IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 8, AUGUST 2002 1815 An Image Change Detection Algorithm Based on Markov Random Field Models Teerasit Kasetkasem and Pramod Kumar Varshney, Fellow, IEEE Abstract—This paper addresses the problem of image change detection (ICD) based on Markov random field (MRF) models. MRF has long been recognized as an accurate model to describe a variety of image characteristics. Here, we use the MRF to model both noiseless images obtained from the actual scene and change images (CIs), the sites of which indicate changes between a pair of observed images. The optimum ICD algorithm under the maximum a posteriori (MAP) criterion is developed under this model. Examples are presented for illustration and performance evaluation. Index Terms—Change detection, Markov random fields, max- imum a posteriori (MAP) criterion, multitemporal image analysis. I. INTRODUCTION T HE ABILITY to detect changes that quantify temporal effects using multitemporal imagery provides a funda- mental image analysis tool in many diverse applications. Due to the large amount of available data and extensive computational requirements, there is a need for change detection algorithms that automatically compare two images taken from the same area at different times and determine the locations of changes. Usually, in the comparison process [1]–[4], differences between two corresponding pixels belonging to the same location for an image pair are determined, based on some quantitative measure. Then, a change is labeled if this difference measure exceeds a predefined threshold, and no change is labeled, otherwise. Most of the comparison techniques described in [1] only consider information contained within a pixel, even though intensity levels of neighboring pixels of images are known to have significant correlation. Also, changes are more likely to occur in connected regions rather than at disjoint points. By using these facts, a more accurate change detection algorithm can be developed. To accomplish this, a Markov random field (MRF) model for images is employed in this paper so that statistical correlation of intensity levels among neighboring pixels can be exploited. MRF has long been recognized as an accurate model to describe a variety of image characteristics such as texture. Under this model [5]–[8], the configuration (intensity level) of a site (pixel) is assumed to be statistically independent of configurations of all remaining sites excluding itself and its neighboring sites when configurations of its neighboring sites are given. In other words, the configuration of a pixel Manuscript received July 28, 2001; revised May 27, 2002. This research was supported by the National Aeronautics and Space Administration under Grant NAG5-11227. The authors are with the Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13244 USA (e-mail: tkasetka@syr.edu; varshney@syr.edu). Publisher Item Identifier 10.1109/TGRS.2002.802498. given the configurations of the rest of the image is the same as the configuration of a pixel given the configurations of its neighboring pixels. Furthermore, the MRF is known to be equivalent to the Gibbs field [6] whose probability density function (pdf) is given by (1) where set of sites contained within an image; vector of configurations (intensity levels) over ; normalizing constant; Gibbs potential function. A Gibbs potential function is a function of configurations and cliques. A clique [5], [6], denoted by , is defined as a set of sites whose elements are mutual neighbors. Studies reported in [9], [10] have tried to employ the MRF model for image change detection (ICD). In [9], one image is subtracted from the other, pixel by pixel, and two thresholds (one low and one high) are then selected. If the difference intensity level of a pixel is lower than the low threshold, then this pixel is put in the absolute unchanged class. If the intensity level is greater than the high threshold, the corresponding pixel is put in the absolute changed class. The remaining pixels whose difference intensity levels are between these two thresholds are subjected to further processing where the spatial-contextual information based on the MRF model is considered. A similar approach can be found in [10]. Again, this algorithm can be divided into two parts. In the first part, a pixel-based algorithm [1] determines an initial change image (CI) that is further refined based on the MRF model in the second part. Some information is lost while obtaining the initial CI, since the observed data are projected into a binary image whose intensity levels represent change or no change. We observe that studies in [9] and [10] do not fully utilize all the information contained in images; moreover, the preservation of MRF properties is not guaranteed. In [11], the effect of image transformations on images that can be modeled by MRFs is studied. It has been shown that MRF properties may not hold after many transformations such as resizing of an image and subtraction of one image from another. For some specific transformations, MRF properties are preserved, but a new set of potential functions must be obtained. Since a difference image can be looked upon as a transformation, MRF modeling of a difference image in [9] and initial CI in [10] may not be valid. This provides the motivation for the development of an ICD algorithm that uses additional information available from the image and preserves 0196-2892/02$17.00 © 2002 IEEE