Hyperspectral image unmixing over benthic habitats
Miguel Vélez-Reyes*, Samuel Rosario, Enid M. Alvira, and James A. Goodman
Laboratory for Applied Remote Sensing and Image Processing
Center for Subsurface Sensing and Imaging Systems
University of Puerto Rico at Mayagüez, P.O. Box 9048, Mayagüez, PR 00681-9048
ABSTRACT
Benthic habitats are the different bottom environments as defined by distinct physical, geochemical, and biological
characteristics. Hyperspectral remote sensing is a remote sensing technology with great potential to map and monitor the
complex dynamics associated with estuarine and nearshore benthic habitats. Advantages of hyperspectral remote sensing
technology include both the qualitative benefits derived from a visual overview, and more importantly, the quantitative
abilities for systematic assessment and monitoring. Low spatial resolution of satellite or airborne sensors such as
HYPERION or AVIRIS requires the application of unmixing techniques for mapping or soft classification of the sea
floor bottom. Unmixing of the seafloor is complicated by the presence of the water column and variable bathymetry
which requires
Hyperspectral sensors in particular are rapidly emerging as a more complete solution, especially for the analysis of
subsurface shallow aquatic systems. The spectral detail offered by hyperspectral instruments facilitates significant
improvements in the capacity to differentiate and classify benthic habitats. This paper reviews two techniques for
mapping shallow coastal ecosystems that both combine the retrieval of water optical properties with a linear unmixing
model to obtain classifications of the seafloor. Example output using AVIRIS hyperspectral imagery of Kaneohe Bay,
Hawaii is employed to demonstrate the application potential of the two approaches and compare their respective results.
Keywords: coastal remote sensing, hyperspectral imagery, benthic habitat mapping, unmixing, bathymetry, water
optical properties
1. INTRODUCTION
Benthic habitats vary widely as a function of geographic location, environmental characteristics and water depth, and are
characterized according to their dominant structural features and biological communities. One method for classifying
benthic habitats is based upon the overlying water depth [1]: the hadal zone (over 6,000 meters deep), the abyssal zone
(2,000 to 6,000 meters), the bathyal zone (200 to 2,000 meters), and the nearshore and estuarine zones (less than 200
meters). Estuarine and nearshore benthic habitats, which could be monitored using satellite remote sensing, can be
further divided into categories such as submerged mudflats, sandflats, rocky hard-bottom habitats, seagrass beds, kelp
forests, shellfish beds, and coral reefs. These habitats support a wide diversity of marine life by providing spawning,
nursery, refuge, and foraging grounds for fisheries species. They provide an important function in nutrient cycling, as
well as contributing to the removal of contaminants from the water. Benthic organisms within these habitats are
important members of the lower food web, consuming organic matter and phytoplankton and serving as food sources for
higher-level consumers. Benthic habitats also serve as shelter, and provide storm protection by buffering wave action
along coastlines.
Knowledge of seafloor habitats is necessary for the development and implementation of resource management policies
[1]. For instance, benthic habitat mapping provides a means to both identify essential fish habitat and to characterize it in
the context of the larger seafloor for determining the most effective means for preservation. Important habitats, such as
coral reefs, can be monitored over time using benthic mapping techniques that facilitates effective management and
preservation of these ecosystems. Benthic habitat mapping is also a useful tool for determining the effects of habitat
change due to natural or human impacts.
*
Corresponding Author
Remote sensing is an increasingly important tool for evaluating the complex spatial dynamics associated with estuarine
and nearshore benthic habitats. Large-scale mapping applications typically rely on the visual interpretation of aerial
photographs and multispectral imagery (e.g., NOAA mapping of shallow habitats in U.S. marine environments [2,3]) or
on more complex image analysis techniques using multispectral satellite data (e.g., NASA-sponsored global Millennium
Coral Reef Mapping Project [4]). Results of these efforts represent significant improvements over previously available
large-scale map resources. However, because of the immense scope of each project, the maps still have limitations with
respect to small-scale resource assessment. For instance, individual reefs are described according to general categories
and spatially explicit quantitative habitat information is limited. In contrast with such multispectral approaches,
hyperspectral instruments provide much greater spectral detail, and thus an improved ability to extract a greater amount
of information from an optically complex environment. Hyperspectral remote sensing has been utilized to retrieve
information of coastal environments such as coastal optical water properties and constituents [5,6,7,8,9], benthic habitat
composition [10,11,12], and bathymetry [13,14]. Additionally, more complex modeling schemes based of physical
approaches have also been used to simultaneously retrieve multiple layers of information from a single image
[15,16,17,18,19,20,21,25]. Essentially, the spectral detail offered by hyperspectral instruments facilitates significant
improvements in the capacity to differentiate and classify benthic habitats.
Figure 1: Changes in Rrs as a function of water depth for a sand bottom and phytoplankton chlorophyll content: (a) with a
phytoplankton chlorophyll content of 0.01 mg/m3 and (b) with a phytoplankton chlorophyll content of 2.0 mg/m3. Signatures
calculated using HYDROLIGHT 4.1 [Sequoia Scientific, Inc].
Unmixing of hyperspectral imagery is based on the linear mixing model, which is commonly used to unmix
hyperspectral imagery over land. When trying to unmix hyperspectral imagery to determine benthic habitat composition,
we are confronted with the spatially variant optical properties of the water column and variable bathymetry, which
introduce additional distortion to the bottom endmember signature that needs to be removed. Figure 1 show the effects of
bathymetry and phytoplankton chlorophyll content in the remote sensing reflectace (more later), Rrs, for sand. This
paper compares two closely related hyperspectral unmixing analysis techniques for benthic habitats, developed by
Goodman [25,26,27] and Castrodad [20,21], that can be used for mapping of shallow coastal ecosystems. The
approaches are both based on Lee’s semianalytical model [23,24], with expanded linear mixing to model bottom
reflectance. Both approaches propose different methodologies for simultaneous retrieval of the bathymetry, optical
properties, and abundance fractions for the bottom composition.
The paper is organized as follows. First, Lee’s bio-optical model and his approach for retrieval of optical properties and
bathymetry for shallow waters is summarized. Second, Goodman’s approach is described, which combines the optical
parameters retrieved using Lee’s method with a linear unmixing variable endmember approach to estimate bottom
fractional composition. Although the three basic bottom endmembers are constant throught the image (coral, seagrass
and sand) their apparent surface reflectance representation accounts for the pixel bathymetry and optical properties
which are spatially variant. Third, Castrodad’s approach is described, which is a nonlinear optimization approach that
simultaneously retrieve the optical properties, the bathymetry, and the abundances at each pixel. As we shall see in the
experimental results, using AVIRIS data over Kaneohe Bay in Hawaii, the nonlinear optimization approach seems to
capture better some of the spatial features of the endmember distribution at the bottom however with a significantly
higher computational complexity.
2. BACKGROUND
2.1. Lee’s semianalytical bio-optical model
Remote sensing reflectance, Rrs, is an AOP defined as the ratio of the water leaving radiance, Lw(), to downwelling
irradiance incident on the water surface, Ed(). Rrs is a function of the absorption, a(λ), volume scattering, β(λ), bottom
albedo, ρ(λ), bottom depth, H, subsurface zenith angle, θw, subsurface viewing angle from nadir, θ, viewing azimuth
angle from the solar plane, φ, and the constituents in the water. Thus, Rrs can be expressed as a function of these
parameters:
R rs λ  
L w λ 
 f a λ , βλ , ρλ , H, θ w , θ, 
E d λ 
(1)
where λ represents wavelength. The model for Rrs proposed by Lee in [23,24] is given by:
R rs 
0.5r rs
1  1.5r rs
(2)
where rrs is the subsurface remote-sensing reflectance, which is the ratio of the upwelling radiance to the downwelling
irradiance evaluated just below the surface given by:




