A picture viewed from its center of projection generates the same retinal image as the original scene, so the viewer perceives the scene correctly. When a picture is viewed from other locations, the retinal image specifies a different scene, but we normally do not notice the changes. We investigated the mechanism underlying this perceptual invariance by studying the perceived shapes of pictured objects viewed from various locations. We also manipulated information about the orientation of the picture surface. When binocular information for surface orientation was available, perceived shape was nearly invariant across a wide range of viewing angles. By varying the projection angle and the position of a stimulus in the picture, we found that invariance is achieved through an estimate of local surface orientation, not from geometric information in the picture. We present a model that explains invariance and other phenomena (such as perceived distortions in wide-angle pictures).