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Water 2015, 7, 794-817; doi:10.3390/w7020794
water
ISSN 2073-4441
www.mdpi.com/journal/water
Article
Target Detection Method for Water Mapping Using
Landsat 8 OLI/TIRS Imagery
Luyan Ji 1,*, Xiurui Geng 2, Kang Sun 2, Yongchao Zhao 2 and Peng Gong 1,3,4
1 Ministry of Education Key Laboratory for Earth System Modelling, Centre for Earth System
Science, Tsinghua University, Beijing 100084, China; E-Mail: penggong@berkeley.edu
2 Key Laboratory of Technology in Geo-Spatial Information Processing and Application System,
Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China;
E-Mails: gengxr@sina.com (X.G.); sunkang-1234@163.com (K.S.); ofcours_sure@sina.com (Y.Z.)
3 Department of Environmental Science, Policy and Management, University of California, Berkeley,
CA 94720-3114, USA
4 Joint Center for Global Change Studies, Beijing 100875, China
* Author to whom correspondence should be addressed; E-Mail: jily@mail.ustc.edu.cn;
Tel.: +86-010-6277-2750; Fax: +86-010-6279-7284.
Academic Editor: Jun Xu
Received: 11 October 2014 / Accepted: 3 February 2015 / Published: 13 February 2015
Abstract: Extracting surface water distribution with satellite imagery has been an important
subject in remote sensing. Spectral indices of water only use information from a limited
number of bands, thus they may have poor performance from pixels contaminated by
ice/snow, clouds, etc. The detection algorithms using information from all spectral bands,
such as constrained energy minimization (CEM), could avoid this problem to some extent.
However, these are mostly designed for hyperspectral imagery, and may fail when applied
to multispectral data. It has been proved that adding linearly irrelevant data to original data
could improve the performance of CEM. In this study, two kinds of linearly irrelevant data
are added for water extraction: the spectral indices and the spectral similarity metric data.
CEM is designed for targets with low-probability distribution in an image, but water bodies
do not always satisfy this condition. We thereby impose a sensible coefficient for each pixel
to form the weighted autocorrelation matrix. In this study, the weight is based on the
orthogonal subspace projection, so this new method is named Orthogonal subspace
projection Weighted CEM (OWCEM). The newly launched Landsat 8 images over two
lakes, the Hala Lake in China with ice/snow distributed in the north, and the Huron Lake in
OPEN ACCESS
Water 2015, 7 795
North America, a lake with a very large surface area, are selected to test the accuracy and
robustness of our algorithm. The Kappa coefficient and the receiver operating characteristic
(ROC) curve are calculated as an accuracy evaluation standard. For both lakes, our method
can greatly suppress the background (including ice/snow and clouds) and extract the complete
water surface with a high accuracy (Kappa coefficient > 0.96).
Keywords: water extraction; CEM; OWCEM (orthogonal subspace projection weighted
CEM); Landsat 8 OLI/TIRS
1. Introduction
Surface water information is vital for water resources, climate, and agriculture studies [1]. Surface
water change is critically important for studies on the land use/cover (LULC), climate, and other forms
of environmental change in the world. With the rapid development of remote sensing technology,
satellite data can provide continuous coverage of the earth’s surface both in space and in time. Thus
remotely sensed data has become an important source for earth surface change monitoring [2].
Applications using remote sensing related to water resources include flood hazard/damage assessment
and management, change in surface water resources, water quality assessment and monitoring, and
water-borne disease epidemiology [3].
To date, a number of water extraction techniques using optical imagery have been developed, which
can be categorised into four basic types: (a) statistical pattern recognition techniques including
supervised [4–6] and unsupervised classification methods [7]; (b) linear unmixing [8]; (c) single-band
thresholding [9,10]; and (d) spectral indices [3,11–14].
Among these, the most commonly used category is the spectral index due to its ease of use.
McFeeters [11] developed the normalized difference water index (NDWI) using the reflectance of the green
(band 2) and near-infrared (band 4) bands of Landsat TM (Thematic Mapper). Rogers and Kearney [15]
used another NDWI for water extraction where they applied bands 3 and 5 of Landsat TM. Xu [12]
revised McFeeters’s NDWI to overcome the inseparability of built up areas and named it the modified
NDWI (MNDWI), in which the SWIR (short wave infrared) band (Landsat TM band 5) was used to replace
the NIR (near infrared) band (band 4) in McFeeters’s NDWI. MNDWI is one of the most widely used
water indices for a variety of applications, including surface water mapping, land use/cover change analyses,
and ecological research [16–18]. Feyisa et al. [3] introduced a new automated water extraction index
(AWEI) improving the classification accuracy in areas that include shadow and dark surfaces. The index
includes two indices: AWEInsh and AWEIsh. They are a linear combination of the blue (band 1), green
(band2), NIR (band4), SWIR 1 (band 5), and SWIR 2 (band 6) bands of Landsat TM. AWEInsh is mainly
used in areas with an urban background, while AWEIsh is primarily designed to remove shadow pixels.
