Covariance matrices have recently been a popular choice for versatile tasks like recognition and tracking due to their powerful properties as local descriptor and their low computational demands. This paper outlines similarities of covariance matrices to the well-known structure tensor. We show that the generalized version of the structure tensor is a powerful descriptor and that it can be calculated in constant time by exploiting the properties of integral images. To measure the similarities between several structure tensors, we describe an approximation scheme which allows comparison in a Euclidean space. Such an approach is also much more efficient than the common, computationally demanding Riemannian Manifold distances. Experimental evaluation proves the applicability for the task of object tracking demonstrating improved performance compared to covariance tracking.