Visual anisotropy has been demonstrated in multiple tasks where performance differs between vertical, horizontal, and oblique orientations of the stimuli. We explain some principles of visual anisotropy by anisotropic smoothing, which is based on a variation on Koenderink's approach in [1]. We tested the theory by presenting gaussian elongated luminance profiles and measuring the perceived orientations by means of an adjustment task. Our framework is based on the smoothing of the image with elliptical gaussian kernels and it correctly predicted an illusory orientation bias towards the vertical axis. We discuss the scope of the theory in the context of other anisotropies in perception.