However, the extraction result of the above water index-based methods may not be ideal. For
example, when using these indices, pixels with ice/snow or clouds can also show a high value, sometimes
even higher than water pixels. The main reason is that they only use partial spectral information, and have
not taken the background information into consideration. In other words, a simple band combinations like
NDWI or AWEI cannot differentiate pixels containing liquid water from pixels containing water in other
Water 2015, 7 796
form, such as ice/snow or cloud. One way to solve this problem is to use information from all bands,
together with the statistical differences between water and background.
With hyperspectral data, a series of algorithms have been developed for target detection and
successfully applied for various applications [19–21]. The common hyperspectral detection algorithms
include orthogonal subspace projection (OSP) [22–24], constrained energy minimization (CEM) [20,22],
and matched filter (MF) [21,25–32]. The OSP uses the linear mixture model and white Gaussian noise
assumption. It requires the spectral signature of both target and background. It is usually hard for OSP
to produce optimal results in real time. CEM is a linear filter, which constrains a desired target signature
while minimizing the total energy of the output of other unknown signatures. CEM requires prior spectral
knowledge of a target and utilizes second-order statistical information on images. Under the assumption
of a low-probability distribution for the target in an image, the CEM detector can distinguish the target
of interest from the background very well. Comparative studies show that the CEM generally
outperforms the OSP in terms of eliminating an unidentified signal sources and suppressing noise.
However, they are closely related and essentially equivalent provided that the noise is white with large
SNR (single-to-noise ratio) [23]. In a Bayes or Neyman–Pearson case, when the target and background
classes follow multivariate normal distributions with the same covariance matrix, an MF detector can
get optimal detection results. In fact, the MF and CEM detectors have a very similar mathematical
formula, and the main difference is that an MF detector requires the data to be centralised first.
The above target detection algorithms can exhibit very good performance in hyperspectral remote
sensing. However, they may fail for multispectral imagery due to the lack of spectral bands. Ren et al. [33]
have proposed a generalised constrained energy minimization (GCEM) for detecting targets in
multispectral images with a dimensionality expansion approach. They expanded bands by generating the
second-order correlated and nonlinearly correlated new variables, producing a total of (L2 + 5L)/2 new
variables, where L is the number of bands. GCEM outperforms CEM for multispectral imagery but it is
very sensitive to noise and the selection of the desired target signature.
Geng et al. [34] have proved that adding any newly derived variable linearly uncorrelated with the
original image, even a noisy band, would be beneficial to the performance of CEM in terms of output
energy. The conclusion serves a theoretical base to improve the performance of CEM for multispectral
target detection. That is to increase the dimensionality of data by adding new variables that can be
derived from the original data but are not linearly correlated with the original data. According to this
theory, more un-correlated data means better performance, but on the other hand, more data also means
greater computational complexity and memory requirement. GCEM has provided a way for data
expansion, but it is not target-oriented and the number of variables added is huge. For example, for a
7-band multispectral data, it will produce 42 additional channels. If the added channels cannot highlight
the difference between the target and background, their impact to increase CEM’s performance is of
little use and may increase the sensitivity to the target signature selection instead. So how to add useful
data for water extraction is a key problem that is of interest to us.
Another problem related to CEM for water extraction is that water bodies in an image may not always
satisfy the low-probability distribution constraint. For large targets, CEM would shine with both high
rates of omission and false positive errors. This can be attributed to the fact that the autocorrelation
matrix used in CEM is calculated from both target and background pixels. So, when the target size is
large in an image, the performance of CEM would be poor. Geng et al. [35] have proposed a new strategy
Water 2015, 7 797
by multiplying a weight coefficient for each pixel in the process of constructing the autocorrelation
matrix, which aims to lessen the contribution of pixels with spectral characteristics similar to the target.
We followed this idea and developed a new weight expression according to the idea of OSP, named the
OSP-weighted CEM (OWCEM). In this paper, we introduce this new strategy for water detection with
multispectral images.
2. Study Areas and Data Source
2.1. Test Sites
Two water bodies of different areas were selected. One was the Hala Lake (see Figure 1a), located in
Qinghai Province, China, with an estimated water surface area of 590 km
2
. It is surrounded by high
mountain ridges, such as the glaciated Shule Nanshan, along the northern to northwestern fringe of the
basin [36]. Ice/snow surrounding the lake is an important reason for choosing Hala Lake. It helps us to
assess the accuracy of OWCEM when ice/snow exists. The other one was Huron Lake, which has a very
large area. It is bounded on the east by Ontario, Canada, and on the west by the state of Michigan of the
United States (see Figure 1b). Lake Huron is the second-largest of the Great Lakes, with a surface area
of 59,600 km
2
. Lake Huron was selected to evaluate the performance of our algorithm when the area
percentage of water in an image is large.
Figure 1. The locations of study areas: (a) Hala Lake and (b) Lake Huron.
Water 2015, 7 798
2.2. Landsat Images
Landsat 8 Operational Land Imager (OLI)/Thermal Infrared Sensor (TIRS) images were selected for
their improved signal to noise performance over Thematic Mapper (TM) and Enhanced Thematic
Mapper Plus (ETM+) images. The band allocations among TM, ETM+, and OLI/TIRS are shown in
Table 1. The images were acquired from the United States Geological Survey (USGS) Global
Visualization Viewer (GLOVIS) portal (http://earthexplorer.usgs.gov/). To test the robustness of our
algorithm to the existence of cloud, images with clouds were purposely selected on purpose.
