Multispectral Remote Sensing Image Change Detection Based on Markovian Fusion

Qiongcheng Xu, Yunchen Pu, Wei Wang*, Huamin Zhong

*corresponding author

Dept. of Automatic Control, Shanghai Jiaotong University, and Key Laboratory of System Control and Information

Processing, Ministry of Education of China, 800 Dong Chuan Road, Shanghai, 200240, China

E-mail: wwang@sjtu.edu.cn

Abstract—This paper presents a novel multispectral remote

sensing image change detection (CD) algorithm based on

Markovian fusion. This new method intends to obtain the

optimal change map (change detection result) by fusing information contained in each band. The optimal change map

are modeled as Markov Random Fields (MRF) which takes

into account not only the spectral information of multiple

bands but also the contextual information of both the pixels in

the optimal change map and the relationship between the optimal change map and change maps of each band

respectively, and thus, leads to a more accurate and robust

change detection result. In the analysis of difference image, an

unsupervised threshold selection algorithm based on Bayesian

decision theory is introduced, which aims at extracting the changed information from the images. The finding of optimal

change map is equivalent to minimizing the total Gibbs

potential function by using simulated annealing algorithm. The

experimental result of the proposed algorithm compared with

the change map of each band is presented, which indicates that the proposed method improves the result effectively and is

superior to any band’s change map.

Keywords- change detection; multispectral remote sensing

image; bayesian decision theory; Markovian fusion; Gibbs

potential function

I. INTRODUCTION

Remote sensing image change detection, as a branch of

remote sensing technology, aims at detecting change information from images acquired at the same place, but on

different dates [1]. Remote sensing image change detection has been widely used in fields such as updating of

the fundamental geographic information, urban planning management, detection on agriculture and forestry, the

assessment of nature disasters and military reconnaissance. Multispectral remote sensing image change detection is a

change detection process based on multiple bands which are

acquired information from a range of wavelengths in the spectrum [2].

Usually the change detection is based on images of single-band which is selected from multip le bands using

optimal band selection methods like data dimensionality reduction performed by principal components analysis (PCA)

[3], the spatial and spectral autocorrelation-based approaches

[4] and etc. However, for multispectral remote sensing images, one single-band may not include all change

information because each band contains its specific information that the other bands don’t. Therefore, it is

necessary to take into account every band of the remote sensing images for change detection with high accuracy.

The usual steps of single-band image change detection

are as follows:(1) Preprocessing: main ly includes geometric registration and radiometric calibrat ion.(2) Performance of

change detection: In general, difference map, generated from the two given images, is binarized into changed and

unchanged areas by thresholding the intensity levels of pixels

in the difference map[5]. (3) The accuracy assessment of change detection: change error matrix and Kappa coefficient

is often used to assess the accuracy of change detection. As for mult ispectral remote sensing image change

detection, the second step mentioned above could be extended to: (2a) For each band of the two given image,

difference image is generated; (2b) Change detection method is applied to obtain the change map (b inary change detection

result image) of each band; (2c) image fusion method is

performed to generate the optimal change map based on all change maps generated from each band as mentioned in step

(2b). In this paper, a novel multispectral remote sensing

image change detection algorithm based on Markovian fusion is proposed. First, for each band, change detection

based on image differencing is used, and then Bayesian

decision of thresholding is applied to obtain the change map in each band, which may different from the other bands’,

because different bands contain different specific information as is mentioned above. Afterwards, the fusion of

all change maps is proposed to generate the optimal change map based on the theory of Markov Random Fields (MRF).

The theory of Markov Random Fields is based on the

spatial-contextual information included in the neighborhood of each pixel [6]. In the MRF model, the configuration (eg.

intensity level) of a site (eg. pixel) is assumed to be statistically independent of configurations of all remaining

sites excluding itself and its neighboring sites. Furthermore, MRF model is known to be equivalent to the Gibbs field, so

the optimal change map, which is considered as a MRF model, could be derived by minimizing the Gibbs potential

function. In this paper, the potential function ofthe optimal

change map consists of two parts. One part expresses the correlation between the labels of pixel and the labels of its

neighbors in the optimal change map. The other part denotes the relationship between the optimal change map and the

change maps derived from each band. The fusion of all change maps generated from each band could eliminate the

noises which occur when using only one band’s information.

