(1)
This paper investigates the use of polarimetric
information extracted from SIR-C/X-SAR complex images for crop
discrimination. The test site is the Bebedouro Hydrology super
site in Brazil. In addition to the widely used absolute values
of complex channels (amplitude), another two channels, modulus
and phase from complex correlation coefficient between HH and
VV complex channels, were also investigated. The phase of the
correlation coefficient is a smoothed version of phase difference
information between HH and VV, and was used in lieu of it. Five
classes; corn, soya beans, stubble, bare soil and a regional savanna
type named "caatinga" were defined. To assess the discrimination
power of the extracted features, confusion matrix of maximum likelihood
and Jeffreys-Matusita distance were calculated. Results showed
that phase information can greatly improve the classification
accuracy and the modulus of correlation coefficient also carries
discrimination power.
The objective of this report is to evaluate the
performance of SIR-C L-band polarimetric information for crop
classification in a semi-arid irrigated region in northeast Brazil.
Amplitude and extracted channels using modulus and phase from
complex correlation coefficient were used. Section 2 describes
the features used, section 3 briefly describes the site and material,
section 4, methodology, section 5 presents the results and conclusions
follow on section 6.
In this section we introduce two features for information
extraction used: phase difference and complex correlation coefficient.
2.1 Phase Difference
The phase difference (hh - vv) between the two co-polarized
channels is calculated by
(1)
where 
and 
indicate the real and imaginary parts, respectively. Shh
and Svv are obtained from the scattering matrix
(co-polarized complex scattering components). Phase differences
can also be calculated between cross-polarized channels.
2.2 Complex correlation coefficient
The complex correlation coefficient between the
co-polarized elements of the Stokes matrix is calculated as:
(2)
from which one can obtain the magnitude and the phase.
This definition can also be extended to the cross-polarized channels.
The study area includes the "Projeto de Irrigação
de Bebedouro (PIB)", a SIR-C/X-SAR Supersite situated at
the region of the "Sub-médio São Francisco
(907'S, 4018'WGr)", about 40 km Northeast from Petrolina,
Pernambuco state [2].
3.1 Site description
The "PIB" is divided in 2 parts , "PIB I" and "PIB II", with total area about 3500 ha and 2000 ha, respectively. "PIB I" is constituted by small properties from 5 to 12 ha, large areas owned by private enterprises, natural vegetation reserve areas and small residence centers. "PIB II" has an area belonging to private enterprises and another for Basic Seeds Production Service of EMBRAPA, the Brazilian Agronomic Research Institute.
In this study we focus on "PIB II" area, specifically the region composed by 4 central pivots with classes of corn, soya beans, stubble and bare soil, plus the natural savanna ("caatinga") class.
At the time of the SIR-C/X-SAR overpasses (imagery
acquisition), the region was surveyed and a fully agronomic characterization
of crops was accomplished.
3.2 Images parameters
Images were acquired by the Space Shuttle SIR-C/X-SAR
mission in April 1994. Table I shows image parameters used in
this study, acquired on April, 13.
Table I - Image parameters
| Frequency | L(1.254 GHz) C(5.304 GHz) |
| Polarization | HH, HV, VV, VH |
| Incidence angle | 37.97 |
| Platform altitude | 219.38 Km |
| Orbital direction | descending |
| Number of looks | 16 looks |
| Geometric representation | Ground range |
| Pixel space | rg 12.5m / az 12.5m |
As mentioned previously only L-band complex images in three polarizations (HH, HV, VV), were investigated in this study. Figure 2 shows an image in HH-polarization from the study area along with the analyzed classes. Table II presents the number of samples and number of pixels dor each class.
Figure 2 - L Band, HH polarization, classes : 1 -
corn, 2 - soya beans, 3 - stubble, 4 - bare soil, 5 - "caatinga"
Table II - Study classes, numer of samples and pixels
|
| |
| corn | 2 | 6245 |
| soya beans | 2 | 6635 |
| stubble | 1 | 1498 |
| bare soil | 1 | 5592 |
| "caatinga" | 4 | 5245 |
We investigated the following combinations to assess
the discrimination power of the extracted features:
It is considered here that these features follow a joint gaussian distribution due to high number of looks of the original channel and the averaging process involved in correlation coefficient computation. Even the phase, for high values of correlation coefficient, can be approximately considered gaussian, because in this case, all phase histograms were relatively narrow and entirely included into [-p,p] range around the mode, as in [3].
The evaluation of the contribution of these channels
combinations for crop discrimination is made in two ways :
4.1. Maximum Likelihood Classification
The most common supervised classification, the Maximum likelihood classification method ([4] [5]), is used to classify the training areas of the study classes.
The average performance, AP, average abstention
AA, and average confusion, AC, given by AC = 1-(AP+AA), were derived
from the confusion matrix calculated for each set of channels.