All Landsat images used were at the L1T level. The radiometric processing was done automatically using
the Global Mapper (GM) software package developed in [37]. This processing included atmospheric
correction and the topographic correction. Descriptions of the Landsat 8 images used in this study are
presented in Table 2.
Table 1. The band designations between Landsat 5/7 and Landsat 8.
Sensor
Bands
Costal
Aerosol Blue Green Red NIR SWIR
1
SWIR
2 Panchromatic Cirrus TIRS 1 TIRS 2
TM - 1 2 3 4 5 7 - - 6
ETM+ - 1 2 3 4 5 7 8 - 6
OLI/TIRS 1 2 3 4 5 6 7 8 9 10 11
Table 2 Description of Landsat OLI/TIRS scenes and corresponding reference data.
Test
Site Path/Row Central
Latitude/Longitude
Acquisition
Date
Image
Size
Cloud
Cover
Water
Cover Reference Data
Hala
Lake 135/033 38°89' N/97°69' E 01/06/2013 7691/7501 5.08% 1.75%
FROM-GLC: base
image acquired on
09/08/2009
Huron
Lake 020/029 44°59' N/82°71' W 13/07/2013 7901/8021 1.29% 76.40%
FROM-GLC: base
image acquired on
20/09/2009
2.3. Reference Data
The reference data used in the accuracy assessment was selected from the land cover map with the
same path and row of the Finer Resolution Observation and Monitoring of Global Land Cover
(FROM-GLC) [37] product using Landsat TM images. Due to the difference between the acquisition
dates of the images used in FROM-GLC and our study, there exist some mismatches. However, we have
carefully examined the land cover maps with our Landsat 8 images, and found that the mismatching portion
was actually statistically very low. Therefore, the corresponding land cover maps of FROM-GLC were
used as ground reference images in this study (see Table 2).
Water 2015, 7 799
3. Methods
3.1. CEM
CEM is originally derived from the linearly constrained minimized variance adoptive beam-forming in
the field of digital signal processing. It uses a finite impulse response (FIR) filter to constrain the desired
signature by a specific gain while minimizing the output energy of the filter [20,22].
Assume that we are given a finite set of observations S = {x1, x2, …, xN}, where xi = (xi1, xi2, …, xiL)T
for 1 ≤ i ≤ N is a sample pixel vector; N is the total number of pixels, and L is the number of bands
(generally L << N). Suppose that the desired signature d is also known a priori. The objective of the
CEM is to design an FIR linear filter w = (w1, w2, …, wL)T to minimize the output power subject to the
constraint, 11
L
T
ll
ldw
=
==
dw . Then the problem yields:
() ( )
2
1
1
min min
1
N
TT
i
i
T
N=
=
=
ww
wx wRw
dw
(1)
where
1
(1 / ) NT
ii
i
N=
=
Rxx
(2)
turns out to be the sample autocorrelation matrix. The solution to (1) is called the CEM operator with a
weight vector wCEM given by:
1
1
CEM T
−
−
=Rd
wdR d
(3)
The CEM technique has been successfully applied to small target detection from hyperspectral data,
since the number of bands for a hyperspectral image is usually large enough to distinguish the target
from other ground objects spectrally. If we want to utilise CEM on images with fewer bands, one possible
way is to add artificial variables. Geng et al. [34] proved that adding any linearly irrelevant data to the
original data, even if that data was noisy, would always be beneficial to the performance of CEM in
terms of output energy. According to this theory, we can use CEM on multiband images by adding bands
with useful information, such as spectral index data.
3.2. Band Expansion
In order to improve the performance of CEM, we need to expand the dimensionality of the
multispectral image. The data added should satisfy two criteria: (1) the data should not be the linear
expression of the original bands; and (2) the data should highlight the characteristics of the target while
suppressing that of the background. According to the previous knowledge on water in remote sensing,
two kinds of data could be added. The first one is the spectral index, and the second is the spectral
similarity metric with the target.
Water 2015, 7 800
3.2.1. Water Index
So far, two water indices have shown their superiority in many applications related to water. The first
one is the MNDWI:
ρρ
MNDWI ρρ
g
reen SWIR
g
reen SWIR
−
=+
(4)
In Landsat 8’s band designation, we can rewrite MNDWI as:
b
and3 band6
MNDWI
b
and 3 + band 6
−
=
(5)
The second is Feyisa’s AWEI, which includes two indices for non-shadow and shadow
surfaces, respectively:
AWEInsh = 4×(band3 − band6) − (0.25 × band5 + 2.75 × band7) (6)
AWEIsh = band2 + 2.5 × band3 − 1.5 × (band5 + band6) − 0.25 × band7 (7)
Clearly, MNDWI is the non-linear expression of band 3 and 6, so we can directly use it in OWCEM.
