Transcript No Slide Title

Subsurface Object Recognition by Means of Regularization Techniques
for Mapping Coastal Waters Floor
Luis O. Jiménez-Rodríguez 1, Alejandra Umaña-Díaz2, Jose Díaz-Santos3, Gerardino Neira-Carolina4, Javier Morales-Morales5, Eladio Rodriguez6
University of Puerto Rico Mayagüez Campus
Abstract
Problem Formulation
A fundamental challenge to Remote Sensing is mapping the ocean floor in coastal shallow waters where variability,
due to the interaction between the coast and the sea, can bring significant disparity in the optical properties of the
water column. The objects to be detected, coral reefs, sands and submerged aquatic vegetation, have weak signals,
with temporal and spatial variation. In real scenarios the absorption and backscattering coefficients have spatial
variation due to different sources of variability (river discharge, different depths of shallow waters, water currents) and
temporal fluctuations. This paper presents the development of algorithms for retrieving information and its application
to the recognition, classification and mapping of objects under coastal shallow waters. A mathematical model that
simplifies the radiative transfer equation was used to quantify the interaction between the object of interest, the
medium and the sensor. The retrieval of information requires the development of mathematical models and
processing tools in the area of inversion, image reconstruction and detection. The algorithms developed were applied
to one set of remotely sensed data: a high resolution HYPERION hyperspectral imagery. An inverse problem arises
as this spectral data is used for mapping the ocean shallow waters floor. Tikhonov method of regularization was used
in the inversion process to estimate the bottom albedo of the ocean floor using a priori information in the form of
stored spectral signatures, previously measured, of objects of interest, such as sand, corals, and sea grass.
La Parguera
Forward Model – Matrix Form
 b1    rrs 1   S col 1   a
b   r    S    11
col
2 
 2   rs 2
0
  .
 .  
.
b  AP  


 
.
.
  .

 
  .
 .  
.


 
bd  rrs d   S col d   0


  s, Z 
ds
s
where J(z) is a source function. The term is the medium transmittance from level s=0 to level s=Z, and defined as:
2
 0
P(i)
Preg(i)
2
2
rrs
dp
 0.084 0.170u u
b
u
ab
where rrs is the subsurface remote sensing reflectance, w is solar zenith angle,  is the bottom albedo, H is the
bottom depth, a is the absorption coefficient and b is the backscattering coefficient, the last two being wavelength
dependent. The signal the sensor receives is what is known as above-surface remote sensing reflectance (Rrs) and is
related to the subsurface remote sensing reflectance by:
0.5rrs
Rrs 
1  1.5rrs
(a)

Define Eki() as the error for every pixel after inverting the kth pixel in the imagery at each  for
the albedo of the ith spectral signature as:
 opt
ki






2
[email protected], tel. (787) 832-4040 x3248,
aUmañ[email protected], tel. (787) 834-7620 x2295
3 [email protected], tel. (787) 832-4040 x2295
4 [email protected], tel. (787) 832-4040 x2295
5 [email protected], tel. (787) 832-4040 x2295
6 [email protected]
2
Future Work
Further development and tuning of this algorithm. It will be applied to the case of one object of interest versus an
unknown background. Addition of spatial information.
Adaptation and application to Bio-Med Testbed will be in place.
References
[1]
[2]
1
[3]
0.5
[4]
[5]
0
0
0.1
0.2
opt(ki)
0.3
0.4
0.5

0.6
0.7
0.8
0.9
1
Figure 2. Choosing the optimum value opt(ki) from the set [0, 1).
1
As can be observed the data was well analyzed even on the conditions of lack of precise knowledge of the parameters
of the shallow ocean waters. The incorporation of physics-based models plus the fusion of a priori information in the
forms of store signatures about the solution increases the detection performance of objects of interests under shallow
coastal waters. The use of a methodology that incorporates a priori information increases classification accuracy when
compared to methodologies that do not.
2
where Preg(k) is the regularized pixel k , and P0(i) is the a priori estimate of the ith signal without
the medium, which are calibrated stored spectral signatures. The optimum opt(ki) for kth pixel
and ith signal will be selected
 as point of maximum curvature of the error function Eki(), defined
1.5
as:



Eki  

 arg max
3
i

 2


1

E



ki
 

The resulting stored spectral signature approach P0(i) and regularization parameter is obtained
by:
 opt ( k )  arg min Eik  opt ( ki)  
i
(c)
Conclusion
Selecting the Regularization Parameter by minimizing the Euclidean
Distance
E ki    Preg k  P0i
(b)
Figure 4. Ikonos imagery (a), classification using the spectral signatures without inversion (b), classification after inversion and regularization (c).
Figure 1. Relation between the parameter , the regularized albedo Preg and the stored spectral signature P0.
Thus, this model depends on the following variables H, w, , a and b. The bottom albedo () is the quantity we want
to attain after the inversion process.
CONTACT:
(a)
Figure 3. Hyperion imagery (a), classification using the spectral signatures without inversion (b), classification after inversion and regularization (c).

