PC image. This data
matrix, along with the labelled image resulting from EPS, was used as data input to
IMORM. IMORM computes a table of facet adjacencies from the labelled facet
image and iteratively fuses adjoining facets that are mutually most similar in terms
of a multi-variate distance under a user-de® ned threshold, for which the multi-variate
data matrix is used. The multi-variate data matrix (with the facet statistics) and the
adjacencies are updated at each iteration to include facet fusions. IMORM stops
when no more fusions are possible, either because there are no mutually optimum
adjacent pairs of facets or because their multi-variate distances exceed the threshold.
Facet statistics are computed with Principal Components ( PC) of the image for
IMORM because multivariate distances can then ignore the o € -diagonal elements
of covariance matrices, speeding up the computation. IMORM processing partitioned
the 1992 image into 2052 segments, which represented a 42-fold reduction in number
of image elements (® gure 1 ). Similar results were produced for the 1988± 1990 images.
Classi® cation of segments produced by IMORM has the additional advantage
of preserving edges between di€ erent categories since it iteratively merges facets that
were originally produced by EPS. This avoids the blurring that typically occurs with
techniques based on window slicing.
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A. L obo et al.
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Image segmentation and discriminant analysis for mapping a grassland
71
3.3. L inear Canonical Discriminant Analysis (L CDA)
Following the segmentation of the image, the next step in developing the land
cover map was to attribute a category to each individual segment in the image. This
was done through the application of linear canonical discriminant analysis ( LCDA;
Dillon and Goldstein 1984, McLachlan 1992, Richards 1993) to a new multi-variate
data matrix that collected per-segment statistics. This new data matrix consisted of
four variables associated with each segmentÐ the per-segment means for each of the
three CIR channels and the coe cient of variation (CV ) for the PC-1 image Ð
producing a 2052 segment by 4 variable matrix.
LCDA requires a training sample setÐ in our case a subset of segments representing known categories of land cover in the ® eldÐ to develop a linear transformation
of the original data matrix that maximizes statistical separability among the di€ erent
categories represented in the image. In LCDA, the transformation is constructed
from the training set in such a way that it minimizes the variance among segments
placed in the same group and maximizes the variance among di€ erent groups. The
transforming matrix is the matrix of eigenvectors obtained from the eigenanalysis of
1
W Õ B , where W is the within-groups covariance matrix and B is the between-groups
covariance matrix. Discriminant analysis also acts as a feature reduction technique
because the number of discriminant axes (s) ful® lls:
s< min (m g Õ
1
)
( 1)
where m is the number of variables and g the number of groups. The actual value
of s is given by the Bartlett signi® cance test ( Legendre and Legendre 1983, McLachlan
1
1992 ) consecutively applied with the m Õ k (k ranging from 0 to m Õ ) eigenvalues
from the above eigenanalysis that remain after acceptance of the ® rst k axes. The
2
test is compared against the x value with (m Õ k ) ( g Õ k Õ 1 ) degrees of freedom for
a chosen signi® cance level.
The segments used for the matrix of training samples were identi® ed as follows:
We visually examined the 1992 CIR image after segmentation and identi® ed a range
of segments with di€ erent spectral qualities to visit at the site. Locations corresponding to forty two of the image segments were visited on the ground. At each of the
2
42 ® eld locations, a 0´25 m square area was sampled to determine percentage cover
by rocks, abundance of perennial bunch grasses, abundance of late blooming, deeply
rooted Calycadenia and Hemizonia plants and the abundances of dominant annual
species. Inspection of the data for these 42 inventories suggested that they could
be grouped into four di€ erent categories, which were also distinguishable in the
displayed CIR composite. The ® eld descriptions of these four categories are as
follows:
1. Bunch grasses: sites dominated by the annual plant species L inanthus , and the
tarweeds (genera Calycadenia and Hemizonia ); tall, perennial bunch grasses
present; and less than 1 per cent cover by exposed rocks.