D C  
D B  
1
  1

  1

rrs  rrs dp 1  exp  
 u  κH    Bρexp  
 u  κH 








cos

cos

π
cos

cos



 
w
w

 
 
 
  






(3)
BottomContribution
WaterColumn Contribution
where B is the bottom albedo at 550 nm, ρ is a representative bottom albedo normalized to one at 550 nm, and rrsdp is
the remote-sensing reflectance for optically deep waters given by:
rrs dp  (0.084  0.170u )u
DuC and DuB are the optical path-elongation factors for scattered photons from the water column given by:
DuC  1.03(1  2.4u )0.5 DuB  1.05(1  5.5u )0.5
and
u  bb  a  bb 
  a+bb
The total absorption coefficient, a, is the sum of the absorption of pure water, aw, the gelbstoff absorption, ag, and the
phytoplankton absorption, a:
a  a w  aφ  a g
where
a g  G exp  0.014  440 and a   a0    a1   ln P P
G is the gelbstoff absorption coefficient at 440 nm, and P is the phytoplankton absorption coefficient at 440 nm.
The total backscattering coefficient, bb, is given by:
bb  bbw  bbp
where bbw is the backscattering coefficient of pure water and bbp is the backscattering coefficient of suspended particles,
which are defined as:
Y
 400  and
 400 
b bp  BP 
b bw  0.0038


