A Contrario Fusion for Detecting Change in Satellite Imagery

Interest is growing in the numerous methods of automatically detecting change in satellite imagery, especially due to the many ways they can be applied to analyze the Earth’s surface or the environment (monitoring vegetation, updating maps, risk management, etc.). However, change detection using fusion images based on an a contrario approach is a new method introduced by[5]. The main objective of this study is to introduce a process for using fusion of change indicators based on a contrario modeling. The first aim of this study is to show that change exists between different bandwidths raw of the same source image and that the rate of change remains practically the same from one source image to another. The second objective is to determine a rate of change between multi-temporal images.


Introduction
Nu merous methods of detecting change have been used, notably by [1] and [2]. And this methods were classified by [3] according to their intervention levels, we find (i) at the pixel level, analysis by change vectors, simple detectors and regression, (ii) at the characteristic level, analysis by texture, principal co mponents analysis , analysis of shape, vegetation index differencing and wavelets, and finally, (iii) at the object level, methods for direct mu lti-date classification, post-classification comparison and fuzzy post-classification comparison, artificial intelligence, artificial neuron network s and expert systems.
Applying the a contrario approach to image processing is based on detecting unexpected structures, in other words, highly unlikely or more exactly, ext remely "rare" under the a priori model [4].Thus, "events" can be detected without making any hypotheses about the shape of these events, but simp ly by testing consistency in contrast with an a priori model (called a naï ve model), which justifies qualitative a contrario detection [5].
The main objective of this study is to show that the fusion of change indicators based on a a contrario approach improves change detection.
Change indices used by [5] include those of the "absolute differencing", those of the "absolute differencing of textural parameters" and those of the "information measurements". Automatic change detection by the fusion of changeindic ators depends upon two essential points, namely, analyzing change indicator images and fusionning these images of change indicators at the decision-making level [5]. The algorith m proposed by [5] involves considering that, at each new iteration, a change indicator is selected fro m the library of change indicators in such a way as to form the image of this indicator. The fusion is done traditionally using Dempster's rule of co mb ination.
The limits of these methods can be found, on one hand, i n the difficulty of choosing change indicators and, on the other hand, in the method used to fuse these indicators.
The question that must be raised is this: fro m what thresholds are the changes detected in the images describing texture and d ifferencing images extracted fro m images sources considered significant?
First, a contrario change ind icators fusion will be describ ed with the principal aim of showing that change exists between different bandwidths extracted fro m the same image source. The second objective will be to determine the rate of change between these multi-temporal images. Finally, the results of the change indicator fusion using a contrario modeling will be presented and discussed.

Data and Study Area
A set of four mu lti-date and mu ltispectral images were used in this study. some pretreat ments were carried out on the optical images to improve the quality of these images especially those dating fro m 1987 and 1998 and to minimiz e the noise transmitted by the sensors. these pretreatments consisted in applying filters and put the images in a geographic reference. Table 1 gives an exact description of the data used: images sources and change indicators images.
The study area chosen is located north of Tunis, bordered by a marsh named Sebkhet Ariana on the east and the Lake of Tunis and Tunis-Carthage airport on the southeast, extending to the northwest to the neighborhood of Soukra. This area is characterized by the heterogeneity of the environment, especially due to the presence of the marsh, a mo re or less high-traffic urban area, a green belt and streets. The study area chosen is located north of the city of Tunis and bordered by a marsh named Sebkhet Ariana in the east, by the Lake of Tunis and the Tunis-Carthage airport in the southeast, and extending to the neighborhood of Soukra in the northwest. This area is a heterogeneous environment, especially due to the presence of the marsh, and a rather densely populated urban area, with green belt and roads.

Descripti on of a General Problem of Fusion
Bloch affirmed that the objective of images fusion was principally to imp rove the three main tasks of detecting, identifying and recognizing shapes [6]. Thus, imp lementing fusion methods can occur for segmentation, reconstruction and change detection or also for updating informat ion about a phenomenon or scene.  [8] Fusion can be a process or a sequence of tasks which must include three fundamental stages[7] ext racting characteristic s, combination and decision-making. Successfully fusion data lies in choosing a strategy (centralized, decentralized, hybrid) in wh ich can be found the informat ion and the type of informat ion to be combined. The fusion process can be shown by the Houzelle general d iagram [8] as shown by Figure.1. The fusion cell operates according to black bo x principle wh ich receives inputs and produces outputs.

Change Indicators
Mascle proposed improving change detection based on the use of a single change indicator by co mbin ing the results of change detection of different indicators [5]. On a single image, regions or groups of pixels are detected whose obser ved measurements are unexpected. Explanation for deviating fro m the expected measurement, which includes change in land use either due to man-made or natural orig ins, local modification of environ mental factors, etc. called "change qualification" by [5], is generally determined by additional informat ion after the "change detection" .
Indicators used in the a contrario fusion process include those indicators deduced from textu re descriptors, namely:  local entropy  local standard deviation  local range And the last indicator was calculated fro m basic arith metic operators like applied image d ifferencing, univariate image differencing (UID) where each output pixel contains the absolute value of the difference calculated pixel by pixel [9].

