In the context of multi-temporal synthetic aperture radar (SAR) images for earth monitoring applications, one critical issue is the detection of changes occurring after a natural or anthropic disaster. In this paper, we propose a new similarity measure for automatic change detection using a pair of SAR images acquired at different dates. This measure is based on the evolution of the local statistics of the image between two dates. The local statistics are modeled as a Gaussian Mixture Model (GMM), which approximates the probability density function in the neighborhood of each pixel in the image. The degree of evolution of the local statistics is measured using the Kullback-Leibler (KL) divergence. One analytical expression for approximating the KL divergence between GMMs is given and is compared with the Monte Carlo sampling method. The proposed change detector is compared to the classical mean ratio detector and also to other recent model-based approaches. Tests on the real data show that our detector outperforms previously suggested methods in terms of the rate of missed detections and the total error rates.