In remote sensing, image-based change detection techniques, analyze two images acquired over the same area at different times t₁ and t₂ to identify the changes occurred on the Earth's surface. Change detection approaches are mainly categorized as supervised and unsupervised. Generating the change index is a key step for change detection in multi-temporal remote sensing images. Unsupervised change detection is generally based on the analysis of the magnitude of change index.
In multispectral remote sensing images, in addition to the magnitude of change index, the direction of change index could be calculated with similarity measures such as spectral angle mapper (SAM). Literature reveals that the magnitude of change index has been widely used in change detection of multispectral images, whereas the use of the direction of change index is always ignored. The magnitude and direction of change indices have different and limited capability for detecting different types of land cover change. These indices contain complementary information about the changed phenomenon. Combining the magnitude and direction of change indices would increase the performance of change detection in multi-temporal multispectral images. 
In this paper, a new fused change index based on the weighted linear combination of magnitude and direction of change indices has been proposed. In the proposed method, the weighting parameter of each index is determined automatically based on the ability of that index for unsupervised change detection. The proposed method uses the Xie-Beni (XB) index as unsupervised change detection validity measure for determining the optimal combination weights. XB is a ratio-type index, which measures the within-cluster compactness against the between-cluster separateness. The more separate the clusters, the smaller the XB index. Hence, the combination weight of each index should be inversely related to XB index. After calculating the fused change index, a thresholding method should be applied to generate the binary change map. In this paper, Otsu's thresholding method has been used because of its simplicity, efficiency, and low computational cost.
The performance of the proposed approach has been evaluated on two bi-temporal and multispectral data sets having different properties (different types of land cover/land use changes). The first data set is made up of a couple of acquired multispectral images on the Urmia Lake (Iran) by the ETM+ sensor (mounted on the Landsat-7 satellite) and TM sensor (mounted on the Landsat-5 satellite) in August 1999 and September 2010 respectively. The second case study was conducted based on a couple of Landsat TM 4, 5 multispectral images acquired on the city of Maraghe (Iran) in June 1989 and June 1998 respectively. These data sets are characterized by a spatial resolution of 30 m×30 m and 6 spectral bands ranged from blue light to shortwave infrared (the 6th band of these images, which is in thermal infrared ranged, is not utilized due to low spatial resolution).
Experimental results show that direction and magnitude of change indices have different and restricted abilities to detect multiple changes due to their different properties. For this reason, direction and magnitude of change indices can only detect three of the four possible change categories, properly. The fusion of magnitude and direction of change indices in the proposed index makes it possible to more accurately detect all of the four change categories as compared with the individual indices alone. The total error (TE) of obtained binary change map (BCM) by proposed index in the first dataset is 10.17% which demonstrates 21.78% and 6.11% improvements in overall accuracy compared with the magnitude and direction of change indices respectively. Similarly, in the second case study, the fused change index (proposed approach) had a significantly lower total error (12.89%) than the magnitude of change index (18.20%) and the direction of change index (29.49%).