 λ 
 λ 
4.3
BP is a combined coefficient accounting for particle backscattering, view angle and sea state, and Y is the parameter
describing the spectral shape, varying from 0 to 2.5, given by:
Y  3.44 1  3.17 exp  2.01Rrs (440) / Rrs (490) 
The explicit dependence of all these terms on wavelength is dropped for notational convenience.
2.2. Lee’s retrieval algorithm for optical properties and bathymetry
The model proposed by Lee [23,24] is parameterized by the parameters P, G, BP, B and H. Estimates of these
parameters are obtained by solving the nonlinear least squares estimation problem:
γˆ Lee  arg min
ˆ γ, ρ 
R rs  R
rs
sand
γ
where
R rs
2
(4)
2
2
2
  [ P, B, G, BP, H ]T , Rrs  R rs λ1  R rs λ 2   R rs λ m T is the measured remote sensing reflectance,


ˆ  R̂ λ  R̂ λ   R̂ λ  T is the model estimated remote sensing reflectance,
R
rs
rs 1
rs 2
rs m
ρsand is a sand spectral
2
signature normalized to one at 550 nm, and a 2   a i2 refers to the Euclidean norm or the square root of the squared
i
summation of components of vector a. We refer to this approach as Lee’s Inversion (LI).
2.3. Goodman’s retrieval algorithm for benthic mapping (LIGU)
Using LI to obtain optical properties and bathymetry, Goodman [25,26,27] proposed modeling remote sensing
reflectance as a linear mixing of the surface contributions of coral, algae, and sand as follows:
3
ˆ rs   x i R rs γˆ Lee , ρi 
R
i 1
where R rs γˆ Lee , ρ i  is the bottom i-th endmember corresponding remote sensing reflectance computed using the
optical parameters and bathymetry estimates
γ̂ Lee computed using (4) for the given pixel. In computing R rs γˆ Lee , ρ i  ,
B = 1 and the endmember reflectance spectra are not normalized. The abundance estimates are obtained by solving a
surface linear unmixing problem:
xˆ  arg minT
x 0 , x 11
3
2
i 1
2
R rs   x i R rs γˆ Lee , ρi 
R rs
(5)
2
2
The abundance fractions need to satisfy a positivity and sum-to-one constraint as shown in (5). This abundance
estimation problem is easily solved using any of several methods for abundance estimation described in the literature.
The resulting two stage approach proposed by Goodman [25,26,27], where water optical properties are estimated first by
solving (4) and bottom composition is then determined through unmixing by solving (5), is denoted in the rest of the
paper as LIGU (Lee’s Inversion with Goodman’s Unmixing).
2.4. Castrodad’s combined inversion and unmixing algorithm for benthic mapping
The joint estimation of optical properties, bathymetry and abundances using a nonlinear iterative procedure was
proposed in [20,21]. The method builds on LIGU by iteratively refining estimates of the optical properties and
abundance fractions. Furthermore, the method takes advantage of the fact that by working with the subsurface remote
sensing reflectance, rrs(), defined in (3), instead of the remote sensing reflectance, Rrs(), as in LIGU, the resulting
estimation problem is partially linear in the unmixing coefficients and nonlinear in the optical properties. That structure
has certain computational advantages as we shall see later. From (2), we can convert Rrs to rrs using:
rrs 
R rs
0.5  1.5R rs
The bottom albedo is modeled as a linear mixture of coral, sand, and algae, defined by:
=Ax
(6)
where A=[sand, coral, sea grass], with the reflectance signatures are normalized to one at 550 nm. The water optical
properties, bathymetry, albedo at 550 nm, and the abundances are estimated simultaneously by solving the nonlinear
least squares optimization problem:
γˆ , xˆ   arg
where
rrs  rˆrs γ, Ax  2
2
min
γ, x 0 , x T 11
rˆrs γ, ρ  is computed using (3) with  given by (6).
rrs
2
(7)
2
The least squares problem (7) has the particular structure of being linear in the abundances, x, while nonlinear in the
optical properties and bathymetry, . This type of nonlinear least squares problem is known as partially linear, for which
efficient solution methods are proposed in the literature [28,29]. The method used in [20, 21] is a simple two-stage
Gauss-Seidel iteration as follows:
Initialization Step: Compute the initial estimate of the of the optical properties and reflectance at 550nm,
using Lee’s method (4).
Iterate until convergence

Compute the left hand side of the unmixing model using:
b

( i)
j
 rrs  r̂rs
dp (i)
C (i) 

  1

D̂ u


(i)
(i)  


1

exp


κ̂
Ĥ




 cos(θ w ) cosθ 0 





Compute the endmember matrix
A(i)  T(i) A
where T is a diagonal matrix with entries
t
(i)
jj
B (i)
  1
D̂ u  (i) (i) 
1 (i)

 κ̂ Ĥ 
 B̂ exp  

π
cos(θ
)
cos(θo


w
 

and A is the endmember matrix given in (6).

