Implementation of the Johnson criteria for infrared images is the probabilities of a discrimination technique. The inputs to the model are the size of the target, the range to it, and the temperature difference against the background. The temperature difference is calculated without taking the background structure into consideration, but it may have a strong influence on the visibility of the target. We investigated whether a perceptually based temperature difference should be used as input. Four different models are discussed: 1. a probability of discrimination model largely based on the Johnson criteria for infrared images, 2. a peak signal-to-noise ratio model, 3. a signal-to-clutter ratio model, and 4. two versions of an image discrimination model based on how human vision analyzes spatial information. The models differ as to how much they try to simulate human perception. To test the models, a psychophysical experiment was carried out with ten test persons, measuring contrast threshold detection in five different infrared backgrounds using a method based on a two-alternative forced-choice methodology. Predictions of thresholds in contrast energy were calculated for the different models and compared to the empirical values. Thresholds depend on the background, and these can be predicted well by the image discrimination models, and better than the other models. Future extensions are discussed.