The human capacity to recognize complex visual patterns emerges in a sequence of brain areas known as the ventral stream, beginning with primary visual cortex (V1). We developed a population model for mid-ventral processing, in which nonlinear combinations of V1 responses are averaged in receptive fields that grow with eccentricity. To test the model, we generated novel forms of visual metamers, stimuli that differ physically but look the same. We developed a behavioral protocol that uses metameric stimuli to estimate the receptive field sizes in which the model features are represented. Because receptive field sizes change along the ventral stream, our behavioral results can identify the visual area corresponding to the representation. Measurements in human observers implicate visual area V2, providing a new functional account of neurons in this area. The model also explains deficits of peripheral vision known as crowding, and provides a quantitative framework for assessing the capabilities and limitations of everyday vision.