P0(i)
 1
Eik()

  1
 1
  1

C
B


rrs  r 1  exp 
 Du  kH    exp 
 Du  kH 


cos(

)

cos(

)
w
w
 
 
 
 

dp
rs
k  ab
Sea Reef
Wate
r

Selection of the regularization parameter
where (r) is the extinction coefficient.
A semi-analytical model based on the RTE was used to mathematically represent the propagation of the signal
through the medium. The model used was proposed by Lee in [3, 4]. In this model the signal received by the sensor
is represented as:
and
Carbona
te Sand
P0 represents the spectral signature of an object of interest (spectral signatures of coral reefs,

2
pollution plume, sand, grass, etc.). For computational purposes 2 has been expressed as  
1 
with   0,1.
Z
  s, Z   exp     r dr 
 s

DuB  1.041  5.4u 
Sea Grass
(Thalasia)
Preg  (At A  2I)1 (At b  2P0 )
The radiance received by a spaceborne or airborne instrument looking at nadir at an altitude of Z (km) is described by
the RTE for plane parallel atmospheres as stated by Lenoble [1] is given by:
rrs  0.084 0.170u u
2
Preg  arg min AP  b 2   2 P  P0
Radiative Transfer Equation (RTE)
0.5
2
1
Inverse problem solution using Tikhonov regularization can be expressed as:
or
dp
2
The data to be analyzed was gathered using
Hyperion sensor and IKONOS sensor.
Data was calibrated and atmospheric corrected
using ACORN.
In the case of Hyperion imagery we choose the
fifteen most independent bands using the SVDSS
feature selection method [2].
3
where P is the least square solution.
This formulation is often used when the problem is overdetermined, meaning that A   mxn
with m > n. In this case m = n as a consequence the least square problem can be stated as
P = A-1b. Yet, this formulation does not account for the uncertainties (H, w, a and b) present in
the problem.
The goal of this research is to analyze the spectral signals to retrieve
information
content
through
inversion
methods,
feature
extraction/dimensional reduction and the detection/classification methods in
hyperspectral data analysis under conditions of lack of precise knowledge of
medium parameters, i.e. absorption and scattering properties of water, along
with absorption and scattering of chlorophyll, organic material and
suspended sediment present in the medium. This will improve the detection
of objects embedded in highly complex medium.
o
0
0
.
.
  1




B
 Du  kH  meanwhile S col  rrs dp 1  exp  1  Du C  kH  
where aii  exp 


 
  
  cos( w )
  cos( w )

is the water column contribution at i wavelength. Our interest is to estimate (i) from the
measured Rrs.
Goal
with,
.
0
P  arg min AP  b
L Z   L (0)  0, Z    J  s 
   1  
   2 


 . 
 . 



.  . 
... add     
d 

0 ...
a22 ...
.
.
Spaceborne Multispectral and Hyperspectral
Data
La Parguera is in the southwest coast of Puerto Rico
in the municipality of Lajas.
1
Inverse Problem
Z
Experimental Results
[6]
[7]
Lenoble, J., Atmospheric radiative transfer. A. Deepak Publishing, 1993.
Vélez M., Jiménez L. “Subset Selection Analysis for the Reduction of Hyperspectral Imagery”, Geoscience and Remote Sensing Symposium
Proceedings, 1998. IGARSS '98. IEEE International Volume 3, pp 1577 -1581, 1998.
Zhongping, L., Carder, C., Mobley, C., Steward, R., Patch, J., “Hyperspectral remote sensing for shallow waters: 1. A semianalytical model” Applied
Optics, vol. 37, No.27, September 20 1998, pp. 6329-6338.
Zhongping, L., Carder, C., Mobley, C., Steward, R., Patch, J., “Hyperspectral remote sensing for
shallow waters: 2. Deriving bottom depths and water properties by optimization” Applied Optics, vol. 38 No18, June 20 1999,
pp. 3831-3843.
Jimenez, L.O., Rodriguez-Díaz, E., Velez-Reyes, M., DiMarzio, C., ”Image Reconstruction and Subsurface Detection by the Application of Tikhonov
Regularization to Inverse Problems in Hyperspectral Images, ” SPIE Asia-Pacific, Hangzhou China, October 2002.
Rodriguez-Díaz, E., Jimenez-Rodriguez, L.O., Velez-Reyes, M., "Subsurface Detection of Coral Reefs in Shallow Waters using Hyperspectral Data,”
SPIE AeroSense 2003, Orlando, Florida, April 2003.
Jimenez, L.O., Umaña-Díaz, A., Díaz-Santos, J., Geradino-Neira, C., Morales-Morales, J., Rodriguez, Díaz, E., “Subsurface
Object Recognition
by Means of Regularization Techniques for Mapping Coastal Waters Floor, ” SPIE Europe, Bruges, Belgium, September 2005.
Acknowledgments
This project was partially supported by the Engineering Research Centers Program of the National Science Foundation under
Award # EEC-9986821
The authors want to acknowledge Dr. James Goodman who works at LARSIP, University of Puerto Rico at Mayaguez for
providing the calibrated store signatures.