Meanwhile, the fusion can also withhold the important change information in every band that other bands don’t

contain. Therefore the change detection result is more

accurate and robust. The remainder of this paper is organized as follows. In

Section II, the Markovian fusion-based multispectral remote sensing image change detection method is presented. In

Section III, the proposed algorithm is applied to a pair of 3-bands simulated images, and the experimental results are

discussed. Conclusions are drawn in Section IV.

II. METHOD

A. The Analysis of Differencing Map of each Band

Image differencing, as one of the most popular methods for change detection, has the advantage of both simplicity

and convenience. The processing of image differencing

includes: (1) given two images and , subtract image from image pixel by pixel; (2) select a suitable threshold

to separate changed pixels from the unchanged ones (i.e. if

the pixel value is greater than the threshold, this pixel is considered as a changed pixel and is highlighted). Although

image differencing method takes advantage of

straightforward as well as rapid calculation, its accuracy is based on high quality of the images and precise geometric

calibration [5]. In aforementioned step (2), the threshold value is critical

since too low a value will cause false alarm while too high a value will mark some changed pixels as unchanged ones [5].

Lorenzo Bruzzone has proposed a Bayesian approach to threshold selection, which is used in this paper [7].

Let two images (with single band) be and , of size , which are acquired at different times, and

. The difference map is calculated by the method of image differencing over

and . To segment into changed and unchanged areas ,

every pixel in should be classified into changed class

or unchanged class . Then a change map (CM) is

generated to label every pixel as changed or unchanged in terms of a binary image , where denotes the pixel at the location changed while denotes unchanged. In

regard of the characteristics of remote sensing images,

could be modeled as a mixture density composed by classes and , both of which have Gaussian density functions

[7].

Given a threshold , could be separated by the following conditions: if , then , otherwise

. Therefore, should satisfy the following equation:

|

| (1)

Simplified based on the Bayesian theory:

|

| (2)

To solve this equation, the knowledge of the a-priori probabilities

and the probability density functions

| of the two classes are required.

As is discussed above, the two classes are modeled as

Gaussian distributions respectively. | could be written

as

|

√

(3)

Where is the mean value of , and is the standard

deviation of . To gain , an iterative technique is

introduced, which exploits the expectation maximization (EM) algorithm for the estimation of the statistical terms

associated with the gray levels of changed and unchanged pixels in the difference map. The detailed steps and the

estimation of the statistical terms to gain the threshold could be found in [7].

B. Markovian Fusion of Change Maps from each Band

Assume that a pair of mult ispectral remote sensing

images has K bands. For every band, a change map is

generated from its difference map which is obtained by

the means of image differencing method, where the subscript label denotes the k th band. It is observed that every change

map is different from each other because every band

contains information that other bands don’t. Thus, in order to produce the optimal change map OCM, a Markovian fusion

method of all is proposed in this paper.

Through this method, optimal change map could be produced which contains useful information of all bands

while eliminates the noises which are derived from single-band change detection, thus, leading to a more accurate and

robust change detection result.

Markov Random Fields (MRF) modeling has been widely applied in image analysis including change detection

because many image properties seem to fit a MRF model. By using MRF model, statistical correlation of intensity levels

among neighboring pixels can be explo ited [8]. In this paper, a second-order 8-neighbourhood system is employed, which

denotes that the intensity level of each pixel in the image is

only dependent of eight pixels around it. Given a change

map , is defined as the set of neighborhood of

the pixel at the location , where denotes the

neighborhood.

To obtain the optimal change map OCM, maximum a posteriori probability (MAP) decision criterion is applied

which is defined as: |

| (7)

The MRF is known to be equivalent to the Gibbs field [8],

thus the formula above could be written as:

|

|

{

} (8)

where Z is a normalized constant, and is the total Gibbs potential function.

