Visual Difference Predictor (VDP) models have played a key role in digital image applications such as the development of image quality metrics. However, little attention has been paid to their applicability to peripheral vision. Central (i.e., foveal) vision is extremely sensitive for the contrast detection of simple stimuli such as sinusoidal gratings, but peripheral vision is less sensitive. Furthermore, crowding is a well-documented phenomenon whereby differences in suprathreshold peripherally viewed target objects (such as individual letters or patches of sinusoidal grating) become more difficult to discriminate when surrounded by other objects (flankers). We examine three factors that might influence the degree of crowding with natural-scene stimuli (cropped from photographs of natural scenes): (1) location in the visual field, (2) distance between target and flankers, and (3) flanker-target similarity. We ask how these factors affect crowding in a suprathreshold discrimination experiment where observers rate the perceived differences between two sequentially presented target patches of natural images. The targets might differ in the shape, size, arrangement, or color of items in the scenes. Changes in uncrowded peripheral targets are perceived to be less than for the same changes viewed foveally. Consistent with previous research on simple stimuli, we find that crowding in the periphery (but not in the fovea) reduces the magnitudes of perceived changes even further, especially when the flankers are closer and more similar to the target. We have tested VDP models based on the response behavior of neurons in visual cortex and the inhibitory interactions between them. The models do not explain the lower ratings for peripherally viewed changes even when the lower peripheral contrast sensitivity was accounted for; nor could they explain the effects of crowding, which others have suggested might arise from errors in the spatial localization of features in the peripheral image. This suggests that conventional VDP models do not port well to peripheral vision.