Compute the abundance estimate solving the unmixing problem:
γ̂ ( 0 ) ,
xˆ (i 1)  arg minT
x0 ,x 11
b (i)  A (i) x
2
2

ˆ
Update the bottom albedo ρ

Update the optical properties, bathymetry, and bottom albedo at 550 nm by solving:
(i 1)
 Axˆ (i 1)
γˆ (i 1)  arg min
γ

rrs  rˆrs γ, ρˆ (i1)
rrs

2
2
2
2
End of iteration loop
Notice that this algorithm simultaneously estimates the optical properties, bottom albedo at 550 nm, bathymetry and the
bottom abundances, such that as new estimates of water column properties become available they are used to further
refine the bottom albedo, and vice versa. Although this algorithm can be considered an improvement over previous
approaches, the main drawback is that it is much slower (as described in [30]) than LIGU and other approaches.
Speeding up this method is a subject of current work. For discussion purposes, we refer to this algorithm as the
Combined Inversion and Unmixing at the Bottom (CIUB).
3. EXPERIMENTAL RESULTS
In this section, AVIRIS data is used to illustrate results and compare the two algorithms. The AVIRIS data was extracted
from a hyperspectral image of Kaneohe Bay, Hawaii. Additionally, bathymetry data collected using the Scanning
Hydrographic Operational Airborne LIDAR Survey (SHOALS) system is available for the same area to use for
evaluating bathymetry estimates from LIGU (and LI by definition) and CIUB.
Previous work using Lee’s model [23,24,25,26,27] provided upper and lower bounds used for constraining the
estimation, as given in Table 1. An error tolerance of 10-10, or a maximum number of 1000 iterations, were selected as
the stopping criteria for the CIUB nonlinear optimization routine.
Table 1: Bounds used in the LIGU and CIUB optimization procedures.
H
BP
G
P
Lower Bound
0.2
0.001
0.002
0.05
Upper Bound
33
0.5
3.5
1
0.6
Sand
Coral
0.5
Algae
Reflectance
0.4
0.3
0.2
0.1
0.0
400
450
500
550
600
650
700
Wavelength (nm)
Figure 2: Average endmember spectra for Kaneohe Bay in Hawaii [25,26,27].
The hyperspectral AVIRIS data used for validation was first preprocessed using atmospheric and sunglint corrections. It
was atmospherically corrected using Tafkaa [25,32], and was sunglint corrected with a 750 nm normalizing correction
described in [24]. Of the original 224 band AVIRIS image from 370-2500 nm, the Lee model (LI) utilizes 38 bands in
the ranges 400-675 nm and 720-800 nm for estimating water properties and bathymetry. However, due to strong light
attenuation affecting wavelengths larger than 675 nm, the LIGU and CIUB algorithms compute the abundance estimates
using only data in the range from 400-675 nm.
For purposes of spectral unmixing, three endmembers are considered: sand, coral and algae. The endmember spectra
were collected in situ from Kaneohe Bay, Hawaii [25,26,27]. These spectra were measured with a modified GER-1500
spectrometer contained within a custom underwater housing. Figure 2 shows the average measured reflectance
signatures for each of the three endmembers. The abundance vector estimate, x̂ , for these endmembers was obtained
using a Nonnegative Sum to One algorithm (NNSTO) described in [30,31], where the abundance fractions must sum to
one and must be individually equal to or greater than zero.
A small 50x50 pixel portion of the AVIRIS image of Kaneohe Bay was used to test the algorithms. Water depth
estimates from the SHOALS survey were available and compared to the bathymetry estimates obtained with the
estimation algorithms. However, there is no way of knowing the exact values for B, BP, G and P because they were not
measured at the time of the AVIRIS data acquisition. As a result, the agreement of the depth estimates with SHOALS
measurements is the primary measure of the retrieval accuracy for both algorithms.
3.1. Remote Sensing Reflectance Estimation
Figure 3 shows RGB composites of the measured AVIRIS Rrs compared with estimated Rrs using LIGU and CIUB. The
estimated Rrs from CIUB, Fig. 2(c), appears qualitatively more similar to the calibrated AVIRIS image, Fig. 2(a), than
that retrieved using LIGU, Fig. 2(b).
(a)
(b)
(c)
Figure 3: RGB composite of apparent reflectance data (R=703nm, G=539nm, B=500nm): (a) AVIRIS Image, (b) LIGU, (c) CIUB.
(a)
(b)
(c)
Figure 4: Bathymetry and bathymetry estimates (in meters): (a) SHOALS, (b) estimate from LIGU, (c) estimate from CIUB.
(a) m=0.8891; b=0.4694
(b) m=0.9806; b=0.2892
