Fu Wei

Guo Ziqi

Liu Caixia

Zhang Baogang

Zhou Qiang

CiteSeerX

USING LOCAL TRANSITION PROBABILITY MODELS IN MARKOV 
RANDOM FIELD FOR 
MULTI-TEMPORAL IMAGE CLASSIFICATION 
 
Fu Wei*, Guo Ziqi, Zhou Qiang, Liu Caixia, Zhang Baogang 
State Key Laboratory of Remote Sensing Science, jointly sponsored by the Institute of Remote Sensing 
Applications of Chinese Academy of Sciences and Beijing Normal University 
Beijing, 100101, China 
*Corresponding author. Email address: fuwei_irsa@yahoo.cn  
 
 
1. INTRODUCTION 
 
Classification of the remote sensing images is mainly based on the spectral information in pixel level, which often 
results in the problem of spectral confusion, that is to say the same objects with different spectral and different 
objects with the same spectral. Meanwhile there are multi-temporal and multi-sensor images and pixels on multi-
temporal image show dependencies in both the spatial and temporal domains. So we consider adding spatial and 
temporal information to improve discriminative power and remove the spectral confusion brought by only 
considering spectral information on single date image.  
The local property of an image shows that the gray value of one pixel only relates to the gray values of its 
neighborhood and Markov Random Field model can symbolize this local property [1]. Markov Random Fields 
(MRF) is a commonly used probabilistic model for image analysis, whose basic idea is to model the contextual 
correlation among image pixels in terms of conditional prior probabilities of individual pixels given their 
neighboring pixels [2]. As the Gibbs model is equivalent to Markov property of random field, the Gibbs random 
field model was used to describe the neighborhood random filed [3]. Previous work of image analysis using MRF 
often focus on the spatial neighborhood modeling, but in classification of the multi-temporal remote sensing 
images modeling of temporal neighborhood has extended the applied area of MRF. 
 
2. METHODS 
2.1. Data Source 
 
The study area is located in the central part of China, and Poyang Lake is the largest fresh lake in China through 
which water flows to Yangtze River. At the same time it is an important international wetland taking vital part in 
keeping the ecological variety. Two Beijing-1 images of this area obtained on 7 August 2007 and 1 January 2008 
were used in our research. 
 
2.2. Procedure 
The process was divided into a few steps. Firstly, the class conditional probability ( ( ) / ( ))P d i c i , which is 
modeled by a Finite Gaussian Mixture (FGM) distribution of the spectral data d (i), was estimated by the 
Expectation Maximization (EM) algorithm and this estimation converged to the Maximum likelihood estimation 
(MLE). Spectral energy function is specified as follows: 
( ( ), ( )) log ( ( ) | ( ))spectralU c i d i p d i c i                                                       (1) 
The initial classification map using Maximum Likelihood Classification (MLC) was used as the initial 
classification of the spatial-temporal contextual algorithm in this paper.  
Secondly, MRF was used to model the conditional prior probability 1 1 2( ( ) | ( ( )), ( ( ))s TP c i c N i c N i  , that is to say 
class prior probabilities of images under the condition of the spatial and temporal neighborhood class label 
information 1( ( )sc N i  and 2 ( ( )Tc N i . A Gibbs Random Field (GRF) was used to specify the conditional prior 
probability by energy function of the class label of the pixel and its neighboring pixels:  
1 1 2( ( ) | ( ( )), ( ( ))s TP c i c N i c N i = 1 2( ( ), ( ( ))) ( ( ), ( ( )))s s T TU c i c N i U c i c N i                                  (2) 
Specification of spatial energy function is as follows: 
( )
( ( ), ( ( ))) ( ( ), ( ))
s
s s s
j N i
U c i c N i I c i c j                                                           (3) 
where s  is a spatial association parameter; I(c(i),c(j)) is the association factor between class c(i) and class 
c(j).The temporal energy function was modeled by a transition probability matrix which defines the probability of 
one pixel belonging to one land cover type at time T1 given that it belongs to one land cover type at time T2. 
Specification of temporal energy function is as follows: 
1 2 1 2
( )
( ( ), ( ( ))) ( ( ) | ( ))
T
T T
j N i
U c i c N i P c j c j                                                       (4) 
Where T is a temporal relation parameter; 1 2( ( ) | ( ))P c j c j  is the temporal transition probability from class 2 ( )c j to 
class 1( )c j . 
To estimate the transition probabilities, it can be specified as a global model by assuming spatial stationarity of 
the transition probabilities or a local model which is adaptive to the spatial variation of the transition probabilities 
[4]. In this paper, we divided the whole image into a few sub-images according to the spatial variation and used an 
iterative EM-like algorithm to estimate the local transition probabilities of each sub-image [5]. Such estimates 
were initialized by assigning equal probabilities to each pair of classes and the algorithm was iterated until 
convergence. Model parameters s  and T  involved in the spatial and temporal energy functions are crucial to 
determine the importance of different energy functions and in this paper the two parameters were determined by 
cross-validation. 
Lastly, spectral energy from the EM algorithm and spatial-temporal conditional prior probabilities from MRF 
were integrated into posterior estimates by Bayes rule, the optimal classification was achieved when the 
classification corresponds to maximum a posteriori (MAP). The combination of the MAP method with the MRF 
modeling makes the classification task equivalent to the minimization of a total energy function and the iterative 
conditional mode (ICM) algorithm, a simple and computationally moderate solution, was used to optimize the 
MRF–MAP estimates as it converges to a local, but usually good, minimum of the energy function [6]. 
 
