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Contextual classification with IRS LISS-II imagery
PHOTOGRAMMETRY & REMOTESENSING ELSEVIER
ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
Contextual classification with IRS LISS-II imagery Ravi Shankar Thakur, Onkar Dikshit * Department of Civil Engineering, Indian Institute of Technology, Kanpur-208016India
Received 10 February 1996; accepted 7 August 1996
Abstract A non-linear probabilistic relaxation contextual algorithm has been used to improve the classification results of the Gaussian maximum likelihood (GML) classifier. The research has been conducted at two study sites. The first is the Singrauli mines area in the Sidhi district and the second is the Bhopal city area, both in the state of Madhya Pradesh (India). IRS LISS-II data, with a spatial resolution of 36.25 m and radiometric resolution of 7 bits per pixel, have been used for the research. The GML classification has been performed with bands 1 (0.45-0.52/zm), 3 (0.62-0.68/xm), and 4 (0.77-0.86/zm). The overall classification accuracy for the 6-class GML classification for the Singrauli site was 90.70%. For the Bhopal site, the 5-class GML classification accuracy was 91.46%. When the non-linear probabilistic relaxation contextual algorithm with two different forms of compatibility coefficients was applied to this initial classification from the GML classifier, the overall classification accuracies after 20 iterations improved to 94.36 and 94.58% for compatibility coefficients based on correlation and mutual information, respectively, for the Singrauli site. For the Bhopal site the improvements were 94.98 and 92.39%, respectively, The overall classification accuracies with contextual information with both forms of compatibility coefficient were found to be statistically significantly different from and better than the GML classification for the Singrauli site. However, for the Bhopal site this was true only when the correlation based compatibility coefficient was used. Keywords: context; probabilistic relaxation; muitispectral classification
1. Introduction The conventional per-pixel classifiers do not incorporate spatial information from an image, which is very important for a visual recognition system. In practice, per-pixel classifiers often achieve far from perfect classification (Gurney and Townshend, 1983). In order to improve classification accuracy it is important to use information not only from individual pixels, but from its spatial domain also. The spatial information is usually subdivided into two * Corresponding author.
types: texture and contexture. Texture refers to the description of variability of grey level values found within part of a scene. Various measures of texture have been successfully applied (Haralick, 1979; Gool et al., 1985; Dikshit, 1992). The context of a pixel (or a group of pixels) refers to its spatial relationship with pixels in the remainder of the scene. The rationale underlying the incorporation of contextual information into the classification process is the presence of positive autocorrelation among pixels (Mather, 1990). An excellent survey of context typology has been given by Gurney and Townshend (1983).
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R. Shankar Thakur, O. Dikshit/ ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
Various attempts have been made to incorporate context in computer classification (Kettig and Landgrebe, 1976; Harris, 1985; Kittler and Foglein, 1986; Haralick and Joo, 1986). With the availability of high-resolution remotely sensed images, the spatial relationship between pixels will play an increasingly important role, and hence contextual classification will be helpful. A context classifier is characterized by the fact that it classifies an unknown pixel using the entire context of the image or a substantially sized context neighbouring the pixel. As a result of incorporation of contextual information, a pixel's most probable interpretation, when viewed in isolation, is likely to change. Hence, contextual algorithms attempt to reduce uncertainty in labelling by: (a) examining the local neighbourhood of each pixel to produce locally consistent labels, and (b) using statistical information on the label relationship present in the whole image. The present research has attempted to estimate the extent to which the application of one of the widely used contextual algorithms - - non-linear probabilistic relaxation - - improves the classification of remotely sensed digital imagery.
2. Objective The investigations in this paper have been motivated by the hypothesis that the classification accuracy of remotely sensed imagery, using the Gaussian maximum likelihood (GML) classifier, can be improved by incorporating additional contextual information. Based on this hypothesis, the objective of this paper is first, to classify the test site imagery using the GML classifier and then to use the nonlinear probabilistic relaxation algorithm to evaluate the extent to which it improves the classification accuracy.
3. Overview of data resources, study sites and methodology The research has been conducted on two study sites. The first is the Singrauli mines area in the Sidhi district and the second is the Bhopal city area, both in Madhya Pradesh (India). The four-band Linear Imaging Self Scanning (LISS-II) data from
93
Indian Remote Sensing Satellite (IRS) have been used for the research. The IRS LISS-II camera operates in four wavelength bands (0.45-0.52, 0.52-0.59, 0.62-0.68, and 0.77-0.86 #m) with a spatial resolution of 36.25 m and a radiometric resolution of 7 bits per pixel. To delineate training and test areas, topographic maps at 1 : 50,000 scale have been used along with field visits. The basic approach used in the research is to apply two levels of classification strategies, one by the classical per-pixel GML classifier and the second by the pixel-based contextual reclassifier using non-linear probabilistic relaxation, on study site images and to generate classification products. These products are then compared with the test areas to compute classification accuracies.
4. Theoretical background The GML classifier is one of the most widely used supervised per-pixel classifiers which assumes a Gaussian probability distribution of class parameters. In this classifier a set of normalized probability values, Pi ()~kIX), are calculated for each pixel vector X, one for each class )~k. The normalized probability for a pixel ai to get the class label )~k is given by the following equation: P/(Xklx) =
p( Xl~.k) P(,kk)
M
(1)
E p(XI)~j)P().j) j=l where M is the total number of classes, P()-k) the a priori probability of class )~k and p(Xl).k) the probability density function for class )~k, which is given by 1 p(XlZk) = (2zr)a/2lExk ll/2
× [exp ( - I ( X -
]z).t) t E~.~1 ( x -
"~.k))]
(2)
where d is the number of spectral bands, •xk and/zx, are covariance matrix and mean vector, respectively, for class )~k, Z~I is the inverse of the covariance matrix for class Zk and ] • ] is the determinant of a matrix. When the GML classifier is applied, a set of normalized probability values are calculated for each pixel vector X, one normalized probability value for each specified class. This pixel is then allocated
R. Shankar Thakur, O. Dikshit / lSPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
94
to the class which has the maximum normalized probability value for that pixel. The probabilistic relaxation model attempts to reduce the uncertainty of labelling in a two-fold manner (Harris, 1985): (i) by examining the local neighbourhood of each pixel to produce a locally consistent label, (ii) by using statistical information on the label interrelationship present in the whole image. The relaxation involves a set of pixels A = a l , a2, a3, . . . , aN and a set of classes A = ~-1, ~-2, ~-3. . . . . ~.M. For each pixel ai, w e have a set of local measurements which are used to estimate the probabilities Pi ()~j) of pixel ai having label )~j. These probabilities satisfy the following equation (Hsiao and Sawchuk, 1989): M