Figure 1. ( Top left ) Digitized CIR image of 1992. ( Top right) Boundaries of the segments
resulting from IMORM overlaid on the CIR image. (Bottom left) Land-cover map
obtained from classifying the segments after LCDA, with the boundaries of gopher
disturbances for the period 1988± 1991 overlaid in black. Red = tall bunch grasses;
light blue=dense annuals; light green =sparse annuals; deep blue=gravel, small stones
and rocks. Bottom right =boundaries of the land cover map overlaid on the CIR image.
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72
A. L obo et al.
2. Dense annuals: sites dominated by a dense carpet of short-lived, early ¯ owering
annuals, few tarweeds and no perennial grasses present; 1 to 10 per cent cover
by small exposed rocks.
3. Sparse annuals: sites with only sparsely distributed annual plant species, no
perennial grasses present; gravelly terrain.
4. Bare ground: no ¯ owering plants present; terrain composed of gravel, small
stones and rocks.
For each of these four land cover categories, we selected eight representative sites
and used the corresponding 32 segments from our image as the training set for
the LCDA.
Once the discriminant transform was developed from the training set, it was
applied to all of the segments in the image and the linearly transformed data space
(discriminant space) was used to generate the ® nal classi® cation of all of the segments
in the image. This was done by comparing the position of each segment in the
discriminant space to the position of the centroids of the groups identi® ed in the
training set. The individual segments were then classi® ed as belonging to the closest
(in terms of multi-variate distance to a centroid ) group.
A number of multi-variate measures can be used to assign individual segments
to classes. Since there are advantages and disadvantages to both Maximum
Likelihood (ML) and minimum Euclidean Distance ( MED), we applied both separately and constructed three maps of land cover types: one using ML, another one
using MED, and, ® nally, a third one produced by a logical combination of the
former two (see § 4´2 below).
3.4. Comparison of segment based classi® cation to pixel based classi® cation
The training areas were used to compare the discriminating power of per-segment
statistics versus per-pixel statistics. We built a per-pixel data matrix analogous to
the above mentioned per-segment data matrix from the pixel values in the three CIR
channels and the CV of pixel-centred 3 by 3 windows in PC-1. For both the persegment and the per-pixel data matrices we measured the separability between land
cover types i and j according to the Je € ries-Matusita distance q i,j ( Richards 1993,
McLachlan 1992 ):
q i,j= 2( 1 Õ
1
B = (m i Õ
8
eÕ
B
)
mj)
t
A B
ž
Õ
i
ž
2
j
Õ
1
(m i Õ
1
m j ) + ln
2
A
KA BK
KKKK
ž
ž
i
+ž
1/2
i
/2
j
ž
j
1/2
B
( 2)
where m i and m j are the vectors of centroids, S i and S j are the covariance matrices
and t stands for matrix transpose.
Three classi® cations were performed using maximum likelihood: (i ) segments
identi® ed after LCDA of per-segment statistics; (ii ) individual pixels identi® ed after
LCDA of per-pixel statistics; and (iii ) individual pixels identi® ed after LCDA of persegment statistics. One more segment-based classi® cationÐ analogous to (i )Ð was
produced using the minimum Euclidean distance metrics, and a ® fth one (explained
below) by combination of the ML and MED segment-based classi® cations.
73
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Image segmentation and discriminant analysis for mapping a grassland
3.5. V alidation
Due to the rapid biological dynamics of the system, validation of the ® ve land
cover maps had to be performed by photo-interpretation of the CIR image. Two
hundred random points were located in the image and attributed to one of the four
land cover categories. The type of cover according to each of the ® ve maps produced
by the aforementioned classi® cation methods was also recorded for the same points
and ® ve error matrices were built with this information. The Kappa coe cient of
agreement and its 95 per cent con® dence interval were used as an overall measure
of accuracy ( Hudson and Ramm 1987). This index measures the relative weight of
the diagonal of a contingency table. The `producer’s’ and `user’s’ accuracies
(Congalton 1991 ) were also computed for each cover type from the error matrices.
Producer’s accuracy is the complement of the `omission error’, that is, the error due
to not classifying as A all pixels of type A , while user’s accuracy is the complement
of the `commission error’, which is the error due to classifying as A pixels that
actually are not of type A .
