Stochastic background models incorporating spatial correlations can be used to enhance the detection of targets in natural terrain imagery, but are generally difficult to apply when the statistics are non-Gaussian. Chapple and Bertilone (see Opt. Commun., vol.150, p.71-76, 1998) proposed a simple stochastic model for images of natural backgrounds based on the pointwise nonlinear transformation of Gaussian random fields, and demonstrated its effectiveness and computational efficiency in modeling the textures found in natural terrain imagery acquired from airborne IR sensors. In this paper, we show how this model can be used to design algorithms that detect small targets (up to several pixels in size) in natural imagery by identifying anomalous regions of the image where the statistics differ significantly from the rest of the background. All of the model-based algorithms described here involve nonlinear spatial processing prior to the final decision threshold. Monte Carlo testing reveals that the model-based algorithms generally perform better than both the adaptive threshold filter and the generalized matched filter for detecting low-contrast targets, despite the fact that they do not require the target statistics needed for constructing the matched filter.