Principle of the a Contrario Method for Change Indicators Fusion
Extracting change indicators on N sources images makes it possible to generate a set of "change indicator" images. These "change indicator" Mn images are fused after estimating probability images and according to certain decision-making criteria based on -significant thresholds.
When the null hypothesis, called H0, is tested, probability can be calculated assuming that this hypothesis is true and that the alternative hypothesis H1 is false.
If the event of the "probability of no change" is considered, estimating the p robability of change in the a contrario hypothesis is such that: H0: "the probability P of having the measurement at any given pixel less than threshold α." The probability of obtaining change P(Mn) in a bino minal distribution within a series of k trials : There is pract ically the same probability, thus one chance in two, for change: with P: "the probability of having an ng gray level" with ng vareing fro m  The approach described will make it possible to calcu late the rate of false identifications of change (RFC). Thus, for each threshold value, a rate of correct identifications of change was calculated (RCC) and a curve was drawn describing the evolution of the rate of change as a function of the considered thresholds. The last stage consists of deducing a binary mask which results in detecting changes fro m -significant p-values. Figure 2 provides a description of the approach used to implement the a contrario fusion of change indicators.  Modeling requires an estimation phase done by calculating the p-values associated with M (n,n) , followed by the combination stage. Finally, the process ends with decision-making. Figure 3 gives a description of the fusion structure which is centralized.

Results of Change Detection by a Contrari o Fusion Change Indicators
As regards generating change indicator images, those images extracted fro m images sources concern to: Local entropy of image I at gray level where each output pixel contains the value of entropy in a 9 by 9 window around the corresponding pixel in the input image. Figure  4.A shows an entropy image related to the SPOT1 image dating fro m 1987.
Local standard deviation of image I at gray level, where each output pixel contains the standard deviation calculated in a 3 by 3 window around the corresponding pixel in the input image.   figure 6.B is calculated fro m the (images sources) mu ltispectrals images : SPOT1 and SPOT4. Change detection by a contrario fusion of the appropriate indicators was applied, first on multispectrals images with the same temporal resolution, then on multi-temporal images by choosing to combine bandwidths with the greatest amount of information. Applying the fusion algorith m on a single mu ltispectral source image SPOT1 co mposed of three bandwidths: xs1, xs 2 and xs3 dating fro m 1987 allows the detection of change. Figure 7.D shows the change image calculated for a threshold of 10-3 with a RCC of 19.61%. Thus, calculating the correlation coefficient between the three bandwidths of the source image described in Table 2 shows that there is a strong correlat ion between bandwidths xs 1 and xs 2 and that this correlation beco mes weaker in the second and third bandwidths.  Even though it is in the same source image, these bandwidths do not contain the same amount of informat ion. The reflectance emitted by objects on the ground varies according to wavelength. RCC made it possible to highlight useful information and eliminate redundancy between the bandwidths . App ly ing a cont rario fus ion of ch ange indica tors on the mult ispectral source image SPOT3 co mposed of three bandwidths, xs1, xs2 and xs3 dating fro m 1998 ( Figure  8.A, B and C) give a threshold of 10 -3 and a RCC of 15.46% as indicated in Figure 8.D which shows the obtained change image. Table 3 provides the correlation coefficients between the three bandwidths of the SPOT3 image. Bandwidths xs1 and xs2 were observed to be highly correlated, although bandwidths xs2 and xs3 showed a strong decorrelation. The algorith m in question was then applied to the mu ltispectral SPOT4 source image dating fro m 2000 and composed of three bandwidths: B1, B2 and B3 (Figure 9.A, B and C). The correlation coefficients between the three bandwidths fro m the SPOT4 image are given in Table 4.  Knowing that the change detection algorithm operates by taking different values of threshold, for each threshold value , a RCC is obtained. The study results are summarized by the graph in Figure 10. The lower limit of this algorith m is 10 -3 while the upper limit is 10 -40 . The question addressed in this study was for what -significant threshold value can a valid RCC be obtained, given that the smaller the threshold, the greater the RCC and that from 10 -7 , 80% change has already been reached. In addition, the study on change detection in relation to mult ispectrals images fro m the same sensor shows that, for a threshold of 10 -3 , changes could be detected since the different bandwidths did not have the same amount of informat ion. The RCC was also nearly constant at 15% for the different bandwidths in a single image source. These analyses led to opting for a threshold of 10 -4 . Figure 11 provides a change image for a threshold of 10 -4 with a rate of correct change identification (RCC) of 44.80%.
The calculated correlat ion coefficient between mult i-date sources images is given in Table 5 which shows that the correlation decreases with time. Figure 11. Change image by a contrario fusion of change indicators

Conclusions
Applying the method of change detection based on a contrario fusion of change indicators between 1987 and 2003 gave a RCC of 44.80%. However, applying a tradit ional change method such as differencing provided a rate of change of 86.83% ( figure.12). Moreover, applying a change detection method based on a contrario differencing, [10] obtained a rate of change of 57.34% as shown by figure 13. These rates of change were validated co mpared to on-site reality for plots of land established between 1987 and 2003, thus stipulating that the region underwent an overall change of 54.98%. Co mbin ing change indicators a contrario seems to give good results compared with the traditional method of change detection. Nevertheless, change detection based on a contrario differencing gave the best results. These results are presented in Table 6.
Change detection based on a contrario fusion of change indicators made it possible to calculate overall rates of change. A more detailed study would provide rates of change concerning each theme corresponding to specified land use. In addition, fu rther in formation could be incorporated such as integrating other indicators in the fusion process as well as using classified images to improve the approach used here. Table 6. Proportion of change when applying algorithms for simple differencing, a contrario differencing, a contrario fusion and a ground truth