3.6. Classi® cation of the 1988 ± 1990 images and identi® cation of Gopher Mounds
In an attempt to examine temporal changes in land cover over a ® ve-year period,
we classi® ed each of the images available from 1988 through 1990 based on the
statistics derived from the 1992 image. Each of the 1988± 1990 images was ® rst
segmented by IMORM. An important feature of the 1988± 1990 images was the
presence of gopher disturbances. Because in 1992 there were no gopher disturbances
observable in the digitized CIR image in the area of the study (although they were
easily observable in other parts of the image), segments interpreted as gopher disturbances were interactively identi® ed in the 1988± 1990 images and a ® fth land cover
category, `gopher disturbance’, was introduced in the training set for the LCDA and
per-segment classi® cation of the 1988± 1990 images.
4.
Results
We found that segment-based classi® cation was superior to pixel-based classi® cations in discriminating among the four land cover categories that we identi® ed on
the ground. First, separabilities among the four land cover categories as measured
by the Je € ries-Matusita distance were much greater using per-segment statistics than
per-pixel statistics (tables 1 and 2 ), which indicates that per-segment statistics provide
Table 1. Separabilities according to the Je€ ries-Matusita distance between the land cover
categories using per-pixel statistics. The possible range is 0± 2 ( low± high separability).
Observed categories
Observed
categories
Bunch grasses
Dense annuals
Sparse annuals
Bare ground
Bunch
grasses
Dense annuals
Sparse annuals
Bare ground
0´00
1´45
1´65
1´86
1´45
0´00
1´01
1´64
1´65
1´01
0´00
1´27
1´86
1´64
1´27
0´00
74
A. L obo et al.
Table 2. Separabilities according to the Je€ ries-Matusita distance between the land cover
categories using per-segment statistics. The possible range is 0± 2 ( low± high separability).
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Observed categories
Observed
categories
Bunch grasses
Dense annuals
Sparse annuals
Bare ground
Bunch
grasses
Dense annuals
Sparse annuals
Bare ground
0´00
1´98
1´99
2´00
1´98
0´00
1´86
2´00
1´99
1´86
0´00
2´00
2´00
2´00
2´00
0´00
the information for a better classi® cation. Therefore, per-segment statistics were used
for the LCDA. Second, per-segment allocation also produced more accurate classi® cations. We present both results separately, followed by results on the analysis of
gopher disturbance.
4.1. L CDA
The discriminant function developed through LCDA was successful in discriminating among the four land cover categories identi® ed in the ® eld, when applied to
the training set of 24 segments from the 1992 image (® gure 2). This is indicated by
a signi® cant Bartlett coe cient (table 3 ). The analysis also indicates that all three
axes of the linear discriminant function contain useful information for the classi® cation, as indicated by a signi® cant Bartlett value when only the third discriminant
axis is included in the model (table 3). The four cover classes are separated in groups
in the plane associated with the ® rst two discriminant axes, although the two annual
vegetation classes lie very close together (® gure 2 ). The latter two are much better
separated by inclusion of the third discriminant axis which can be seen by the
projection of the training set in the plane associated with the ® rst and third
discriminant axes (® gure 2).
4.2. Classi® cations
The accuracy of per-pixel and per-segment classi® cations (tables 4 to 8) re¯ ects
their respective separabilities (tables 1 and 2 ), with classi® cation of segments using
per-segment statistics (tables 6 to 8) producing higher accuracies than classi® cation
of pixels using per-pixel statistics (table 4 ). The worst result is obtained by classifying
pixels using per-segment statistics (table 5 ).