But AWEInsh and AWEIsh are the linear expressions of band 2, 3, 5, 6, and 7. To satisfy the linearly
irrelevant constraint, we can modify the two indices as MAWEInsh and MAWEIsh:
MAWEInsh = AWEInsh/(band3 + band5 + band6 + band7) (8)
MAWEIsh = AWEIsh/(band2 + band3 + band5 + band6 + band7) (9)
3.2.2. Spectral Similarity Metrics
The common indices to measure the similarity between two spectra include correlation (corr),
Euclidean distance (d), spectral angle distance (SAD), and spectral information distance (SID) [38].
For two spectra (pixels), x = (x1, x2,…,xL)T nd y = (y1, y2,…,yL)T, the corr, d, SAD and SID metrics can
be defined as follows:
()()
corr
T
−⋅−
=−⋅−
xx yy
xx yy (10)
1
SAD cos
T
−
=
xy
xy (11)
d = ||x-y|| (12)
SID = D(x||y) + D(y||x) (13)
where
() ( )
1
D|| log /
L
lll
l
p
pq
=
=
xy (14)
() ( )
1
D|| log /
L
lll
lqqp
=
=
yx (15)
and
Water 2015, 7 801
1
/L
ll j
j
p
xx
=
=
, 1
/L
ll j
j
qy y
=
=
(16)
Therefore in our algorithm, we use 14 channels: 7 Landsat 8 bands (band 1–7), 3 water indices
(MNDWI, MAWEInsh, MAWEIsh), and 4 spectral similarity metrics (corr, SAD, d and SID). The
additional 7 new variables can help improve CEM’s performance on water detection, since they are
generated according to people’s understanding of the spectral properties.
3.3. CEM Based on Orthogonal Subspace Projection-Weighted Autocorrelation Matrix
Besides the limitation of the number of bands, another problem when using CEM to extract water in
Landsat images is that CEM has a low-probability distribution assumption for a target. In the CEM
detector expression (Equation (3)), the function of R−1 is to suppress the background. However, when
calculating the autocorrelation matrix R, all pixels, including the target pixels, will be involved. When
the target is small, the influence of including target vectors when calculating R can be neglected. But
this influence cannot be ignored in the case of a large target. For this reason CEM is mostly considered
as a small target detector.
However, water in a Landsat image is not always “small.” The proportion of water could be large, for
example, the seawater in an image of a coastal area. Therefore, when calculating R, we should eliminate
the influence of target vectors to R as much as possible. Geng et al. [35] proposed a way to reconstruct
R, which they named the weighted autocorrelation matrix R*, and defined as:
1
*(g(,))
NT
iii
i
cf
=
=
Rxdxx
(17)
where c is a constant; f(x) is a monotonically increasing function for x ≥ 0 with f(0) = 0; g(x,y) is the
function to measure the spectral similarity between vector x and y, which decreases as the similarity of
x and y increases. For example, let f(g(x,y)) be the Euclidean distance between x and y, i.e.,
f(g(x,y)) = ||x − y||. If xi = d, we have f(g(xi,d)) = 0, which indicates that the contribution of the target to
R* is zero. On the other hand, if xi is a background vector, we have f(g(xi,d)) > 0. Therefore, R* mostly
reflects the two-order statistics of the background.
The Euclidean distance emphasizes the difference in spectral value, but it cannot reflect the
dissimilarity in spectral shape. In this paper, we introduce another way to separate the target from the
background by applying the OSP operator [22–24] P = I − dd+, where d+ is the pseudo-inversion of d.
Let (,) T
iii
g=xd xPx
and f(x) = x, then we have:
()
1
*1/ NTT
i iii
i
N=
=
R x Pxxx . (18)
We name this new R* as the orthogonal subspace projection-weighted (OW) autocorrelation matrix,
and the new CEM detector as the OWCEM detector. In this study, we apply OWCEM to the original data
with 7 additional variables, as illustrated in Figure 2. Besides the Landsat series data, OWCEM can also
be applied to other multispectral data, such as the multispectral images from the Sentinel 2 satellite that
is scheduled to be launched soon.
Water 2015, 7 802
Multispectral
image
3 water index bands:
MNDWI, MAWEI
nsh
,
MAWEI
sh
4 spectral similarity
metric bands:
corr, SAD, d, SID
water signature
d
OWCEM
detec tor
R*
OWCEM
result
selection
Figure 2. Flowchart of OWCEM algorithm for water extraction with the multispectral image.
3.4. Pure Water Signature Extraction
It should be noted that the target signature, d, is needed for both CEM and OWCEM. However, the
spectrum of water varies as its composition and depth changes. Sivanpillai et al. [7] categorise water as
clear water, green water, and muddy/turbid water. Sun et al. [39] have followed this categorization. The
colour of green water is dominated by the phytoplankton or floating hydrophytes. Usually, clear water
in true color images appears blue or dark blue and muddy/turbid water appears yellow. However,
in addition to muddy/turbid water, but also shallow water appears yellow. Thus, in this paper, according
to the colour, we classify water into three classes: blue water, green water, and yellow water. Their
typical signature curves are shown in Figure 3. It can be seen that blue water has the highest reflectance
in the blue bands, while green water has high reflectance in the green bands. The spectrum of yellow
water is very similar to that of ice/snow, but with a much lower value.