Figure 5: Scatter plots of depth estimates against SHOAL bathymetry (in meters): (a) LIGU, (b) CIUB.
Figure 6: Comparison of average error in depth estimates by LIGU and CIUB as a function of depth.
3.2. Bathymetry Estimates
Plots of SHOAL retrieved bathymetry and bathymetry estimates from LIGU and CIUP are shown in Figure 4. These
figures show close agreement with the SHOALS data, with the best agreement for shallow water depths. For better
comparison, the scatter plots of the measured SHOALS data versus the estimated H and quantified using a linear
regression are shown in Figure 5. The average error as a function of depth is shown in Figure 6. From these plots, we
can see that CIUB has lower error for depths below 7m. For higher depths, LIGU results in better estimated. This seems
reasonable at higher depth the water attenuates the bottom signature making it less observable. Since CIUB has a larger
number of bottom parameters, which at those depths are relatively unobservable, the retrieval of depth using Lee’s
method in LIGU results in a better estimate since it has fewer parameters.
An additional visualization comparing the SHOALS measurements and model estimates is shown in Figures 7 and 8
where the histograms for the errors for the two approaches are plotted. Notice that CIUB error histogram has a lower
mean and lower variance, which may imply that the algorithm has an overall better performance. However, there is some
indication in Figure 4 that the LIGU algorithm performs better at deeper depths than the CIUB approach. Further
evaluation is required to better evaluate the overall performance of both approaches.
(a) Mean=-0.4030; Variance=2.9698 (in meters)
(b) Mean=0.3385; Variance=2.3367 (in meters)
Figure 7: Depth error histograms: (a) LIGU, (b) CIUB.
CIUB
LIGU
Below 5 meters
Above 5 meters
Figure 8: Histograms comparing bathymetry estimates for depths below and above 5 meters.
(a)
(b)
Figure 6: Abundance estimates RGB color maps of (a)LIGU, (b) CIUB
3.3. Abundance Estimates
To facilitate visualization of the abundance estimates, an RGB composite using an approach described in [25] is created.
The red band corresponds to coral abundance, the green to algae, and the blue to sand. The RGB composite for the
abundance estimates derived in each algorithm is shown in Figure 6. For comparison, Figure 7 shows circles
highlighting areas of interest in the AVIRIS Rrs RGB. The yellow ovals highlight sand areas, the red ovals highlight
coral and the purple oval highlights algae. Additionally, Figure 8 illustrates the individual abundance maps obtained by
both procedures. From a qualitative analysis, CIUB estimates appear to exhibit better performance in the highlighted
areas. However, further quantitative analysis is again needed to confirm this conclusion using imagery with more
extensive knowledge of specific benthic habitat characteristics.
Figure 7: Remote sensing reflectance RGB of AVIRIS dataset.
LIGU Sand
LIGU Coral
LIGU Algae
(a)
(b)
(c)
CIUB Sand
CIUB Coral
CIUB Algae
(d)
(e)
(f)
Figure 8: Abundance Estimates for: (a,b,c) LIGU and (d,e,f) CIUB.
4.
SUMMARY
This paper presented two approaches for combining the retrieval of water column optical properties, bathymetry and
fractional coverage for benthic habitat mapping. The newest approach, CIUB, is based on subsurface remote sensing
reflectance and takes advantage of the partially linear structure of the models proposed by Lee [23,24] and Goodman
[25,26,27] to propose a simple iterative method for simultaneously computing the estimates. The algorithm was tested
with both simulated and real hyperspectral imagery. It was found that the model has the disadvantage of extended
processing speed as compared with the LIGU approach. Nevertheless, results generally demonstrated strong model
performance at shallow depths, but also indicated limitations as a function of increasing depth and turbidity. Ongoing
work is focusing on both improving the computational efficiency of this approach as well as evaluating its performance
using additional hyperspectral imagery.
ACKNOWLEDGEMENTS
This work was primarily supported by the Engineering Research Center Program of the National Science Foundation
under Award Number EEC-9986821. Partial support was also received from the NASA University Research Centers
Program under grant NCC5-518.
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