Within per-segment classi® cation, the overall accuracy of the cover map produced
by maximum likelihood ( table 6) was higher than the one produced by minimum
Euclidean distance (table 7), but the accuracy of the cover type bare ground was
higher in the map obtained by minimum Euclidean distance. The highest accuracy
for bare ground was produced by a logical combination of both maps (® gure 1),
which nevertheless did not signi® cantly increase overall accuracy (table 8):
if ( MAP_ED= bare_soil) then FINAL_MAP = MAP_ED
else FINAL_MAP = MAP_ML
( 3)
75
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Image segmentation and discriminant analysis for mapping a grassland
Figure 2. Ordination with respect to the three discriminant axes, of the 24 segments used to
typify the four terrain categories in the discriminant analysis: 1, Bunch grasses; 2, dense
annuals; 3, sparse annuals; 4, bare ground.
Table 3.
Signi® cance test of the LCDA applied to 24 sites representing four land cover
classi® cation categories, and scores for the canonical transform.
Scores
Axes
1, 2, 3
2, 3
3
d.o.f.
12
6
2
Bartlett value
58´35
35´92
14´78
Axis
p
4´5 Ö 10Õ
2´8Ö 10Õ
6´2Ö 10Õ
8
6
4
1
2
3
Õ
Green
0´0238
0´0759
0´0443
Õ
Red
0´0807 Õ
0´0472
0´0627
Infrared
CV-PC1
0´0775
15´202
0´0511 Õ 4´2232
0´0056
6´4375
where MAP_ED and MAP_ML stand for the maps produced by the Euclidean
distance and the maximum likelihood criterion, respectively, and FINAL_MAP is
the resulting from the `if . . . then . . . else’ rule as indicated.
The error matrix of this combined map (table 8 ) shows a high user’s accuracy,
except for bare ground. We discuss this problem in § 5.
76
A. L obo et al.
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Table 4. Error matrix for a classi® cation of pixels by ML after performing a LCDA using
per-pixel statistics. Numbers represent cross-categorization s of 200 randomly chosen
pixels based on classi® cations assigned to the pixels according to ML classi® cation
(Mapped Categories) and photo-interpretation (Observed Categories).
Observed categories
Mapped categories
Bunch grasses
Dense annuals
Sparse annuals
Bare ground
Bunch
grasses
Dense
annuals
Sparse
annuals
Bare
ground
Producer’s
accuracy
User’s
accuracy
24
12
3
2
7
56
12
6
5
22
37
6
0
0
1
7
0´59
0´69
0´53
0´88
0´67
0´62
0´70
0´33
The diagonal represents the number of correct identi® cations. The estimated value of
Kappa is 0´444 (s.d.=0´050 ). Percentage accuracy is 62 per cent. `Producer’ s’ and `User’s’
accuracies were calculated using the methods described in § 3.6.
Table 5.
Error matrix equivalent to table 4 for a classi® cation of pixels by ML after
performing LCDA using per-segment statistics.
Observed categories
Mapped categories
Bunch grasses
Dense annuals
Sparse annuals
Bare ground
Bunch
grasses
Dense
annuals
Sparse
annuals
Bare
ground
Producer’s
accuracy
User’s
accuracy
35
5
1
0
81
0
0
0
70
0
0
0
8
0
0
0
0´85
0´00
0´00
0´00
0´18
0´00
0´00
The estimated value of Kappa is Õ
0´045 (s.d.=0´109 ). Percentage accuracy is 17´5 per cent.
Table 6. Error matrix equivalent to table 4 for a classi® cation of segments by ML after
performing LCDA using per-segment statistics. The estimated value of Kappa is 0´77
(s.d.=0´037 ). Percentage accuracy is 84´5 per cent.
Observed categories
Mapped categories
Bunch grasses
Dense annuals
Sparse annuals
Bare ground
Bunch
grasses
Dense
annuals
Sparse
annuals
Bare
ground
Producer’s
accuracy
User’s
accuracy
34
4
2
1
2
72
6
1
3
6
57
4
1
1
0
6
0´83
0´89
0´81
0´75
0´85
0´87
0´88
0´50
4.3. Gopher disturbance
We were unable to classify the 1988± 1990 images successfully, as a high proportion of the segments in these images could not be assigned to any one of the land
cover categories at the 95 per cent con® dence level. The inability to assign segments
successfully can be traced to the fact that there was poor interdate colour calibration
Image segmentation and discriminant analysis for mapping a grassland
Table 7.