Then, our problem is equivalent to the min imization of

total Gibbs potential function which can be expressed as a set of local Gibbs potential function :

∑ ∑

(9)

The local Gibbs potential function consists of two

parts:

1) The correlation in the optimal change map: between

the label of pixel and the labels of its neighbors:

∑

(10)

where

{

， (11)

is the indicator function to

determine the relationship of a pixel and its neighbor pixel.

2) The relationship between the optimal change map and

the change maps derived from each band. In this part,

potential function has two components. The first component is the relationship of pixel in the

optimal change map and the corresponding pixel in each change map :

∑

(12)

Where

{

(13)

{ |

|

| |

(14)

is expressed as the potential function while is a

weight function which indicates that if the classification of

is the same as that of , the larger the

difference between the pixel and the threshold

values , the higher the degree of confidence in the

decision of the classification of [9]. The second component is the relationship between the

pixel in the optimal change map and the

neighborhood of the corresponding pixel in each change map

:

∑

(15)

where

∑

(14)

{

，

(16)

is defined as the potential function while is a

weight function which indicates the degree of confidence of

the kth band by using manhattan distance [10]. A smaller manhattan distance indicates fewer noises besides the change

information as discussed in [10], and thus, heavier weight is consigned to that band in terms of . In this paper,

∑

(17)

where denotes the manhattan distance of .

Therefore, the local potential function could be expressed as:

(18)

C. Algorithm

In order to obtain the optimal change map, s imulated

annealing (SA) algorithm is adopted because SA algorithm has been a powerful method to solve optimization problems

by converging to an approximated global optimization [11].

SA algorithm prescribes a schedule which guarantees convergence to the global maximum of the objective

function by lowering temperature, which simulates the procedure of “annealing” [12]. At a high temperature, many

of the stochastic changes will actually decrease the objective function, but when the temperature is gradually lowered, it

concentrates on states that maximize the objective function.

In this paper, given two images and with K bands, the steps of the Markovian fusion change detection algorithm

based on SA are as follows:

1) Apply Image Preprocessing of both geometric and radiometric calibration.

2) For each band, perform the image differencing method to the image

and of each band and the

difference map are generated for

further analysis. Thereafter, Bayesian Decision of

thresholding is used to each difference map to determine the threshold automatically to get

the change map where

denotes changed while denotes

unchanged. 3) Initialize the optimal change map . Label of every

pixel is determined by criterion that:

∑

Initialize temperature T, and set the times of iteration

within same temperature. 4) Temperature is fixed at T, and update OCM by

minimizing the total Gibbs potential energy

defined in (8). 5) Repeat step 4) times. 6) Decreasing temperature T. 7) Repeat step 4)-6) until the temperature reaches 0, and

the optimal change map is produced with

minimum .

III. EXPERIMENTAL RESULTS

Consider a pair of 3-bands simulated images of size for the proposed method as shown in Fig. 1(a)

and (b). It is observed that Fig. 1(a) and (b) have radiometric

difference as well as changes, and their corresponding ground truth of change detection result is shown in Fig. 2

where changed pixels are highlighted while unchanged pixels are dark. Changes occur in the square region from

pixel (1, 1) to (48, 48). The proposed algorithm is applied to

Fig.1 (a) and (b) and the results are shown in Fig. 3. It is apparent that the result of the proposed algorithm

shown in Fig. 3 (a) is much better than any of the change map of each band as shown in Fig. 3 (b)-(d) because more

changed pixels are detected while less unchanged pixels are included. As is shown in Fig. 3(b)-(d), the change map of

each band is different, and it seems that band 2 is the best

change detection result, which still includes many errors. However, the optimal change map could eliminate the errors

effectively when compared with that of each band. Fig. 4 displays the total Gibbs potential energy with the

decreasing of temperature. It is observed that at a high temperature, the potential energy first, increases dramatically,

then, when the temperature decreases near to zero, the

potential energy tends to be steady and much lower and decreases to minimum at the temperature of zero. Thus, a

global minimum could be reached by using SA algorithm. To assess the accuracy of the change detection result, a

