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. (1) 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 these feature statistics. 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. The minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics, and a novel information criterion is derived for feature selection. The minimax entropy principle is applied to texture modeling. Relationship between our theory and the mechanisms of neural computation is also discussed.