AP is calculated using the population weighted average of the
corrected classification index for each class (main diagonal of
the confusion matrix). Similar procedure was used for AP calculation
using index data over abstention column.
4.2. J-M Distance
The Jeffries-Matusita distance between a pair of
probability distributions is defined as [6]
(3)
where 
and 
are the conditional probabilities density functions (pdf) of the
ith and jth class distributions. For normally distributed
classes equation (3) becomes
(4)
in which
(5)
The JM distance can be used for measuring the separability
of a fixed set of channels and a given set of classes; or can
be used for a chosen subset of channels, also considering a fixed
set of classes. If the set has more than two classes, one can
choose the best subset either by maximizing the average JM distance
between a pair of classes, or by maximizing the minimum distance
between some pair of classes, for each set of channels.
5.1. Classification
The three amplitude bands corresponding to HH, HV
and VV polarization will be called original channels. Average
performance (AP) of 61.4%, (see Table III), and an average confusion
of 38.6% was obtained using maximum likelihood classification
of this original data. Average abstention (AA) in this table and
in the next ones was null because the classification threshold
was fixed to classify all points. Considering the classes individually
one can notice that bare soil class had a result of 89.21%, higher
than the AP, on the other hand, soya beans class had a result
of 34.05%, well under average, confused almost in the same proportion
between stubble and "caatinga" classes. This behavior
is due to the fact that the average tone value of these classes
where quite close as it can be depicted from Table IV. The other
classes showed results close to the average performance.
Table III - Confusion Matrix using HH, HV e VV Amplitude
| true
classified | soya beans | ||||
| corn |
65.56 % | 8.12 % | 14.46 % | 1.32 % | 10.52 % |
| soya beans | 6.86 % | 34.05 % | 29.14 % | 9.60 % | 20.32 % |
| stubble | 5.80 % | 8.41 % | 65.02 % | 19.75 % | 1.00 % |
| bare soil | 1.00 % | 0.59 % | 9.17 % | 89.21 % | 0.01 % |
| caatinga | 9.28 % | 25.07 % | 6.93 % | 0.57 % | 58.13 % |
Average performance (AP) : 61.4 %
Average confusion (AC) : 38.6 %
Table IV- Average tone means and Standard deviation for HH, VV and HV channels.
| HH | 0.3453 | 0.2514 | 0.2104 | 0.1363 | 0.2864 | |
| 0.1129 | 0.1012 | 0.0718 | 0.0539 | 0.0832 | ||
| HV | 0.1116 | 0.1022 | 0.0642 | 0.0336 | 0.1449 | |
| 0.0328 | 0.0425 | 0.0212 | 0.0133 | 0.0440 | ||
| VV | 0.4074 | 0.2207 | 0.2078 | 0.1524 | 0.2598 | |
| 0.1422 | 0.0809 | 0.0924 | 0.0606 | 0.0783 |
Table V shows the classification result when using
modulus and angle of complex correlation coefficient. Average
performance improves, in comparison to the previous classification,
from 61.4% to 69.1%. Corn and soya beans classification accuracy
also improved, from 65.5% to 87% and from 34% to 45.8%, respectively.
The main factor in improving the separability of corn class is
the phase difference between HH and VV (around 
, see Table VI).
Table V - Confusion Matrix using the modulus and angle of complex correlation coefficient
true classified |
| ||||
| corn |
87.00 % | 9.37 % | 0.19 % | 0.00 % | 3.42 % |
| soya beans | 1
2.76 % | 45.89 % | 6.61 % | 0.22 % | 34.50 % |
| stubble | 0.06 % | 0.00 % | 60.08 % | 29.17 % | 10.68 % |
| bare soil | 0.00 % | 0.00 % | 12.41 % | 87.41 % | 0.17 % |
| caatinga | 3.20 % | 22.36 % | 17.21 % | 0.01 % | 57.19 % |
Average performance (AP) : 69.1 %
Average confusion (AC) : 30.9 %
The behavior of modulus of complex correlation is
also very different in this case. Soya beans showed a reduction
in confusion in relation to stubble, but increased in relation
to "caatinga". This result can be explained by the classes
average when using the modulus of the complex correlation coefficient
(see Table VI), in this case the average of soya beans (=0.2556)
differentiates from stubble (=0.6239), which is diverse from the
previous case. Stubble class reduced the performance in 5% and
increased the confusion with bare soil in 10%. "Caatinga"
class kept the same performance index, but reduced the confusion
with corn class and increased in relation to the stubble class,
as said above. Although some isolated results were not satisfactory,
the use of combination of these extracted features from the polarimetric
data improved the overall classification. HV channel was not used
in this case.