Z
Pi(~'J) = 1
Vai E A; 0 <_ Pi(~.j) < 1
(3)
j=l
Generally a 3 x 3 neighbourhood has been used in updating the probabilities which represents a set of eight-connected neighbours of the pixel under consideration (Peleg and Rosenfeld, 1978). The normalized probabilities calculated by Eq. (1) are used as the initial probabilities, PiO(~.k). Hence
Pi°(~.k) = Pi(LklX)
(6)
The compatibility coefficients are computed only for neighbouring pixel pairs and are assumed to be zero for non-neighbouring pixel pairs. So for an eight-connected neighbour, there will be nine compatibility coefficient matrices (8 for neighbours, one for itself). The two popular ways of computing compatibility coefficients are based on correlation and mutual information (Peleg and Rosenfeld, 1978). The compatibility coefficient based on correlation has the following form: ri,i+~ (~.j, ~'k) :
These probabilities are updated using a set of compatibility coefficients ri,i+8(~.j, ~'k) where rij : AxA---> [-1, 1] and (1) ri,i+t~(~.j, ~'k) > 0; if classes )~j and )~k are compatible for pixel ai and ai+8, respectively. (2) ri,i+~(Lj, ~,k) < 0; if classes )~j and Lk are incompatible for pixel ai and ai+8, respectively. (3) ri,i+~().j, )~k) -=" 0; if neither labelling is constrained by other. (4) The magnitude of ri,i+8(~ j, ~.k) represents the strength of compatibility. Afterwards, the probabilities are updated by using the following updating rule: p/m (~.k)[1 + qm (~-k)] M
PiY+l (3"k) =
(4)
1
N
~_~ [PI(Xj) - -f(~.j)][Pi+8(~,k) -- P'(~-k)] i
cr(Lj)cr()~k)
where Pi (~.j) is the initial estimate of the probability of labelling pixel ai with )~j, P()~j) is the average of Pi(Lj) for all pixels and ~r(Lj) is the standard deviation of P/()~j). The ideal compatibility coefficient matrix should be symmetric. Rosenfeld et al. (1976) proposed a compatibility coefficient based on mutual information. An estimate of mutual information, that is the contribution of )~k to the information about ~j, can be expressed as Ii,i+8().k, ).j) = In -~
P/~ (~j)[1 d- q?(Lj)]
-~
P(~.k) P(3.j)
j=l
where
(7)
;
8~ A
(8)
where P(Lk) is the probability of any pixel having label )~k and P/.~+8(Lk.Zi) is the joint probability of a pair of pixels having labels Zk and )~j. These quantities can be computed by the following equations: ^
M
qm(Xk) = Z ~EA
di+8 E
ri,i+8(~.k,~.j)P~+8(Xj)
(5)
j=l
and m is the iteration number, d~+8 the set of neighbour weights that can be used to give different neighbours different degrees of influence in the neighbourhood function, i + 8 the specific neighbour of a given pixel ai at location i, and A the neighbourhood about the particular pixel being considered.
?(xk) = ~1 ~.= piO(~.k) 1
N
i'i,,+8(Zk, Z~) = ~ ~
i=1
(9)
P°(Zk)P°÷8(Zj)
(10)
R. Shankar Thakur, O. Dikshit /1SPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
95
Extreme values of the coefficient from Eq. (8) result only when one of the events involved is extremely rare. Therefore, events that cause
(i) The sum of absolute probability differences should become small after a few iterations, i.e.
~,i+8(Xk, Xj). k(xk)k(zj) '
i~A
36 A
(11)
to be outside the range [e -5, e +5] should be ignored. Thus the values of Ii.i+~(Xk,Xj) can be considered to lie in the range [-5, 5] and the compatibility coefficient based on mutual information is defined as ri,i+8()~k ' ~.j) -~. gli, 1 i+8(~k, ~.j) =
i=~
N
i-----I
VX ~ A (14)
(ii) The final probabilities should not be too far away on the average from initial ones. Therefore, convergence of the process to an arbitrary set of final probabilities unrelated to initial ones is not desirable. Thus the following equation should be satisfied: lea
N E PiO~k)Pi+,(Xj) N
threshold1;
E [Pim(x) - P/°(X)[ < threshold2; YX E A
N
In
y ~ IP7(X) - Pm+l(Z)l <
(12)
(15)
(iii) The entropy of probabilistic classification after applying relaxation should be less than the entropy of the initial ones, i.e.
i=l
which lies in the range [ - 1, 1]. There are two main approaches of implementing relaxation-based contextual classification. The first one is proposed by Rosenfeld et al. (1976) and the second is by Peleg (1980). In the present work, the first approach has been used. Therefore, the step-bystep procedure for only this method is described below. (1) By using the mutual information coefficients as the compatibility coefficients and an 8-connected neighbourhood, calculate ri.i+8(Xk, ~'j). These coefficients are fixed throughout the iteration process. For this step use Eqs. (8)-(12). (2) With the initial labelling probabilities for each pixel and compatibility coefficients, the process can be iterated using the updating factor given by Eq. (5). For an 8-connected neighbourhood with equal weights to all neighbouring pixels, this equation takes the following form: 1
M
q'~(~.D = E -8 E ri'i+a(~'k'XJ)Pim+'s()~'i) SEA
-
P/m( )ln m(Z) < iEA
¥)~ ~ A
(16)
In Eqs. (18) and (19), threshold1 and threshold2 represent user-specified threshold values. The results of classification are compared by using the khat index, x, which is the proportion of agreement after chance agreement is removed from consideration. It is given by the following formula (Bishop et al., 1975): M
j=l
(3) The updating factor is then used to compute, p/m+l (Xk) by using Eq. (4) (4) Steps (2)-(3) are repeated until the stopping criterion is met. (5) The final pixel classification is the maximum probability class for each pixel. There are several ways for evaluating the relaxation iteration performance and their termination conditions (Hsiao and Sawchuk, 1989):
M
NE P0 -
~c -- - 1 -
Pc
p~
Yii-E i=1
-
Yi+'Y+i i=1
(17)
M
N 2 -- E
Yi+" Y+i
i=1
where
P0
is
proportion
of
agreement
Po = i Y ~ I Yii), Pc proportion of chance agree1
(13)
P ? a ) l n P?(Z);
iEA
M
ment (pc = ~ ~ i = i Y/+ • Y+i), Yij is an element in the M x M confusion matrix with M classes, Yi+ is the row marginal total (Yi+ = ~ = 1 Yij), g+j the
•
(
)
column marginal total Y+J = Y~4 t Yq • and N Is the total number of elements in the confusion matrix M
M
y,
For an individual class, the khat index is given by the following equation (Bishop et al., 1975):
xi =
Pii -- Pi+ " P+i Pi+ -- pi+ " P+i
=
N Y i i -- Yi+ " g+i N Y i + -- Yi+ • Y+i
(18)
R. Shankar Thakur, O. Dikshit / ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
96
The khat index is used to perform a pairwise test of significance using the normal curve deviation to determine if two confusion matrices are significantly different. The test statistic for this purpose is given by (Congalton et al., 1983; Congalton and Mead, 1986): Z
=
xa -
(19)
xb
~//O'2[ga] -.[--(T2tKb]
where Z is the test statistic for testing significant difference in large samples, Ka and rb are khat indices for two error matrices a and b, and trz~[Xa] and cr2[xb] are asymptotic variances for the corresponding khat indices. For the overall classification and an individual class these are given by Eqs. (20) and (21), respectively. tr2[x] = (01(1
2(1
- 01) +
-- 01)(20102 -- 03) (I -
i=l j=l
(20a)
M i-1 M
M
i--1 j = l M
E 2
-
i=1 M
Yi+" Y+i M
i=1 j = l
(20b)
M
E 03 ~---
E'i(Yi+ "~ Y+i)
i=1 M
M
i=1 j=X M
4=
E Y/J(Y/+ q- y+i)2 i=1 M M 3
i=1 j = l
1
(Pi+ -- Pii)
~r~[Ki] = N p~+(1
p+i) 3
[ ( P i + -- Pii)
X (Pi+" P+i -- Pii) q- Pii(1 -- Pi+ -- P+i Jr- Pii)]
(21) where (Pi+ = Yi+/N), (P+i = Y+i/N), and (Pii = Yii/N). The significance tests are based on the asymptotic normality of the khat statistic. For example, if Z exceeds 1.96 for a two-tailed test, then the difference between two classification confusion matrices is significant at the 95% probability level.