2×2 changed/unchanged error matrix is introduced in this paper [13]. It is shown in Table I that the change error matrix

obtained by comparing the change detection result with the ground truth. denotes the number of changed pixels

which are incorrectly detected to be unchanged, while

denotes the number of unchanged pixels which are

incorrectly detected to be changed. and denote the

number of changed and unchanged pixels which are correctly detected respectively. and denotes the

number of changed and unchanged pixels in the ground truth

respectively, while and denotes the number of changed and unchanged pixels in the change detection result

respectively. .

The following variables can be computed from the change error matrix:

False alarms:

Missed alarms:

Total error rate:

Kappa coefficient:

∑

∑

The relationship between the classification quality and

Kappa coefficient is shown in Table II [14]. Table IV shows that the proposed method could

eliminate errors effectively especially the missed alarm,

compared with traditional ways of single-band image change detection.

Kappa coefficient can be calculated based on Table III and Table IV as shown in Table V. From Table V, it is

observed that the Kappa coefficient of the proposed algorithm is much larger than that of the each band. Also, the

result of each band is different from each other a lot as Band

2 is the best result while band 1 is the poorest.

(a) (b)

Figure 1. Simulated images of size 128 128.

Figure 2. Groudtruth.

(a) (b)

(c) (d)

Figure 3. Change detection results: (a) optimal change map using CD algorithm based on Markovian fusion. (b)-(d) change map of band 1,2, and

3 respectively.

Figure 4. Total Gibbs potential energy as a function of temperature.

IV. CONCLUSION

In this paper, a novel multispectral remote sensing image change detection method based on Markovian fusion is

proposed. By using simulated annealing algorithm, the optimal change map is obtained which has the minimum of

total Gibbs potential. Th is new method takes into account all bands of the images rather than a single band, which can not

only withhold all useful change information but also

eliminate the noises from each band, thus resulting in a more accurate and robust change detection result.

In the total Gibbs potential function, the parameters such as the weight functions and the weight of every component

in the local Gibbs potential function should be chosen reasonably. The choice of the parameters in the SA

algorithm such as the criterion of initial temperature

selection, the iteration stop criterion also has influence on the change detection result.

In conclusion, as for mult ispectral remote sensing images, change detection based on single-band will cause loss of

important information. However, the Markovian fusion method proposed in this paper can not only contain all

important change information but also eliminate noises from

each band, and therefore, improves the change detection result robustly and effectively.

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TABLE I. CHANGE/NOCHANGE ERROR MATRIX

CD Result Ground Truth

Unchanged Changed Sum

Unchanged

Changed

Sum

TABLE II. T HE RELATIONSHIP BETWEEN THE CLASSIFICATION

QUALITY AND KAPPA COEFFICIENT

Kappa Coefficient Q uality

<0 Worst

0-0.2 Poor

0.2-0.4 Reasonable

0.4-0.6 Good

0.6-0.8 Very good

0.8-1.0 Excellent

TABLE III. CHANGE/NOCHANGE ERROR MATRIXOF THE PROPOSED

CD ALGORITHM

CD Result Ground Truth

Unchanged Changed Sum

Unchanged 13937 24 13961

Changed 143 2280 2423

Sum 14080 2304 16384

TABLE IV. T HE COMPARISON OF THE OPTIAML CHANGE MAP AND

THE CHANGE MAP OF BAND 2

Optimal Change Map Change Map of Band 2

Flase Alarms 1.02% 2.24%

Missed Alarms 1.04% 13.06%

Total Error Rate 1.02% 3.76%

TABLE V. KAPPA COEFFICIENT AND QUALITY OF THE PROPOSED

ALGORITHM AND CHANGE MAP OF EACH BAND

O ptimal

Change Map

CM of

Band 1

CM of

Band 2

CM of

Band 3

Kappa

Coefficient 0.9589 0.5907 0.8449 0.7747

Quality Excellent Good Excellent Very good