77
Error matrix equivalent to table 4 for a classi® cation of segments by MED after
performing LCDA using per-segment statistics.
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Observed categories
Mapped categories
Bunch grasses
Dense annuals
Sparse annuals
Bare ground
Bunch
grasses
Dense
annuals
Sparse
annuals
Bare
ground
Producer’s
accuracy
User’s
accuracy
25
12
4
0
0
72
9
0
0
30
37
3
0
1
1
6
0´61
0´89
0´53
0´75
1´00
0´63
0´73
0´67
The estimated value of Kappa is 0´539 (s.d.=0´051 ). Percentage accuracy is 70´0 per cent.
Table 8. Error matrix equivalent to table 4 for the ® nal image-derived land cover map, which
is a map produced by a logical combination of the two maps obtained by ML and
MED criteria for classi® cations of segments (see § 4.2 for a full explanation).
Observed categories
Mapped categories
Bunch grasses
Dense annuals
Sparse annuals
Bare ground
Bunch
grasses
Dense
annuals
Sparse
annuals
Bare
ground
Producer’s
accuracy
User’s
accuracy
34
4
3
0
2
72
7
0
3
6
58
3
1
1
0
6
0´83
0´89
0´83
0´75
0´85
0´87
0´85
0´67
The estimated value of Kappa is 0´776 (s.d.=0´038 ). Percentage accuracy is 85 per cent.
among the images. As a consequence, the statistics developed from the 1992 training
® elds were not valid for the remaining images.
Although we could not use the 1988± 1990 images in a study of the spatiotemporal dynamics of the grassland at Jasper Ridge, we could use these images in a
study of disturbance patterns over that time period. Segments representing recent
gopher disturbances were easily recognized in the images. These were interactively
classi® ed, producing a disturbance map, for each image from 1988± 1990, that contained two classi® cation categories: `disturbed’ and `not-disturbed’. A composite map
of disturbances was then produced by combining all three disturbance maps; this
was done by applying a logical OR operation to the three original binary maps
(® gure 1 (c)). In the composite map, pixels were thus classi® ed as `disturbed’ if they
had been identi® ed as `disturbed’ in any of the 1988 to 1990 images, otherwise they
were identi® ed as `not± disturbance’. Once the disturbance map was constructed,
we were able to conduct an analysis to determine whether disturbances were
randomly distributed among vegetation cover categories.
For this analysis, we constructed a two-way contingency table showing the
association of gopher disturbances with the 1992 map of cover categories. This
contingency table ( table 9) was constructed by determining the values of 2000
randomly located pixels. The resulting table departs signi® cantly from the null
2
hypothesis of non-interaction ( x = 257´515, d.f.= 3, p < 0´001). The Neu values
( Legendre and Legendre 1983) computed for each cell of the table indicate that
78
A. L obo et al.
Table 9.
Contingency table of correspondence between gopher disturbances and land cover
categories for 2000 randomly located points in the 1992 map.
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Land cover category
Bunch grasses
Dense annuals
Sparse annuals
Bare ground
Gopher disturbance
482
288
219
29
(269´3 )
( 378´3)
(314´6 )
(55´8)
No gopher disturbance
2164
3428
2871
519
(2376´6 )
(3337´7)
(2775´4 )
(492´2 )
Values in brackets are the expectations under the null hypothesis of non interaction. This
hypothesis is rejected by the x 2 test (X 2= 257´515, d.f.=3, n =2000, p = < 0´001).
gopher disturbances were located in bunch grass signi® cantly more often than would
be expected if they were distributed at random within the area. Gopher disturbances
were also found less often in the remaining vegetation types than would be expected
at random.
5.
Discussion
It is surprising that the most obvious land cover category in the image, bare
ground, was the one with the lowest accuracies after classi® cation by LCDA.
Accuracies for this category were actually worse when ML was used as a classi® cation
rule, improving somewhat when the simpler criterion of MED was used. The poor
performance by maximum likelihood was probably the result of poor estimation of
the bare-ground covariance matrix, which might be improved by including a higher
number of training ® elds ( Richards 1993). Although using MED as a classi® cation
rule is preferable to using ML with a poorly estimated covariance matrix, it would
have been best to use maximum likelihood with a well estimated covariance matrix.