5. Experimental methodology First, the conventional GML classification is performed for the two study sites using Eq. (1). The prior probabilities of all classes have been assumed to be equal. Once the initial classification is obtained, the reclassification of the imagery is done by using the non-linear probabilistic relaxation technique under the following steps: (1) The initial normalized probabilities of each pixel for each class are computed from Bayes' theorem (Eq. 6) during GML classification by taking equal prior probabilities, P(~.i), for each class. The probabilistic updating is carried out with the help of the non-linear probabilistic relaxation model, proposed by Rosenfeld et al. (1976). Using the probabilities calculated above, the compatibility coefficients are calculated. The two compatibility coefficients - - correlation compatibility coefficients and mutual information compatibility coefficients (Eqs. 7 and 12) - - have been used here. For an 8-connected neighbour, there are nine compatibility coefficient matrices, eight for a pixel's neighbour and one for itself. The nomenclature of neighbours, used here, is given in Fig. 1. (2) The iteration for updating the probabilities is done as given in Eq. (4), with the help of the neighbourhood operator given by Eq. (13). The classification accuracies are computed over the test image at each of the 20 iterations.
6. Results and discussion By following the procedure described in Section 5, test imageries of two study sites have been classified using the GML and contextual classifiers.
R. Shankar Thakur, O. Diksh# / ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
97
j-direction
i-direction
Neighbour-1 (i = -1,j = -1) Neighbour-2 (i = -l,j -- 0)
Neighbour-3 (i = -1,j = +1)
Neighbour-4 (i = 0,j -- -1)
Nvighbour-6 (i = 0, j = +I)
N¢ighboar-5 (i -~ 0,j = 0)
N¢ighbour-7 (i = +l,j = -I) N¢ighbour-$ (i = +l,j -- 0) N¢ighbour-9 (i = +1, j ffi +1) Fig. 1. The nomenclature for an eight-connected neighbourhood. The semi-natural environment of the Singrauli area consists of six classes. These are rocky terrain, dense forest, vegetation, clear water, mine dumps and reservoir water. The urban environment of the Bhopal city area consists o f five prominent classes. These are built-up area, open scrub, marshy land, forests and lake water. The results of G M L classification using bands 1, 3, and 4 for training areas and test areas are given in Table 1. The overall classification accuracy for training areas for the Singrauli site is 96.73% and for the Bhopal site 94.40%. Most of the classes have good accuracy ( > 8 5 % ) except marshy land in the case of the Bhopal site. This is due to the fact that this class may include many mixed transition pixels between land and water. For test areas, the sites have accuracies of 90.70 and 91.46%, respectively. For contextual classification, the compatibility coefficients, based on correlation and mutual information compatibility coefficients for 8-connected neighbour, are computed using the probabilities calculated during the G M L classification. For all the nine compatibility coefficient matrices, it was observed that the diagonal matrix elements are positive and comparatively larger numbers. This is reasonable, because the chance of getting one class with
itself is greater. The coefficients for neighbour-5 (i.e. for itself) are symmetrical because it does not have any directional variation, Also, the diagonal elements for neighbour-5 of correlation coefficients are all 1. However, for all other neighbours, the matrices are not symmetric. This is attributed to pixel border effects and rounding-off errors in computation (Peleg and Rosenfeld, 1978). The classification results have been derived for 20 iterations during contextual reclassification and are given in Fig. 2. In general, the overall accuracies increase on increasing the number of iterations and this improvement follows an exponential form. This was expected, and indicates that the initial few iterations are most powerful for improving the accuracy. For the Bhopal site, however, a sudden fall in overall accuracy at iteration number 9 and a gradual fall from iteration number 17 to 20 was observed for classification with mutual information compatibility coefficient. This has been observed mainly due to decrease in accuracy of the forest class. The reason for this observation is not clear, but it is similar to an observation made by Davis et al. (1983). For individual classes, however, the accuracy of classification follows a step-like behaviour, i.e. the accuracy increases
Table 1 Classification accuracies for the GML classification Singrauli study site Class
Bhopal study site Training data
Test data
Training data
Test data
No.
Name
Pixels
% acc.
Pixels
% acc.
No.
Name
Pixels
% acc.
Pixels
% acc.
1 2 3 4 5 6
rocky terrain dense forest vegetation mine dumps reservoirwater clear water overall
104 146 175 118 112 170 825
100.00 98.63 99.43 99.15 100.00 86.47 96.73
812 559 432 427 577 493 3300
94.09 82.47 88.89 88.29 93.76 94.52 90.70
1 2 3 4 5
open scrub built-uparea marshy land forest lake water overall
216 181 144 192 177 910
96.76 94.48 78.47 99.48 98.87 94.40
953 503 642 736 689 3523
90.97 97.81 79.90 91.03 98.69 91.46
Class
98
R. Shankar Thakur, O. Dikshit/ ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
95.00 94.50
~ 94.00 ~ 93.50
- - ~ Smg-CC Sing-MI
~ 93.00
A BhopaMEC
~ 92.50
Bhopal-~
~ 92.00 91.50 91.00 ¢~
~
I'~
O~
'-~
¢~
~
I"~
~'~
Iteration Number Fig. 2. Overall accuracies for contextual classification with iterations. Sing-CC: Singrauli site classification using coefficient of correlation. Sing-MI: Singrauli site classification using coefficient of mutual information. Bhopal-CC: Bhopal site classification using coefficient of correlation. Bhopal-MI: Bhopal site classification using coefficient of mutual information.
and then remains constant for a few iterations and then again increases and then again remains constant for the next few iterations. The classification results have also been subjected to statistical testing to find whether the results are statistically significantly different from each other at the 5% significance level. Tables 2 and 3 give comparisons between different classifications. From these tables the following observations can be made: (1) Overall accuracies for contextual classifications for the Singrauli site using both correlation and mutual information compatibility coefficients are statistically significantly different from and better than classification accuracies without contextual information by using only the GML classifier. Similar observation holds for the Bhopal site with contextual classification using correlation compatibility coefficient only. The overall classification results of contextual classification using mutual information compatibility coefficient are not significantly different from GML classification without context information. (2) For the Singrauli site, results of contextual classifications using correlation and mutual information as compatibility coefficients are not statistically significantly different from each other for any of the classes and for the overall classification. However, for the Bhopal site, results for open scrub, forest and overall classification are statistically significantly different for contextual classification using both forms of compatibility coefficients.
