In appearance-based image processing, high-dimensional statistical models are estimated from low numbers of training samples. Sample scatter matrices are unreliable estimators of class covariances, yet many methods rely on them for dimensionality reduction and often for classification too. This paper argues for regularized covariance estimation and introduces a new method suitable for appearance-based image processing. The method is demonstrated for face detection, where a maximum likelihood classifier trained with regularized covariances achieves discrimination and detection results comparable to those of complicated multimodal and non-linear classifiers.