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This paper presents tensor-based covariance matrices for object modeling and tracking. Unlike the traditional vector-based or matrix-based object representation, this method represents an object with a third-order tensor and has better capability to capture the intrinsic structure of the image data. We flatten the tensor to obtain all of its mode-n unfolding matrices, each one of which can be seen as a sample of observations of some high-dimensional random signals. For every mode-n unfolding matrix, we use the K-L transform to achieve the principal components of the column vectors. The covariance matrix of the reduced-dimensional signal via the K-L transform is used for modeling the object statistics. Based on this modeling, a distance measure is introduced for object tracking using the affine-invariant Riemannian metric. For adapting to the appearance changes of the object across time, we present an efficient, incremental model update mechanism. Experiments show that the proposed tracking method has promising performance.