(3) For spectrally well-defined classes like reservoir water, clear water, and lake water, the contextual classification results are not significantly different from the GML classification. The probabilistic relaxation technique is computationally complex and intensive. It requires considerable computer time and huge disk space. The HP9000/735 systems (RISC CPU at 99 Mhz (Specint92: 109, Specfp92: 168, 144 Mb RAM) take around 110 min of CPU time for a 20-iteration 6class classification for a 512 x 512 pixel image, that is, more that 5 min per iteration. However, there may be scope to make the program more efficient. In this technique, probabilities of each pixel for each class are required to be stored. For a 512 x 512 pixel image, if the probabilities are stored in double float, one file takes around 2.35 Mb of disk space and if the number of classes is 6, then the total is around 14 Mb. 7. Conclusions This research has attempted to use contextual information to improve the classification accuracy. On the basis of the results, the following conclusions have been drawn: (1) For Singrauli area imagery, the 6-class GML classifier gave an overall percentage accuracy of 90.70. When the probabilistic relaxation algorithm was applied, the overall accuracies increased to 94.36% and 94.58%, in 20 iterations, using correla-
R. Shankar Thakur, O. Dikshit/ lSPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
99
Table 2 Statistical analysis for the Singrauli study site Class no.
r¢c
trcc
tCml
~rrni
g'mi
O'mi
Zcc-ml
Zmi-ml
Zec-mi
1 2 3 4 5 6 Overall
0.9749 0.9271 0.8890 0.9069 0.9253 0.9416 0.9314
0.0063 0.0119 0.0160 0.0148 0.0118 0.0115 0.0048
0.9204 0.7941 0.8727 0.8678 0.9253 0.9324 0.8870
0.0109 0.0182 0.0170 0.0172 0.0119 0.0125 0.0061
0.9667 0.9331 0.8836 0,9306 0.9253 0.9250 0.9307
0.0072 0.0115 0.0163 0.0130 0.0118 0.0129 0.0049
4.2986 6.0881 0.6959 1.7172 0.0029 0.5423 5.6729
3.5207 6.4335 0.4606 2.9029 0.0029 -0.4121 5.5735
0.8427 -0.3638 0.2354 -1.1968 0.0000 0.9620 0.1012
x = khat index (Eqs. 17 and 18). Z = Z-statistic for hypothesis testing (Eq. 19). tr = asymptotic standard error for corresponding khat index (Eqs. 20 and 21). ml, cc, mi = subscripts indicating GML and contextual classification using correlation and mutual information coefficients, respectively.
Table 3 Statistical analysis for the Bhopal study site Class no.
rcc
trcc
g'ml
O'ml
Krni
O'mi
Zcc-ml
Zmi-ml
Zcc-mi
1 2 3 4 5 Overall
0.9376 1.0000 0.8055 0.9551 0.9963 0.9366
0.0090 0.0000 0.0167 0.0085 0.0026 0.0046
0.8862 0.9952 0.7615 0.9069 0.9926 0.9034
0.0117 0.0033 0.0180 0.0119 0.0036 0.0056
0.8490 1.0000 0.8251 0.8915 0.9963 0.9043
0.0131 0.0000 0.0162 0.0126 0.0026 0.0056
3.4653 1.4179 1.7854 3.2735 0.8190 4.5499
-2.1107 1.4179 2.6166 -0.8822 0.8190 0.1145
5,5618 0.0000 -0.8366 4.1541 0.0000 4.4392
~c = khat index (Eqs. 17 and 18). Z = Z-statistic for hypothesis testing (Eq. 19). tr = asymptotic standard error for corresponding khat index (Eqs. 20 and 21). ml, cc, mi = subscripts indicating GML and contextual classification using correlation and mutual information coefficients, respectively.
tion coefficients and mutual information coefficients, respectively. Accuracies of all classes as well as the overall accuracy increased, with the increase in number of iterations. The overall classification results are statistically significantly different and better than GML classification. For spectrally well-defined classes, the results of contextual classification are not statistically significantly different from GML classification. (2) For Bhopal area imagery, the 5-class GML classifier gave an overall percentage accuracy of 91.46. The probabilistic relaxation algorithm, while using correlation coefficients, increased the overall accuracy to a maximum of 94.98%, in 20 iterations, and is also statistically significantly different from the GML classification. However, when mutual information coefficients were used, a well-defined behaviour was not observed, with the increase in number of iterations. The overall accuracy at the end of 20th iteration is higher than, but not statistically significantly different from, the GML classification.
(3) From classification results, the correlation seems to be better than the mutual information to calculate compatibility coefficients. However, it would be premature to draw such a conclusion. For a reliable and successful use of the relaxation model, it is important to test this algorithm on various other images. (4) Despite the inherent computational complexity of the contextual algorithm based on probabilistic relaxation, it is suggested that contextual information be used on routine basis with high-resolution images having high spatial information. The processing speeds of computer hardware are continuing to increase rapidly, and particularly, the use of parallel processors will definitely decrease the computation time. References Bishop, Y.M.M., Fienberg, S.E. and Holland, P.W., 1975. Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge.
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Congalton, R.G. and Mead, R.A., 1986. A review of three discrete multivariate analysis techniques used in assessing the accuracy of remotely sensed data from error matrices. IEEE Trans. Geosci. Remote Sensing, 24(1): 169-174. Congalton, R.G., Oderwald, R.G. and Mead, R.A., 1983. Assessing Landsat classification accuracy using discrete multivariate analysis statistical techniques. Photogramm. Eng. Remote Sensing, 49(12): 1671-1678. Davis, L.S., Wang, C.Y. and Xie, H.C., 1983. An experiment in multispectral, multitemporal crop classification using relaxation techniques. Computer Vision, Graphics, and Image Processing, 23: 227-235. Dikshit, O., 1992, Classification of texture in remotely sensed environmental imagery. Ph.D. Thesis, University of Cambridge, UK. Gool, L.V., Dewaele, P. and Oosterlinck, A., 1985. Texture analysis anno 1983. Computer Vision, Graphics and Image Processing, 29: 336--357. Gurney, C.M. and Townshend, J.R.G., 1983. The use of contextual information in the classification of remotely sensed data, Photogramm. Eng. Remote Sensing, 49(1): 55--64. Haralick, R.M., 1979. Statistical and structural approaches to texture. Proc. IEEE, 67(5): 786--804. Haralick, R.M. and Joo, H., 1986. A context classifier. IEEE Trans. Geosci. Remote Sensing, 24(6): 997-1007.