Figure 3. The spectral signatures of three water colors.
A pure water signature can be extracted by endmember extraction algorithms [40,41], or by using
water signatures in a spectral library. In this study, for similarity, we manually pick some pure water
points in the image for each kind of water based on the ground reference maps. Water pixels with
different reflectance levels are selected, and their mean spectrum is calculated as d for CEM and
Water 2015, 7 803
OWCEM. The total number of pixels selected does not have to be large, but the selected pixels should
have representative spectral signatures.
4. Results
In this study, we compared our method, OWCEM with 14 channels, with the water indices MNDWI,
AWEI
nsh
, AWEI
sh
, and CEM with only the original 7 bands. Strictly speaking, both CEM and OWCEM
are detection operators and can be applied to data with any number of channels. However, we simplified
OWCEM for “OWCEM applied to 14 channels (Landsat 8 band 1–7 MNDWI, MAWEI
nsh
, MAWEI
sh
,
corr, SAD, d, and SID)” and CEM for “CEM with original 7 bands (Landsat 8 band 1–7)” in the
following content. In addition, the Kappa coefficient and the receiver operating characteristic (ROC)
curves were calculated to evaluate the performance of the five algorithms.
4.1. Hala Lake
Within the Landsat 8 image, the Hala Lake is a small target, which only occupies 1.57% of the image.
However, both ice/snow and cloud exist in the image, as shown in Figure 1a. The middle area of Hala
Lake is blue, while some edge areas appear dark green. In this study, three pixels for these two kinds of
water were selected as the representatives for CEM and OWCEM, as shown in Figure 4.
(a) (b)
Figure 4. The spectral curves of blue (a) and green (b) water for the Hala Lake image.
The outputs of the five algorithms are presented in Figure 5. Visually, OWCEM could suppress the
background more efficiently compared to water indices and CEM. Water indices have extremely high
values in ice/snow areas (Figure 5b–d), while CEM has high values in cloudy areas (Figure 5e).
For a quantitative comparison with the ground reference map, the water extraction binary results are
required. The most commonly used binarisation is to partition the image by setting a threshold. However,
there is no fixed threshold or threshold range for the three published water indices and CEM. For a fair
comparison, we adopted the following strategy: first, determine the total number of water pixels from
the reference image, denoted as N; second, sort the resulting image (images in Figure 5) in descending
order and mark the first N pixels as water (images in Figure 6). To extract the whole water area for CEM
and OWCEM, we selected the larger value from the results of the blue and green water for each pixel;
finally, the ROC curves and Kappa coefficients of all algorithms were generated.
Water 2015, 7 804
Figure 5. The results of MNDWI, AWEI
nsh
, AWEI
sh
, CEM, and OWCEM for blue and green
water for the Hala Lake image. (a) True colour image; (b) MNDWI; (c) AWEI
nsh
;
(d) AWEI
sh
; (e) CEM (blue water); (f) CEM (green water); (g) OWCEM (blue water); and
(h) OWCEM (green water).
The final water extraction maps for all methods are shown in Figure 6. A visual comparison indicates
that OWCEM produces a better accuracy of water mapping than the water indices and CEM. Only the
ice/snow areas are extracted by MNDWI, AWEI
nsh
, and AWEI
sh
, as shown in Figure 6b–d. The central
part of Hala Lake is missed by CEM, and some ice/snow and cloud areas are extracted by CEM. This is
because when extracting blue water, the CEM output shows a higher value in those cloudy and ice/snow
areas than those in blue water areas (Figure 5e). OWCEM can extract the complete Hala Lake, and some
small ponds and rivers around, but no ice/snow or cloudy areas. However, due to the acquisition time
difference (refer to Table 2), there does exist some omissions on small rivers and ponds. For example,
the long river across the reference image from the upper-left to the lower-right has not been extracted
completely by OWCEM. The corresponding zoom-in images are shown in Figure 7. The reason for this
is that the river water was partially frozen at the acquisition time for the Hala Lake image. Yet, those
Water 2015, 7 805
areas are small, so the Kappa coefficient (see Table 3) is still very high for OWCEM (0.9647).
The Kappa coefficients of MNDWI, AWEInsh and AWEIsh are negative, because no water, but only
ice/snow and cloud were extracted. The ROC curves of the five methods are shown in Figure 8. It can
be seen that the overall performance of OWCEM is better than that for the other four methods. It yields
closely to the (0, 1) of the ROC space, representing OWCEM as an almost perfect classifier.
(a) (b)
(c) (d)
(e) (f)
Figure 6. Comparison of water extraction results of the five algorithms for Hala Lake image:
(a) Reference data; (b) MNDWI; (c) AWEInsh; (d) AWEIsh; (e) CEM; (f) OWCEM.
Water 2015, 7 806
Figure 7. Comparison of a subarea of a river in the Hala Lake image between the reference
and OWCEM result.
Table 3. The kappa coefficients of the five algorithms for Hala and Lake Huron images.
Classifier MNDWI AWEInsh AWEIsh CEM OWCEM
Hala Lake −0.0076 −0.0152 −0.0145 0.4744 0.9647
Lake Huron 0.9843 0.9843 0.9772 0.8473 0.9928
Figure 8. The ROC curves of the five methods for the Hala Lake image.
