We propose a novel approach for tracking an arbitrary object in video sequences for visual surveillance. The first contribution of this work is an automatic feature extraction method that is able to extract compact discriminative features from a feature pool before computing the region covariance descriptor. As the feature extraction method is adaptive to a specific object of interest, we refer to the region covariance descriptor computed using the extracted features as the adaptive covariance descriptor. The second contribution is to propose a weakly supervised method for updating the object appearance model during tracking. The method performs a mean-shift clustering procedure among the tracking result samples accumulated during a period of time and selects a group of reliable samples for updating the object appearance model. As such, the object appearance model is kept up-to-date and is prevented from contamination even in case of tracking mistakes. We conducted comparing experiments on real-world video sequences, which confirmed the effectiveness of the proposed approaches. The tracking system that integrates the adaptive covariance descriptor and the clustering-based model updating method accomplished stable object tracking on challenging video sequences.