The primary purpose of night-vision systems in civilian vehicles is to help drivers detect pedestrians. Pedestrian detection distance with night-vision systems has been modeled based on image metrics. However, the probability of pedestrian detection, in particular considering the factor of distance, has not been modeled based on image metrics. In this paper, we first describe a model of the probability of pedestrian detection, which compares several combinations of image-based clutter, contrast, and pedestrian size metrics using a simple mathematical equation. Next, we describe a model of the probability of pedestrian detection as a function of distance and image-based metrics by combining the model of pedestrian-detection probability and a model that represents the relationship between the distance to a pedestrian and an image-based pedestrian size metric. In the final model, image-based metrics are used to predict pedestrian-detection performance and can also be used to evaluate and support the development of night-vision systems in vehicles.