4.2. Lake Huron
Unlike Hala Lake, Huron Lake occupies the majority of the Landsat 8 image (about 76.4%),
as shown in Figure 1b. In this image, no ice/snow pixels exist. However, thin clouds present on most
Water 2015, 7 807
lake areas, and some thick clouds appear on the land area (Figure 1b). Most parts of the lake are blue,
even when covered by thin cloud. The water at the shore areas appears light green. The signatures of
blue and green water selected for d are shown in Figure 9.
(a) (b)
Figure 9. The spectral curves of blue (a) and green (b) water for the Lake Huron image.
The results of the five algorithms are presented in Figure 10. Comparatively speaking, the result of
OWCEM shows the strongest contrast between the blue/green water and the background, especially for
the blue water. For MNDWI, AWEI
nsh
, and AWEI
sh
, their combinations of bands have also enhanced
the cloud area above land (see Figure 10b–d)). The CEM result for blue water has the worst contrast
effect, because blue water in this image is not a “small target” and only the 7 original bands were used.
(a) (b)
(c) (d)
Figure 10. Cont.
Water 2015, 7 808
(e) (f)
(g) (h)
Figure 10. The results of MNDWI, AWEInsh, AWEIsh, CEM, and OWCEM for blue water
and OWCEM for green water in the Lake Huron image: (a) True color image;
(b) MNDWI; (c) AEWInsh; (d) AWEIsh; (e) CEM (blue); (f) CEM (green); (g) OWCEM
(blue); and (h) OWCEM (green).
The water extraction procedure is the same as that for Hala Lake, and the results are shown in
Figure 11. MNDWI, AWEInsh, and AWEIsh have all missed some water areas covered by thicker cloud,
but extracted some land areas with thick clouds (Figure 12c–e). CEM has the worst performance. Both
cloud and cloud shadow areas on the land part have been extracted by CEM (Figure 12f). In addition,
some water areas near the bank have been missed. The water area extracted by OWCEM is much more
complete and even the water areas covered by light cloud have been extracted. However, water covered
by very thick cloud cannot be extracted by OWCEM either (Figure 12g). The kappa coefficients of the
five algorithms are tabulated in Table 3. OWCEM has the highest value (0.9928) while CEM has the
lowest (0.8473). The ROC curves are shown in Figure 13. The performance of MNDWI is very close to
that of OWCEM. Overall, OWCEM still performs best, even though the percentage of water is very
large in the image. To further investigate the influence of target size on CEM, we applied CEM to the
14-channel data. The corresponding kappa coefficient became even lower (0.3290), which again indicates
that CEM has poor performance for a large size targets, and may perform worse when more data is added.
The main reason for this is that the autocorrelation matrix R of this image used in the CEM detector mostly
represents the statistical information on water, not the background. By introducing a weight when
constructing the autocorrelation matrix, OWCEM has no limit on target size.
Water 2015, 7 809
Figure 11. Comparison of water extraction results of the five algorithms for the Lake
Huron image. Areas in circles indicate the missing water areas. (a) Reference data;
(b) MNDWI; (c) AWEInsh; (d) AWEIsh; (e) CEM; and (f) OWCEM.
Water 2015, 7 810
(c) (d) (e)
(f) (g)
Figure 12. Details of water extraction results using the five algorithms for the Lake
Huron image: (a) True colour image; (b) reference; (c) MNDWI; (d) AWEI
nsh
; (e) AWEI
sh
;
(f) CEM; and (g) OWCEM.
Figure 13. The ROC curves of the five algorithms for the Lake Huron image.
Water 2015, 7 811
4.3. Analysis on Correlation between Channels
The above results on the two lakes indicate that adding water index and spectral similarity metric
channels in OWCEM can greatly improve the accuracy of water mapping. Tables 4 and 5 tabulate the
correlation coefficients between the 7 additional channels and all 14 channels used in the Hala Lake and
Lake Huron images. We find that the correlation coefficients between the water indices, and the
correlation coefficients between corr, SAD, and SID are high. Also, the d channel has a high correlation
with the VNIR (visible and near-infrared) bands. To assess the influence of the channel correlation to
the result of OWCEM, we conducted a comparison study by adding (1) a zero mean Gaussian distributed
random noise with a standard deviation of one, denoted as n1; (2) an existing channel disturbed by a
small Gaussian distributed random noise with a mean of zero and a standard deviation of 0.0001, denoted
as n2; and (3) a water index/spectral similarity metric.
Table 4. The correlation coefficient matrix for the data set used in the Hala Lake image.
