A recent Cell paper (Chang & Tsao, 2017 ) reports an interesting discovery. For the face stimuli generated by a pretrained active appearance model (AAM), the responses of neurons in the areas of the primate brain that are responsible for face recognition exhibit a strong linear relationship with the shape variables and appearance variables of the AAM that generates the face stimuli. In this letter, we show that this behavior can be replicated by a deep generative model, the generator network, that assumes that the observed signals are generated by latent random variables via a top-down convolutional neural network. Specifically, we learn the generator network from the face images generated by a pretrained AAM model using a variational autoencoder, and we show that the inferred latent variables of the learned generator network have a strong linear relationship with the shape and appearance variables of the AAM model that generates the face images. Unlike the AAM model, which has an explicit shape model where the shape variables generate the control points or landmarks, the generator network has no such shape model and shape variables. Yet it can learn the shape knowledge in the sense that some of the latent variables of the learned generator network capture the shape variations in the face images generated by AAM.

This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a given set of observed feature statistics, a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them. The second part is the minimum entropy principle for feature selection: among all plausible sets of feature statistics, we choose the set whose maximum entropy distribution has the minimum entropy. Computational and inferential issues in both parts are addressed; in particular, a feature pursuit procedure is proposed for approximately selecting the optimal set of features. The minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics, and an information criterion for feature pursuit is derived. The minimax entropy principle is applied to texture modeling, where a novel Markov random field (MRF) model, called FRAME (filter, random field, and minimax entropy), is derived, and encouraging results are obtained in experiments on a variety of texture images. The relationship between our theory and the mechanisms of neural computation is also discussed.