Table VI- Average and Standard deviation of the Modulus and angle of complex correlation coefficient
| Modulus | 0.4590 | 0.2556 | 0.6239 | 0.7897 | 0.3126 | |
| 0.1397 | 0.1313 | 0.1359 | 0.0823 | 0.1431 | ||
| Angle | -1.6939 | -0.4557 | 0.1430 | 0.1608 | -.0074 | |
| 0.5418 | 1.3094 | 0.2523 | 0.1351 | 0.8240 |
The use of all bands, original and extracted, improved
the classification performance for all classes, as shown in Table
VII. An improvement of 18.1% in relation to the first classification
and of 10.4% in relation to the second was observed, regarding
AP.
Table VII - Confusion Matrix using all channels together: HH, HV,VV, Modulus and angle of the complex correlation coefficient
| true
classes | soya beans | ||||
| corn |
87.15 % | 10.09 % | 0.46 % | 0.00 % | 2.27 % |
| soya beans | 7.59 % | 66.19 % | 5.66 % | 0.11 % | 20.43 % |
| stubble | 0.20 % | 2.46 % | 83.51 % | 12.28 % | 1.53 % |
| bare soil | 0.05 % | 0.00 % | 7.42 % | 92.47 % | 0.05 % |
| caatinga | 2.32 % | 22.45 % | 4.38 % | 0.00 % | 70.82 % |
Average performance : 79.5 %
Average confusion : 20.5 %
Corn class performance held the same index that
obtained in the second classification, while soya beans and stubble
classes improved by about 20% and bare soil and "caatinga"
classes by about 5% and 13% respectively. The confusion between
soya beans and "caatinga" kept the same index observed
in the first classification.
5.2 Distance between distributions
JM distance was calculated for each set of channels
mentioned in the previous section. Table VIII shows minimum and
average JM distances in the analysis of each set of channels separately.
The result of this analysis confirm the ones obtained previously.
As an additional way to measure the relative importance
of the features used here, JM distance was used to select the
best 3 channels out from all 5. Table IX shows all possible combinations
of 3 channels considering all defined classes. The combinations
of the angle of complex correlation coefficient with pairs of
amplitude (HH and HV), (HH and VV) and (HV and VV), that are selections
4, 5 and 6 of Table IX, showed the best performances.
Table VIII - Minimum and average JM Distance
| HH, HV, VV
Amplitude | Modulus and angle compl. cor. coef. | HH,HV,VV Amplitude
Modulus and angle compl. correl. coef. | |
| JM min | 0.364460 | 0.568256 | 0.673633 |
| JM ave | 0.895871 | 1.06852 | 1.31420 |
Table IX - minimum and average JM Distance of 5 bands in combinations from 3 to 3
| JM min | JM ave | ||
| B1/B2/B3 | 0.60 | 1.12 | |
| B1/B2/B4 | 0.57 | 1.16 | |
| B1/B2/B5 | 0.57 | 1.13 | |
| B1/B3/B4 | 0.63 | 1.18 | |
| B1/B3/B5 | 0.59 | 1.20 | |
| B1/B4/B5 | 0.57 | 1.19 | |
| B2/B3/B4 | 0.33 | 0.74 | |
| B2/B3/B5 | 0.24 | 0.75 | |
| B2/B4/B5 | 0.17 | 0.79 | |
| B3/B4/B5 | 0.36 | 0.89 | |
| B1 - Angle of the complex correlation coefficient | |||
| B2 - Modulus of the complex correlation coefficient | |||
| B3 - HH Amplitude | |||
| B4 - HV Amplitude | |||
| B5 - VV Amplitude | |||
Table X - Classification average performance
| |
| HH, HV, VV Amplitude +
Modulus and angle of the complex correlation coefficient |
|
| Angle of the complex correlation coefficient
HV, VV Amplitude | |
| Angle of the complex correlation coefficient
HH, HV Amplitude | |
| Modulus and angle of the complex correlation coefficient | |
| Angle of the complex correlation coefficient
HH, VV Amplitude | |
| HH, HV, VV Amplitude |
It was also performed classifications using these
3 sets of features and the results are shown in Table X, as well
as the results of classifications achieved previously. One notes
that in Table X all combinations with angle showed higher average
performance compared to the combination of the amplitude channels
only.
It was shown that the phase information (between HH and VV) can distinctly improve the discrimination, such that phase information should not be, a priori, discarded in the classification process when using complex polarimetric data.
Modulus of correlation channel can also improve separability, as was observed with respect of classes soya beans and stubble.
Further studies using other features extracted from
complex polarimetric data will be made and tested in other sites
with distinct type of classes.
This work was partially supported by the Projeto Temático CNPq Geotec (Process No. 680.061/940).
The authors would also like to thank Mr. Iedo B.
de Sá and Gilberto Cordeiro from EMBRAPA for their very
valuable logistic help.
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[4] K. Fukunaga, "Introduction to Statistical Pattern Recognition", Academic Press, Inc., 1990.
[5] N.D.A. Mascarenhas e F.R.D.Velasco, "Processamento Digital de Imagens," IV EBAI 1989.
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