Harris, R., 1985. Contextual classification post-processing of Landsat data using a probabilistic relaxation model. Int. J. Remote Sensing, 6(6): 847-866. Hsiao, J.Y. and Sawchuk, A.A., 1989. Unsupervised textured image segmentation using feature smoothing and probabilistic relaxation techniques. Computer Vision, Graphics, and Image Processing, 48: 1-21. Kettig, R.L. and Landgrebe, D.A., 1976. Classification of multispectral image data by extraction and classification of homogeneous objects. IEEE Trans. Geosci. Electronics, 14(1): 19-26. Kittler, J. and Foglein, J., 1986. On compatibility and support functions in probabilistic relaxation. Computer Vision, Graphics, and Image Processing, 34: 257-267. Mather, P.M., 1990. Theoretical problems in image classification. In: M. Steven and J.A. Clarke (Eds.), Application of Remote Sensing in Agriculture. Butterworths, London. Peleg, S., 1980. A new probabilistic relaxation scheme. IEEE Trans. Pattern Anal. Machine Intelligence, 2: 362-369. Peleg, S. and Rosenfeld, A., 1978. Determining compatibility coefficients for curve enhancement relaxation processes. IEEE Trans. Systems Man Cybern., 8(7): 548-555. Rosenfeld, A., Hummel, R.A. and Zucker, S.W., 1976. Scene labelling by relaxation operations. IEEE Trans. Systems Man Cybern., 6(6): 420--433.
ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
Contextual classification with IRS LISS-II imagery Ravi Shankar Thakur, Onkar Dikshit * Department of Civil Engineering, Indian Institute of Technology, Kanpur-208016India
Received 10 February 1996; accepted 7 August 1996
Abstract A non-linear probabilistic relaxation contextual algorithm has been used to improve the classification results of the Gaussian maximum likelihood (GML) classifier. The research has been conducted at two study sites. The first is the Singrauli mines area in the Sidhi district and the second is the Bhopal city area, both in the state of Madhya Pradesh (India). IRS LISS-II data, with a spatial resolution of 36.25 m and radiometric resolution of 7 bits per pixel, have been used for the research. The GML classification has been performed with bands 1 (0.45-0.52/zm), 3 (0.62-0.68/xm), and 4 (0.77-0.86/zm). The overall classification accuracy for the 6-class GML classification for the Singrauli site was 90.70%. For the Bhopal site, the 5-class GML classification accuracy was 91.46%. When the non-linear probabilistic relaxation contextual algorithm with two different forms of compatibility coefficients was applied to this initial classification from the GML classifier, the overall classification accuracies after 20 iterations improved to 94.36 and 94.58% for compatibility coefficients based on correlation and mutual information, respectively, for the Singrauli site. For the Bhopal site the improvements were 94.98 and 92.39%, respectively, The overall classification accuracies with contextual information with both forms of compatibility coefficient were found to be statistically significantly different from and better than the GML classification for the Singrauli site. However, for the Bhopal site this was true only when the correlation based compatibility coefficient was used. Keywords: context; probabilistic relaxation; muitispectral classification
1. Introduction The conventional per-pixel classifiers do not incorporate spatial information from an image, which is very important for a visual recognition system. In practice, per-pixel classifiers often achieve far from perfect classification (Gurney and Townshend, 1983). In order to improve classification accuracy it is important to use information not only from individual pixels, but from its spatial domain also. The spatial information is usually subdivided into two * Corresponding author.
types: texture and contexture. Texture refers to the description of variability of grey level values found within part of a scene. Various measures of texture have been successfully applied (Haralick, 1979; Gool et al., 1985; Dikshit, 1992). The context of a pixel (or a group of pixels) refers to its spatial relationship with pixels in the remainder of the scene. The rationale underlying the incorporation of contextual information into the classification process is the presence of positive autocorrelation among pixels (Mather, 1990). An excellent survey of context typology has been given by Gurney and Townshend (1983).
0924-2716/97/$17.00 © 1997 Elsevier Science B.V. All fights reserved. Pll S0924-27 16(96)00027-5
R. Shankar Thakur, O. Dikshit/ ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
Various attempts have been made to incorporate context in computer classification (Kettig and Landgrebe, 1976; Harris, 1985; Kittler and Foglein, 1986; Haralick and Joo, 1986). With the availability of high-resolution remotely sensed images, the spatial relationship between pixels will play an increasingly important role, and hence contextual classification will be helpful. A context classifier is characterized by the fact that it classifies an unknown pixel using the entire context of the image or a substantially sized context neighbouring the pixel. As a result of incorporation of contextual information, a pixel's most probable interpretation, when viewed in isolation, is likely to change. Hence, contextual algorithms attempt to reduce uncertainty in labelling by: (a) examining the local neighbourhood of each pixel to produce locally consistent labels, and (b) using statistical information on the label relationship present in the whole image. The present research has attempted to estimate the extent to which the application of one of the widely used contextual algorithms - - non-linear probabilistic relaxation - - improves the classification of remotely sensed digital imagery.
2. Objective The investigations in this paper have been motivated by the hypothesis that the classification accuracy of remotely sensed imagery, using the Gaussian maximum likelihood (GML) classifier, can be improved by incorporating additional contextual information. Based on this hypothesis, the objective of this paper is first, to classify the test site imagery using the GML classifier and then to use the nonlinear probabilistic relaxation algorithm to evaluate the extent to which it improves the classification accuracy.
3. Overview of data resources, study sites and methodology The research has been conducted on two study sites. The first is the Singrauli mines area in the Sidhi district and the second is the Bhopal city area, both in Madhya Pradesh (India). The four-band Linear Imaging Self Scanning (LISS-II) data from
93
Indian Remote Sensing Satellite (IRS) have been used for the research. The IRS LISS-II camera operates in four wavelength bands (0.45-0.52, 0.52-0.59, 0.62-0.68, and 0.77-0.86 #m) with a spatial resolution of 36.25 m and a radiometric resolution of 7 bits per pixel. To delineate training and test areas, topographic maps at 1 : 50,000 scale have been used along with field visits. The basic approach used in the research is to apply two levels of classification strategies, one by the classical per-pixel GML classifier and the second by the pixel-based contextual reclassifier using non-linear probabilistic relaxation, on study site images and to generate classification products. These products are then compared with the test areas to compute classification accuracies.