Channel MNDWI MAWEInsh MAWEIsh corr SAD d SID n1 MADWI +
n2
Corr +
n2
B1 0.8092 0.7894 0.6789 0.7224 −0.7271 0.9281 −0.5889 −0.0003 0.8092 0.7224
B2 0.8028 0.7821 0.6678 0.7107 −0.7214 0.9365 −0.5873 −0.0003 0.8028 0.7107
B3 0.7612 0.7349 0.6100 0.6526 −0.6973 0.9624 −0.5815 −0.0003 0.7612 0.6526
B4 0.7027 0.6726 0.5408 0.5797 −0.6578 0.9755 −0.5622 −0.0003 0.7027 0.5797
B5 0.5568 0.5293 0.3927 0.4341 −0.5592 0.9773 −0.4983 −0.0002 0.5568 0.4341
B6 −0.4072 −0.4587 −0.4006 −0.4457 0.0447 0.3687 −0.1337 −0.0001 −0.4072 −0.4457
B7 −0.3466 −0.4085 −0.3409 −0.3981 −0.0032 0.4068 −0.1828 −0.0001 −0.3466 −0.3981
MNDWI 1.0000 0.9934 0.9380 0.9135 −0.8212 0.6131 −0.6612 −0.0002 1.0000 0.9135
MAWEInsh 0.9934 1.0000 0.9430 0.9179 −0.7834 0.5758 −0.6059 −0.0002 0.9934 0.9179
MAWEIsh 0.9380 0.9430 1.0000 0.8907 −0.7662 0.4877 −0.6228 −0.0003 0.9380 0.8907
Corr 0.9135 0.9179 0.8907 1.0000 −0.7217 0.5031 −0.5101 −0.0002 0.9135 1.0000
SAD −0.8212 −0.7834 −0.7662 −0.7217 1.0000 −0.6286 0.9010 0.0002 −0.8212 −0.7217
d 0.6131 0.5758 0.4877 0.5031 −0.6286 1.0000 −0.5740 −0.0003 0.6131 0.5031
SID −0.6612 −0.6059 −0.6228 −0.5101 0.9010 −0.5740 1.0000 0.0002 −0.6612 −0.5101
Table 5. The correlation coefficient matrix for the data set used in the Lake Huron image.
Channel MNDWI MAWEInsh MAWEIsh Corr SAD d SID n1 MNDWI
+ n2
Corr +
n2
B1 −0.1217 −0.1842 −0.1519 −0.1056 −0.0199 0.8368 −0.0299 −0.0001 −0.1217 −0.1056
B2 −0.1539 −0.2128 −0.1824 −0.1368 0.0046 0.8543 −0.0015 −0.0001 −0.1539 −0.1368
B3 −0.3625 −0.3824 −0.3705 −0.3655 0.2165 0.9321 0.2241 0.0001 −0.3625 −0.3655
B4 −0.3316 −0.3677 −0.3371 −0.3445 0.1875 0.9282 0.1787 0.0000 −0.3316 −0.3445
B5 −0.8559 −0.7331 −0.7715 −0.8981 0.8484 0.7830 0.8754 0.0004 −0.8559 −0.8981
B6 −0.7625 −0.6909 −0.6890 −0.8210 0.7032 0.9015 0.7106 0.0004 −0.7624 −0.8210
B7 −0.6181 −0.5957 −0.5680 −0.6761 0.5204 0.9464 0.5097 0.0002 −0.6181 −0.6761
MNDWI 1.0000 0.9547 0.9690 0.8948 −0.8303 −0.5075 −0.8658 −0.0005 1.0000 0.8948
MAWEInsh 0.9547 1.0000 0.9851 0.7579 −0.6469 −0.4524 −0.6802 −0.0004 0.9547 0.7579
MAWEIsh 0.9690 0.9851 1.0000 0.7743 −0.6782 −0.4427 −0.7359 −0.0005 0.9690 0.7743
Corr 0.8948 0.7579 0.7743 1.0000 −0.9578 −0.5923 −0.9322 −0.0005 0.8948 1.0000
SAD −0.8303 −0.6469 −0.6782 −0.9578 1.0000 0.4879 0.9730 0.0005 −0.8303 −0.9578
d −0.5075 −0.4524 −0.4427 −0.5923 0.4879 1.0000 0.4676 0.0002 −0.5075 −0.5923
SID −0.8658 −0.6802 −0.7359 −0.9322 0.9730 0.4676 1.0000 0.0005 −0.8658 −0.9322
Water 2015, 7 812
The resulting kappa coefficients are listed in Table 6. Though n1 has very low correlation with the
other channels (see Tables 4 and 5), the kappa coefficient is not increased when added. This is a
consequence of the fact that n1 contains little useful information. On the other hand, adding MNDWI +
n2 and corr + n2, which are highly correlated with MNDWI and corr, respectively, will be of no benefit
in improving performance either, because those channels have no extra information. However, when the
other water index/spectral similarity metric channel is added, the kappa coefficient increased, as shown
in Table 6. For example, adding d can further increase the kappa coefficient, although it has a high
correlation with the VNIR bands. Therefore, only adding data with extra useful information can improve
the performance of OWCEM. This useful information is derived from people’s physical understanding
of the target. For example, the water indices added in this paper contain people’s empirical knowledge
about the spectral characteristics of the water.
Table 6. The kappa coefficients for different combinations of channels used in OWCEM.
