The tilt illusion is a paradigmatic example of contextual influences on perception. We analyze it in terms of a neural population model for the perceptual organization of visual orientation. In turn, this is based on a well-found treatment of natural scene statistics, known as the Gaussian Scale Mixture model. This model is closely related to divisive gain control in neural processing and has been extensively applied in the image processing and statistical learning communities; however, its implications for contextual effects in biological vision have not been studied. In our model, oriented neural units associated with surround tilt stimuli participate in divisively normalizing the activities of the units representing a center stimulus, thereby changing their tuning curves. We show that through standard population decoding, these changes lead to the forms of repulsion and attraction observed in the tilt illusion. The issues in our model readily generalize to other visual attributes and contextual phenomena, and should lead to more rigorous treatments of contextual effects based on natural scene statistics.