4. Theoretical background The GML classifier is one of the most widely used supervised per-pixel classifiers which assumes a Gaussian probability distribution of class parameters. In this classifier a set of normalized probability values, Pi ()~kIX), are calculated for each pixel vector X, one for each class )~k. The normalized probability for a pixel ai to get the class label )~k is given by the following equation: P/(Xklx) =
p( Xl~.k) P(,kk)
M
(1)
E p(XI)~j)P().j) j=l where M is the total number of classes, P()-k) the a priori probability of class )~k and p(Xl).k) the probability density function for class )~k, which is given by 1 p(XlZk) = (2zr)a/2lExk ll/2
× [exp ( - I ( X -
]z).t) t E~.~1 ( x -
"~.k))]
(2)
where d is the number of spectral bands, •xk and/zx, are covariance matrix and mean vector, respectively, for class )~k, Z~I is the inverse of the covariance matrix for class Zk and ] • ] is the determinant of a matrix. When the GML classifier is applied, a set of normalized probability values are calculated for each pixel vector X, one normalized probability value for each specified class. This pixel is then allocated
R. Shankar Thakur, O. Dikshit / lSPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
94
to the class which has the maximum normalized probability value for that pixel. The probabilistic relaxation model attempts to reduce the uncertainty of labelling in a two-fold manner (Harris, 1985): (i) by examining the local neighbourhood of each pixel to produce a locally consistent label, (ii) by using statistical information on the label interrelationship present in the whole image. The relaxation involves a set of pixels A = a l , a2, a3, . . . , aN and a set of classes A = ~-1, ~-2, ~-3. . . . . ~.M. For each pixel ai, w e have a set of local measurements which are used to estimate the probabilities Pi ()~j) of pixel ai having label )~j. These probabilities satisfy the following equation (Hsiao and Sawchuk, 1989): M
Z
Pi(~'J) = 1
Vai E A; 0 <_ Pi(~.j) < 1
(3)
j=l
Generally a 3 x 3 neighbourhood has been used in updating the probabilities which represents a set of eight-connected neighbours of the pixel under consideration (Peleg and Rosenfeld, 1978). The normalized probabilities calculated by Eq. (1) are used as the initial probabilities, PiO(~.k). Hence
Pi°(~.k) = Pi(LklX)
(6)
The compatibility coefficients are computed only for neighbouring pixel pairs and are assumed to be zero for non-neighbouring pixel pairs. So for an eight-connected neighbour, there will be nine compatibility coefficient matrices (8 for neighbours, one for itself). The two popular ways of computing compatibility coefficients are based on correlation and mutual information (Peleg and Rosenfeld, 1978). The compatibility coefficient based on correlation has the following form: ri,i+~ (~.j, ~'k) :
These probabilities are updated using a set of compatibility coefficients ri,i+8(~.j, ~'k) where rij : AxA---> [-1, 1] and (1) ri,i+t~(~.j, ~'k) > 0; if classes )~j and )~k are compatible for pixel ai and ai+8, respectively. (2) ri,i+~(Lj, ~,k) < 0; if classes )~j and Lk are incompatible for pixel ai and ai+8, respectively. (3) ri,i+~().j, )~k) -=" 0; if neither labelling is constrained by other. (4) The magnitude of ri,i+8(~ j, ~.k) represents the strength of compatibility. Afterwards, the probabilities are updated by using the following updating rule: p/m (~.k)[1 + qm (~-k)] M
PiY+l (3"k) =
(4)
1
N
~_~ [PI(Xj) - -f(~.j)][Pi+8(~,k) -- P'(~-k)] i
cr(Lj)cr()~k)
where Pi (~.j) is the initial estimate of the probability of labelling pixel ai with )~j, P()~j) is the average of Pi(Lj) for all pixels and ~r(Lj) is the standard deviation of P/()~j). The ideal compatibility coefficient matrix should be symmetric. Rosenfeld et al. (1976) proposed a compatibility coefficient based on mutual information. An estimate of mutual information, that is the contribution of )~k to the information about ~j, can be expressed as Ii,i+8().k, ).j) = In -~
P/~ (~j)[1 d- q?(Lj)]
-~
P(~.k) P(3.j)
j=l
where
(7)
;
8~ A
(8)
where P(Lk) is the probability of any pixel having label )~k and P/.~+8(Lk.Zi) is the joint probability of a pair of pixels having labels Zk and )~j. These quantities can be computed by the following equations: ^
M
qm(Xk) = Z ~EA
di+8 E
ri,i+8(~.k,~.j)P~+8(Xj)
(5)
j=l
and m is the iteration number, d~+8 the set of neighbour weights that can be used to give different neighbours different degrees of influence in the neighbourhood function, i + 8 the specific neighbour of a given pixel ai at location i, and A the neighbourhood about the particular pixel being considered.
?(xk) = ~1 ~.= piO(~.k) 1
N
i'i,,+8(Zk, Z~) = ~ ~
i=1
(9)
P°(Zk)P°÷8(Zj)
(10)
R. Shankar Thakur, O. Dikshit /1SPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
95
Extreme values of the coefficient from Eq. (8) result only when one of the events involved is extremely rare. Therefore, events that cause
(i) The sum of absolute probability differences should become small after a few iterations, i.e.
~,i+8(Xk, Xj). k(xk)k(zj) '
i~A
36 A
(11)
to be outside the range [e -5, e +5] should be ignored. Thus the values of Ii.i+~(Xk,Xj) can be considered to lie in the range [-5, 5] and the compatibility coefficient based on mutual information is defined as ri,i+8()~k ' ~.j) -~. gli, 1 i+8(~k, ~.j) =
i=~
N
i-----I
VX ~ A (14)
(ii) The final probabilities should not be too far away on the average from initial ones. Therefore, convergence of the process to an arbitrary set of final probabilities unrelated to initial ones is not desirable. Thus the following equation should be satisfied: lea
N E PiO~k)Pi+,(Xj) N
threshold1;
E [Pim(x) - P/°(X)[ < threshold2; YX E A
N
In
y ~ IP7(X) - Pm+l(Z)l <
(12)
(15)
(iii) The entropy of probabilistic classification after applying relaxation should be less than the entropy of the initial ones, i.e.
