Invariance is an important aspect in image object recognition. We present results obtained with an extended tangent distance incorporated in a kernel density based Bayesian classifier to compensate for affine image variations. An image distortion model for local variations is introduced and its relationship to tangent distance is considered. The proposed classification algorithms are evaluated on databases of different domains. An excellent result of 2.2% error rate on the original USPS handwritten digits recognition task is obtained. On a database of radiographs from daily routine, best results are obtained by combining tangent distance and the proposed distortion model.