Invariant perception of objects is desirable. Contrast constancy assures invariant appearance of suprathreshold image features as they change their distance from the observer. Fully robust size invariance also requires equal contrast thresholds across all spatial frequencies and eccentricities so that near-threshold image features do not appear or disappear with distance changes. This clearly is not the case, since contrast thresholds increase exponentially with eccentricity. We showed that a less stringent constraint actually may be realized. Angular size and eccentricity of image features covary with distance changes. Thus the threshold requirement for invariance could be approximately satisfied if contrast thresholds were to vary as the product of spatial frequency and eccentricity from the fovea. Measurements of observers' orientation discrimination contrast thresholds fit this model well over spatial frequencies of 1 - 16 cycles/degree and for retinal eccentricities up to 23 degrees. Measurements of observers’ contrast detection thresholds from three different studies provided an even better fit to this model over even wider spatial frequency and retinal eccentricity ranges. The fitting variable, die fundamental eccentricity constant, was similar for all three studies (0.036, 0.036, 0.030, respectively). The eccentricity constant for the orientation discrimination thresholds was higher (0.048 and 0.050 for two observers, respectively). We simulated the appearance of images with a nonuniform visual system by applying the proper threshold at each eccentricity and spatial frequency. The images exhibited only small changes over a simulated 4-octave distance range. However, the change in simulated appearance over the same distance range was dramatic for patients with central visual field loss. The changes of appearance across the image as a function of eccentricity were much smaller than in previous simulations, which used data derived from visual cortex anatomy rather than direct measurements of visual function. Our model provides a new tool for analyzing the visibility of displays and for designing equal visibility or various visibility displays.