i=l
which lies in the range [ - 1, 1]. There are two main approaches of implementing relaxation-based contextual classification. The first one is proposed by Rosenfeld et al. (1976) and the second is by Peleg (1980). In the present work, the first approach has been used. Therefore, the step-bystep procedure for only this method is described below. (1) By using the mutual information coefficients as the compatibility coefficients and an 8-connected neighbourhood, calculate ri.i+8(Xk, ~'j). These coefficients are fixed throughout the iteration process. For this step use Eqs. (8)-(12). (2) With the initial labelling probabilities for each pixel and compatibility coefficients, the process can be iterated using the updating factor given by Eq. (5). For an 8-connected neighbourhood with equal weights to all neighbouring pixels, this equation takes the following form: 1
M
q'~(~.D = E -8 E ri'i+a(~'k'XJ)Pim+'s()~'i) SEA
-
P/m( )ln m(Z) < iEA
¥)~ ~ A
(16)
In Eqs. (18) and (19), threshold1 and threshold2 represent user-specified threshold values. The results of classification are compared by using the khat index, x, which is the proportion of agreement after chance agreement is removed from consideration. It is given by the following formula (Bishop et al., 1975): M
j=l
(3) The updating factor is then used to compute, p/m+l (Xk) by using Eq. (4) (4) Steps (2)-(3) are repeated until the stopping criterion is met. (5) The final pixel classification is the maximum probability class for each pixel. There are several ways for evaluating the relaxation iteration performance and their termination conditions (Hsiao and Sawchuk, 1989):
M
NE P0 -
~c -- - 1 -
Pc
p~
Yii-E i=1
-
Yi+'Y+i i=1
(17)
M
N 2 -- E
Yi+" Y+i
i=1
where
P0
is
proportion
of
agreement
Po = i Y ~ I Yii), Pc proportion of chance agree1
(13)
P ? a ) l n P?(Z);
iEA
M
ment (pc = ~ ~ i = i Y/+ • Y+i), Yij is an element in the M x M confusion matrix with M classes, Yi+ is the row marginal total (Yi+ = ~ = 1 Yij), g+j the
•
(
)
column marginal total Y+J = Y~4 t Yq • and N Is the total number of elements in the confusion matrix M
M
y,
For an individual class, the khat index is given by the following equation (Bishop et al., 1975):
xi =
Pii -- Pi+ " P+i Pi+ -- pi+ " P+i
=
N Y i i -- Yi+ " g+i N Y i + -- Yi+ • Y+i
(18)
R. Shankar Thakur, O. Dikshit / ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
96
The khat index is used to perform a pairwise test of significance using the normal curve deviation to determine if two confusion matrices are significantly different. The test statistic for this purpose is given by (Congalton et al., 1983; Congalton and Mead, 1986): Z
=
xa -
(19)
xb
~//O'2[ga] -.[--(T2tKb]
where Z is the test statistic for testing significant difference in large samples, Ka and rb are khat indices for two error matrices a and b, and trz~[Xa] and cr2[xb] are asymptotic variances for the corresponding khat indices. For the overall classification and an individual class these are given by Eqs. (20) and (21), respectively. tr2[x] = (01(1
2(1
- 01) +
-- 01)(20102 -- 03) (I -
i=l j=l
(20a)
M i-1 M
M
i--1 j = l M
E 2
-
i=1 M
Yi+" Y+i M
i=1 j = l
(20b)
M
E 03 ~---
E'i(Yi+ "~ Y+i)
i=1 M
M
i=1 j=X M
4=
E Y/J(Y/+ q- y+i)2 i=1 M M 3
i=1 j = l
1
(Pi+ -- Pii)
~r~[Ki] = N p~+(1
p+i) 3
[ ( P i + -- Pii)
X (Pi+" P+i -- Pii) q- Pii(1 -- Pi+ -- P+i Jr- Pii)]
(21) where (Pi+ = Yi+/N), (P+i = Y+i/N), and (Pii = Yii/N). The significance tests are based on the asymptotic normality of the khat statistic. For example, if Z exceeds 1.96 for a two-tailed test, then the difference between two classification confusion matrices is significant at the 95% probability level.
5. Experimental methodology First, the conventional GML classification is performed for the two study sites using Eq. (1). The prior probabilities of all classes have been assumed to be equal. Once the initial classification is obtained, the reclassification of the imagery is done by using the non-linear probabilistic relaxation technique under the following steps: (1) The initial normalized probabilities of each pixel for each class are computed from Bayes' theorem (Eq. 6) during GML classification by taking equal prior probabilities, P(~.i), for each class. The probabilistic updating is carried out with the help of the non-linear probabilistic relaxation model, proposed by Rosenfeld et al. (1976). Using the probabilities calculated above, the compatibility coefficients are calculated. The two compatibility coefficients - - correlation compatibility coefficients and mutual information compatibility coefficients (Eqs. 7 and 12) - - have been used here. For an 8-connected neighbour, there are nine compatibility coefficient matrices, eight for a pixel's neighbour and one for itself. The nomenclature of neighbours, used here, is given in Fig. 1. (2) The iteration for updating the probabilities is done as given in Eq. (4), with the help of the neighbourhood operator given by Eq. (13). The classification accuracies are computed over the test image at each of the 20 iterations.
6. Results and discussion By following the procedure described in Section 5, test imageries of two study sites have been classified using the GML and contextual classifiers.
R. Shankar Thakur, O. Diksh# / ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
97
j-direction
i-direction
Neighbour-1 (i = -1,j = -1) Neighbour-2 (i = -l,j -- 0)
Neighbour-3 (i = -1,j = +1)
Neighbour-4 (i = 0,j -- -1)
Nvighbour-6 (i = 0, j = +I)
N¢ighboar-5 (i -~ 0,j = 0)
N¢ighbour-7 (i = +l,j = -I) N¢ighbour-$ (i = +l,j -- 0) N¢ighbour-9 (i = +1, j ffi +1) Fig. 1. The nomenclature for an eight-connected neighbourhood. The semi-natural environment of the Singrauli area consists of six classes. These are rocky terrain, dense forest, vegetation, clear water, mine dumps and reservoir water. The urban environment of the Bhopal city area consists o f five prominent classes. These are built-up area, open scrub, marshy land, forests and lake water. The results of G M L classification using bands 1, 3, and 4 for training areas and test areas are given in Table 1. The overall classification accuracy for training areas for the Singrauli site is 96.73% and for the Bhopal site 94.40%. Most of the classes have good accuracy ( > 8 5 % ) except marshy land in the case of the Bhopal site. This is due to the fact that this class may include many mixed transition pixels between land and water. For test areas, the sites have accuracies of 90.70 and 91.46%, respectively. For contextual classification, the compatibility coefficients, based on correlation and mutual information compatibility coefficients for 8-connected neighbour, are computed using the probabilities calculated during the G M L classification. For all the nine compatibility coefficient matrices, it was observed that the diagonal matrix elements are positive and comparatively larger numbers. This is reasonable, because the chance of getting one class with
itself is greater. The coefficients for neighbour-5 (i.e. for itself) are symmetrical because it does not have any directional variation, Also, the diagonal elements for neighbour-5 of correlation coefficients are all 1. However, for all other neighbours, the matrices are not symmetric. This is attributed to pixel border effects and rounding-off errors in computation (Peleg and Rosenfeld, 1978). The classification results have been derived for 20 iterations during contextual reclassification and are given in Fig. 2. In general, the overall accuracies increase on increasing the number of iterations and this improvement follows an exponential form. This was expected, and indicates that the initial few iterations are most powerful for improving the accuracy. For the Bhopal site, however, a sudden fall in overall accuracy at iteration number 9 and a gradual fall from iteration number 17 to 20 was observed for classification with mutual information compatibility coefficient. This has been observed mainly due to decrease in accuracy of the forest class. The reason for this observation is not clear, but it is similar to an observation made by Davis et al. (1983). For individual classes, however, the accuracy of classification follows a step-like behaviour, i.e. the accuracy increases
Table 1 Classification accuracies for the GML classification Singrauli study site Class
Bhopal study site Training data
Test data
Training data
Test data
No.
Name
Pixels
% acc.
Pixels
% acc.
No.
Name
Pixels
% acc.
Pixels
% acc.
