An equation-based triangle orientation discrimination (TOD) performance model was first developed to focus on staring thermal imagers. Specifically, the spatial spectra distribution of a standard triangle pattern is determined. The modulation effects of the overall components of the system on a nonperiodic standard triangle pattern are analyzed and modeled. The matched filter idea is used to characterize quantitatively the spatiotemporal integration of the eye and brain to signal, aliasing, and various noise components over a triangle pattern area, and the perceived signal-to-noise ratio of the staring thermal imager is derived. Further, the TOD performance theoretical model is established. Comparison with the experimental results shows that this theoretical model gives a reasonable prediction of the TOD performance curve for staring thermal imagers. Although more tests and modifications are required, these preliminary results suggest that this model can be developed into a model that predicts the TOD for a wide range of sensors.