Data used for OWCEM Hala Lake Lake Huron
7 Landsat bands, MNDWI 0.8024 0.9428
7 Landsat bands, MNDWI, n1 0.8024 0.9428
7 Landsat bands, MNDWI, MNDWI + n20.8022 0.9427
7 Landsat bands, MNDWI, MAWEIsh 0.9638 0.9761
7 Landsat bands, MNDWI, MAWEIsh, d 0.9640 0.9916
7 Landsat bands, corr 0.5505 0.9907
7 Landsat bands, corr, n1 0.5500 0.9907
7 Landsat bands, corr, corr + n2 0.5501 0.9907
7 Landsat bands, corr, SAD 0.9263 0.9927
5. Discussion and Perspectives
From the results at Hala and Huron Lakes, we find that water indices are more sensitive to ice/snow
while CEM is more sensitive to cloud. OWCEM has a better suppression effect on both snow/ice and
clouds. From the spectral curves of water and ice/snow, it can be observed that the SWIR bands of both
water and ice/snow have a lower reflectance compared to the VIS and NIR bands. Thus, to some extent,
there does exist some similarity between water and ice/snow. However, ice/snow has a much higher
reflectance value than water. Therefore, adding Euclidean distance data could help OWCEM to
distinguish water from ice/snow. The spectral signature for thin cloud is much more complicated, which
usually varies as the ground objects below change. Therefore, it is hard to say which specific additional
channel plays a more important role for OWCEM to suppress cloud. We think all additional channels make
some contribution. For example, from Figures 5 and 10 we can see that both MNDWI and AWEInsh have
a better suppression effect on cloud than CEM, although this is not particularly obvious.
Another advantage of our algorithm is that OWCEM is less sensitive to the selection for d than CEM.
Both OWCEM and CEM use the same pixels for calculating ds, but CEM has missed some water areas
in results of both lakes (see Figures 6e and 11e). This implies that a target pixel with a slightly different
signature in shape or value from the desired signature d may be considered as an undesirable or
background pixel by CEM. However, the situation for OWCEM is much better. This is because the
additional water indices can enhance the information for all water types, thus lowering the impact caused
Water 2015, 7 813
by the spectral differences in the original bands between waters. In practical applications, the most
representative water samples should be selected for OWCEM for better performance.
Therefore, regardless of the distribution of the target, the main advantage for OWCEM outperforming
CEM is the added channels. Suitable additional data could help OWCEM to avoid the drawbacks of
CEM in many aspects. From the above analysis, we can conclude that data which both reflects the
common characteristics of various water types and that highlights the difference between water to
background should be included in OWCEM. In this study, we only show one combination of added
channels, and the result is encouraging. Thus, other useful information could also be tried in the future,
such as shape information, texture, etc.
OWCEM is a supervised classifier, which requires water training samples as input. In fact, the ground
truth maps are generated using the support vector machine (SVM) classifier by selecting samples for 11
level-1 and 28 level-2 land cover types, including water, ice, snow and clouds, etc. From the comparison
results between OWCEM and the reference maps, we can see that the performance of our algorithm is
comparable to that of SVM. However, OWCEM requires much less prior knowledge on samples, which
could therefore save a lot of time in sample selection and adjustment. Moreover, OWCEM outputs are
also suitable for the classification of water types by setting a different d value for different kinds of
water. Taking Hala Lake as an example, by classifying the water types by choosing a larger OWCEM
value, we can get a water-type map of Hala Lake, as shown in Figure 14.
Figure 14. The classification result of Hala Lake by OWCEM.
In addition, it should be pointed out here that the water map in Figures 6 and 11 are extracted by the
new strategy to achieve a fair comparison. However, people tend to use threshold segmentation or other
classifiers for further water extraction. Here, we computed two different indices, the separability index
(SI) [42] and the Jeffries–Matusita (J–M) distance, to measure the degree of separation between the
target and the background. From Figure 15, we can see that OWCEM has the highest value in both
indices, which indicates that water and non-water area are more easily separable with the OWCEM result
than with the other four. The values from OWCEM usually range between −1 and 1. The threshold value
can be determined automatically or manually. Through multiple tries, we found that OWCEM could
achieve a stable threshold range. For these two tests, the suitable threshold is around 0.3.
Water 2015, 7 814
Figure 15. The SI and J–M distance of the five algorithms.
6. Conclusions
The OWCEM developed in this research can deal with a targets having a large probability
distribution. Compared to water indices and CEM, our new algorithm can achieve a consistent
performance with considerably improved accuracy even when ice/snow and/or clouds exist. Our
algorithm is also suitable for other multi-band images. The process used in this study can be regarded as
a standard procedure for applying a CEM-derived or CEM-similar hyperspectral target detection
algorithms from multispectral imagery. Moreover, besides water, other ground objects with unique
signatures, such as green vegetation and urban objects, could also be extracted in the same way.
Acknowledgments
Co-funding of the project leading to these results by the National Basic Research Program of China
(973 Program) under Grant Number 2015CB953701 is kindly acknowledged.
Author Contributions
Luyan Ji: Primary researcher and writer of the research publication; Xiurui Geng, Kang Sun, and
Peng Gong: Technical expertise to the research publication; Yongchao Zhao: Landsat 8 image
atmospheric correction software developer.
Conflicts of Interest
The authors declare no conflict of interest.
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