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Cast shadows induced by moving objects often cause serious problems to many vision applications. We present in this paper an online statistical learning approach to model the background appearance variations under cast shadows. Based on the bi-illuminant (i.e. direct light sources and ambient illumination) dichromatic reflection model, we derive physics-based color features under the assumptions of constant ambient illumination and light sources with common spectral power distributions. We first use one Gaussian mixture model (GMM) to learn the color features, which are constant regardless of the background surfaces or illuminant colors in a scene. Then, we build up one pixel based GMM for each pixel to learn the local shadow features. To overcome the slow convergence rate in the conventional GMM learning, we update the pixel-based GMMs through confidence-rated learning. The proposed method can rapidly learn model parameters in an unsupervised way and adapt to illumination conditions or environment changes. Furthermore, we demonstrate that our method is robust to scenes with few foreground activities and videos captured at low or unsteady frame rates.