1 2 3 4 5 6
rocky terrain dense forest vegetation mine dumps reservoirwater clear water overall
104 146 175 118 112 170 825
100.00 98.63 99.43 99.15 100.00 86.47 96.73
812 559 432 427 577 493 3300
94.09 82.47 88.89 88.29 93.76 94.52 90.70
1 2 3 4 5
open scrub built-uparea marshy land forest lake water overall
216 181 144 192 177 910
96.76 94.48 78.47 99.48 98.87 94.40
953 503 642 736 689 3523
90.97 97.81 79.90 91.03 98.69 91.46
Class
98
R. Shankar Thakur, O. Dikshit/ ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
95.00 94.50
~ 94.00 ~ 93.50
- - ~ Smg-CC Sing-MI
~ 93.00
A BhopaMEC
~ 92.50
Bhopal-~
~ 92.00 91.50 91.00 ¢~
~
I'~
O~
'-~
¢~
~
I"~
~'~
Iteration Number Fig. 2. Overall accuracies for contextual classification with iterations. Sing-CC: Singrauli site classification using coefficient of correlation. Sing-MI: Singrauli site classification using coefficient of mutual information. Bhopal-CC: Bhopal site classification using coefficient of correlation. Bhopal-MI: Bhopal site classification using coefficient of mutual information.
and then remains constant for a few iterations and then again increases and then again remains constant for the next few iterations. The classification results have also been subjected to statistical testing to find whether the results are statistically significantly different from each other at the 5% significance level. Tables 2 and 3 give comparisons between different classifications. From these tables the following observations can be made: (1) Overall accuracies for contextual classifications for the Singrauli site using both correlation and mutual information compatibility coefficients are statistically significantly different from and better than classification accuracies without contextual information by using only the GML classifier. Similar observation holds for the Bhopal site with contextual classification using correlation compatibility coefficient only. The overall classification results of contextual classification using mutual information compatibility coefficient are not significantly different from GML classification without context information. (2) For the Singrauli site, results of contextual classifications using correlation and mutual information as compatibility coefficients are not statistically significantly different from each other for any of the classes and for the overall classification. However, for the Bhopal site, results for open scrub, forest and overall classification are statistically significantly different for contextual classification using both forms of compatibility coefficients.
(3) For spectrally well-defined classes like reservoir water, clear water, and lake water, the contextual classification results are not significantly different from the GML classification. The probabilistic relaxation technique is computationally complex and intensive. It requires considerable computer time and huge disk space. The HP9000/735 systems (RISC CPU at 99 Mhz (Specint92: 109, Specfp92: 168, 144 Mb RAM) take around 110 min of CPU time for a 20-iteration 6class classification for a 512 x 512 pixel image, that is, more that 5 min per iteration. However, there may be scope to make the program more efficient. In this technique, probabilities of each pixel for each class are required to be stored. For a 512 x 512 pixel image, if the probabilities are stored in double float, one file takes around 2.35 Mb of disk space and if the number of classes is 6, then the total is around 14 Mb. 7. Conclusions This research has attempted to use contextual information to improve the classification accuracy. On the basis of the results, the following conclusions have been drawn: (1) For Singrauli area imagery, the 6-class GML classifier gave an overall percentage accuracy of 90.70. When the probabilistic relaxation algorithm was applied, the overall accuracies increased to 94.36% and 94.58%, in 20 iterations, using correla-
R. Shankar Thakur, O. Dikshit/ lSPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 92-100
99
Table 2 Statistical analysis for the Singrauli study site Class no.
r¢c
trcc
tCml
~rrni
g'mi
O'mi
Zcc-ml
Zmi-ml
Zec-mi
1 2 3 4 5 6 Overall
0.9749 0.9271 0.8890 0.9069 0.9253 0.9416 0.9314
0.0063 0.0119 0.0160 0.0148 0.0118 0.0115 0.0048
0.9204 0.7941 0.8727 0.8678 0.9253 0.9324 0.8870
0.0109 0.0182 0.0170 0.0172 0.0119 0.0125 0.0061
0.9667 0.9331 0.8836 0,9306 0.9253 0.9250 0.9307
0.0072 0.0115 0.0163 0.0130 0.0118 0.0129 0.0049
4.2986 6.0881 0.6959 1.7172 0.0029 0.5423 5.6729
3.5207 6.4335 0.4606 2.9029 0.0029 -0.4121 5.5735
0.8427 -0.3638 0.2354 -1.1968 0.0000 0.9620 0.1012
x = khat index (Eqs. 17 and 18). Z = Z-statistic for hypothesis testing (Eq. 19). tr = asymptotic standard error for corresponding khat index (Eqs. 20 and 21). ml, cc, mi = subscripts indicating GML and contextual classification using correlation and mutual information coefficients, respectively.
Table 3 Statistical analysis for the Bhopal study site Class no.
rcc
trcc
g'ml
O'ml
Krni
O'mi
Zcc-ml
Zmi-ml
Zcc-mi
1 2 3 4 5 Overall
0.9376 1.0000 0.8055 0.9551 0.9963 0.9366
0.0090 0.0000 0.0167 0.0085 0.0026 0.0046
0.8862 0.9952 0.7615 0.9069 0.9926 0.9034
0.0117 0.0033 0.0180 0.0119 0.0036 0.0056
0.8490 1.0000 0.8251 0.8915 0.9963 0.9043
0.0131 0.0000 0.0162 0.0126 0.0026 0.0056
3.4653 1.4179 1.7854 3.2735 0.8190 4.5499
-2.1107 1.4179 2.6166 -0.8822 0.8190 0.1145
5,5618 0.0000 -0.8366 4.1541 0.0000 4.4392
~c = khat index (Eqs. 17 and 18). Z = Z-statistic for hypothesis testing (Eq. 19). tr = asymptotic standard error for corresponding khat index (Eqs. 20 and 21). ml, cc, mi = subscripts indicating GML and contextual classification using correlation and mutual information coefficients, respectively.
tion coefficients and mutual information coefficients, respectively. Accuracies of all classes as well as the overall accuracy increased, with the increase in number of iterations. The overall classification results are statistically significantly different and better than GML classification. For spectrally well-defined classes, the results of contextual classification are not statistically significantly different from GML classification. (2) For Bhopal area imagery, the 5-class GML classifier gave an overall percentage accuracy of 91.46. The probabilistic relaxation algorithm, while using correlation coefficients, increased the overall accuracy to a maximum of 94.98%, in 20 iterations, and is also statistically significantly different from the GML classification. However, when mutual information coefficients were used, a well-defined behaviour was not observed, with the increase in number of iterations. The overall accuracy at the end of 20th iteration is higher than, but not statistically significantly different from, the GML classification.
(3) From classification results, the correlation seems to be better than the mutual information to calculate compatibility coefficients. However, it would be premature to draw such a conclusion. For a reliable and successful use of the relaxation model, it is important to test this algorithm on various other images. (4) Despite the inherent computational complexity of the contextual algorithm based on probabilistic relaxation, it is suggested that contextual information be used on routine basis with high-resolution images having high spatial information. The processing speeds of computer hardware are continuing to increase rapidly, and particularly, the use of parallel processors will definitely decrease the computation time. References Bishop, Y.M.M., Fienberg, S.E. and Holland, P.W., 1975. Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge.
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