3. RESULTS 
Accuracy assessments were performed for the MLC and spatial-temporal classifications results by using the 
ground truth data. The results show that the spatial-temporal classification accuracy has been improved compared 
to non-contextual method. Speckles of classification results are reduced due to spatial smoothing with the 
incorporation of spatial information. Spectrum confusion between grass and crop and forest in January, 2008 was 
removed by adding the temporal information in August, 2007 because most grass had disappeared caused by the 
flush water in August. Accuracy of classification using the local transition probabilities of sub-images 
incorporated in the temporal information is higher than classification using the global transition probabilities of 
whole image for both two dates images, showing that local transition probabilities is more accurate than global 
transition probabilities. The temporal energy parameter is larger than spatial energy parameter in 2008, indicating 
temporal information is more useful than spatial information due to the accurate temporal information contained 
in 2007 classified result, and larger temporal weight is found to increase the influence of accurate temporal 
information.  
 
4. CONCLUSIONS 
In conclusion, a spatial-temporal classification algorithm that explicitly integrates spectral, spatial and temporal 
information in multi-temporal images can achieve significant improvements over non-contextual classification. 
MRF is an efficient probabilistic model for analysis of spatial and temporal contextual information. The local 
transition probability in MRF is more accurate than global transition probability, but computationally, the global 
model is the cheapest and fastest model. And the temporal energy parameter will adjust to different transition 
probability to make a better MRF model to improve the classification accuracy. 
5. REFERENCES 
 
[1] A.H.S. Solberg, T. Taxt, A.K. Jain, “A Markov Random Field Model for Classification of Multi-source Satellite Imagery”, IEEE 
TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 41, pp.100-113, 1996. 
 
[2] D. Liu, M. Kelly, P. Gong, “A spatial–temporal approach to monitoring forest disease spread using multi-temporal high spatial 
resolution imagery”, Remote Sensing of Environment, 101, pp.167-180, 2006. 
 
[3] N, Huang, M.H. Zhu, S.R. Zhang, “A Remotely Sensed Image Classification Algorithm based on Gaussian Hidden Markov Random 
Field Model”, Journal of Electronics and Information Technology, 25, pp.50-53, 2003. 
 
[4] D. Liu, K. Song,  J.R.G. Townshend, P. Gong, “Using local transition probability models in Markov random fields for forest change 
detection”, Remote Sensing of Environment, 112, pp.2222-2231, 2008 
 
[5] L Bruzzone, D.F. Prieto, S.B. Serpico, “A Neural-Statistical Approach to Multitemporal and Multisource Remote-Sensing Image 
Classification”, IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 37, pp.2478-2487, 1999. 
 
[6] F. Melgani, S.B. Serpico, “A Markov Random Field Approach to Spatio-Temporal Contextual Image Classification”, IEEE 
TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 41, pp.2478-2487, 2003. 
 


USING LOCAL TRANSITION PROBABILITY MODELS IN MARKOV RANDOM FIELD FOR MULTI-TEMPORAL IMAGE CLASSIFICATION

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USING LOCAL TRANSITION PROBABILITY MODELS IN MARKOV RANDOM FIELD FOR MULTI-TEMPORAL IMAGE CLASSIFICATION

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