In this paper we present a mixture density based approach to invariant image object recognition. We start our experiments using Gaussian mixture densities within a Bayesian classifier. Invariance to affine transformations is achieved by replacing the Euclidean distance with SIMARD's tangent distance. We propose an approach to estimating covariance matrices with respect to image invariances as well as a new classifier combination scheme, called the virtual test sample method. On the US Postal Service handwritten digits recognition task (USPS), we obtain an excellent classification error rate of ? ?, using the original USPS training and test sets.