Unfortunately, the latter could only be accomplished through an increase in the
number of training ® elds. However, this is not easy to accomplish for a relatively
rare land cover category. It would require either using up virtually all the bare
ground cover for the training ® elds (undesirable for accuracy testing) or substantially
increasing the digitized area. Perhaps the use of non-parametric classi® ers and
decision-boundary feature extraction ( Lee and Landgrebe 1993) instead of LCDA
would be a reasonable approach to use for classifying segments, as this would avoid
the use of covariance matrices.
A second explanation for the low accuracy ascribed to predicting the bare ground
category could be the method used in de® ning accuracies, which compared randomly
located, visually classi® ed pixels to the LCDA segment-based classi® cations. The
lower accuracy for classifying bare ground can be traced primarily to three pixels
that were visually identi® ed as sparse annuals, but classi® ed by LCDA as bare
ground (table 8 ). These pixels were actually located within segments that consisted
mostly of bare ground.
Separability matrices show that the categories de® ned here cannot be de® ned at
the pixel level. In fact, this is often implied when using conventional supervised
techniques for image classi® cation: training areas are interactively selected as patches
and rarely as isolated pixels. As a consequence, the conventional procedure involves
a contradiction for the user, since it proceeds in a per-pixel basis. The worst strategy
would be to allocate individual pixels to categories that had been de® ned from
patches, as shown in table 5. This is because of the dependence of both LCDA and
Downloaded By: [Iowa State University] At: 21:08 24 August 2007
Image segmentation and discriminant analysis for mapping a grassland
79
ML on the covariance matrices, which can be very di€ erent for patches (either ® elds
or segments) and individual pixels.
An analogous procedure to the per-segment classi® cation, per-® eld (sometimes
called per-parcel ) classi® cation, has been used to discriminate between agricultural
crops and produced superior results to conventional per-pixel classi® cation
( Landgrebe 1976, Megier et al . 1984, Pedley and Curran 1991). Per-® eld classi® cation
relies on the availability of digitized polygons, which sometimes exist in databases
for agricultural and urban areas. Digitization of equivalent polygons by interactive
drawing of patch boundaries is obviously impractical for natural vegetation and
even unsuitable because of the subjectivity involved in tracing the actual limits.
Image segmentation followed by discriminant analysis proves to give very good
results even in scenes with categories as di cult to discriminate as the ones
studied here.
Another advantage of the classi® cation of segmented images is that misidenti® cations occur as patches and not as scattered individual pixels, which makes them
more obvious and easy to identify. An interesting extension to the protocol developed
here would be the development of a programme that labels segments with a high
variance as suspect.
The use of image segmentation as a step prior to classi® cation by LCDA assumes
that the image has a high spatial resolution relative to the size of the land cover
units being classi® ed, making it an H-resolution scene model in the terminology of
Strahler et al . ( 1986 ). In H -resolution models, the elements of the scene to be
considered are larger than the elements being used to resolve the image (i.e., pixels).
Image segmentation is inadequate for L -resolution scene models, in which the
elements of the scene to be classi® ed are smaller than pixels, and for which techniques
such as spectral mixture analysis (Adams et al . 1986, Smith et al . 1990) are more
appropriate. Nevertheless, both approaches are complementary and their results
could be discussed together to produce a more complete analysis of the scene.
The map presented in ® gure 1 represents a simpli® cation of the overall result,
which actually assigns a vector of likelihoods for each land cover category for every
pixel. Intermediate categories are thus detectable with this method, which is consistent
with a view of landscape types as being a continuum in which several modes are
distinguishable. In this respect our approach is similar to the one of fuzzy classi® cation ( Foody 1992, 1994, 1995 ), although the theoretical aspects of both types of logic
are di€ erent. The vector of likelihoods also provides a mechanism for determining
the overall quality of the classi® cation: if a large proportion of the image contains
low maximum likelihoods for all categories, this would indicate that the legend is
incomplete or inadequate.
