We describe a flexible model for representing images of objects of a certain class, known a priori, such as faces, and introduce a new algorithm for matching it to a novel image and thereby perform image analysis. The flexible model, known as a multidimensional morphable model, is learned from example images of objects of a class. In this paper we introduce an effective stochastic gradient descent algorithm that automatically matches a model to a novel image. Several experiments demonstrate the robustness and the broad range of applicability of morphable models. Our approach can provide novel solutions to several vision tasks, including the computation of image correspondence, object verification and image compression.