We found that insu cient inter-date calibration for the 1988 through 1992 images
of the Jasper Ridge grassland prevented a complete analysis of interannual land
cover dynamics. This emphasizes the greater suitability of airborne digital sensors
versus digitized conventional aerial CIR photography for multidate studies.
Nevertheless, the much higher spatial resolution that can be achieved with conventional aerial photography argues for the simultaneous acquisition of both types of
imagery.
Although a complete study on interannual land cover dynamics was not possible,
results on the location of gopher disturbances were of great interest. They demonstrate a signi® cant positive correlation between the distribution of bunch grasses
and the location of gopher mounds. Interestingly enough, the location of the bunch
Downloaded By: [Iowa State University] At: 21:08 24 August 2007
80
A. L obo et al.
grasses is also closely associated with the location of topographic ridges and deeper
grounds within the study site ( Lobo et al . 1997 ). Understanding these relations is
important to the development of an ongoing study of the ecological dynamics of the
Jasper Ridge grassland. A spatially-explicit model of the Jasper Ridge grassland has
suggested that there is a very strong relation between the development of vegetation
pattern and the spatial and temporal distribution of gopher mounds in the grassland
(Moloney et al . 1992, Moloney and Levin 1996 ). It has also shown that there is a
fundamental di€ erence between landscapes within which disturbances are allowed
to occur everywhere and landscapes within which disturbances are constrained to
occur only in some locations. The image analysis study presented here clearly
demonstrates that gopher disturbances are restricted in distribution and are strongly
associated with a speci® c vegetation type (the bunch grass category). Whether the
distribution of bunch grasses is the result of disturbance (as would be suggested by
the model ), is more closely related to di€ erences in environmental factors (such as
depth of soil ) or just bunch grasses attract the gophers, remains to be seen. A more
detailed comparison of the distribution of vegetation types as predicted by the model
and as determined through image analysis may help us to resolve this issue.
6.
Conclusions
Through the use of image segmentation and LCDA, we have found that the
digitized CIR image from 1992 could be accurately divided into four cover categories:
bunch grasses, dense cover by annuals, sparse cover by annuals, and bare ground.
According to the Je € ries-Matusita metrics of statistical separability, these categories
cannot be de® ned accurately by conventional pixel-based statistics. The analysis of
similar imagery for the 1988± 1990 period has allowed us to determine that a signi® cant positive correlation exists between the location of gopher disturbances and the
distribution of bunch grasses.
Beyond the conclusions drawn here for the speci® c portion of the grassland
studied, the high quality of the land cover map produced indicates that, in the future,
a comprehensive analysis of the grassland’s patch dynamics could be undertaken,
allowing us to characterize the temporal components of pattern formation in a
broader context. Coupling this information to re® ned spatially-explicit dynamic
models would require, from the remote sensing side, a larger extent of the grassland
being covered and a formal procedure for radiometric interdate calibration being
established, probably involving airborne digital sensors. From the modelling side,
there is also the possibility for incorporating the ecosystem level processes (Seligman
and van Keulen 1989 and 1992) into the current demographically based approach
(Moloney and Levin 1996). Pattern output from the spatially explicit models could
then be tested against the patterns observed in the images to determine how well
our understanding of the system has progressed.
Acknowledgements
We would like to thank Si Levin and Chris Field for providing invaluable insights
into the development of this paper. Comments by P. M. Mather ( University of
Nottingham) and by three anonymous reviewers greatly improved the original manuscript. This work was supported in part through grants from the Andrew W. Mellon
Foundation and the National Aeronautics and Space Administration ( NAGW-3124 )
to Simon Levin ( Princeton University), and the Joint Program of the Ministry of
Image segmentation and discriminant analysis for mapping a grassland
81
Downloaded By: [Iowa State University] At: 21:08 24 August 2007
Education and Science of the Government of Spain and The Fulbright Committee,
which supported A. Lobo as a Visiting Fellow at Cornell and Princeton Universities.
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