When three-dimensional surfaces are imaged in perspective, distortions in the surface markings (textures) can convey the shape of the surface. Theories of shape from texture have invoked texture gradients, frequency modulations, and affine deformations. For upright, developable surfaces like the one below, the critical shape information is contained in orientation modulations of the Fourier component that is parallel to the axis of maximum curvature (horizontal). In the figure below, these modulations are visible as sparse contours that are close to horizontal, and reveal that the shape is corrugated in depth, with a central concavity.

For the same corrugation, if the horizontal Fourier component is removed from the texture pattern, the critical orientation modulations are not present in the image, and the perceived shape is qualitatively distorted, despite the presence of texture gradients, frequency modulations, and affine deformations.

Shape can also be perceived as qualitatively veridical if the critical orientation modulations are visible as contrast changes. This second-order information can be used by preceding shape-from-texture computations with an operation such as rectification, squaring, etc.

If the corrugation is not upright, but pitched towards or away from the observer, the critical orientation modulations are provided by pairs of Fourier components of the texture, oriented at angles close to the pitch.

Shape-from-texture experiments have often used textures like polka dots that have isotropic Fourier spectra, overlaid onto purely convex shapes like cylinders. Distortions of such textures in perspective projections convey frequency modulations, but do not convey critical orientation modulations. As a result, concavities and convexities both appear to be convexities. It is possible that the distorted percepts arise because the visual system assumes that the lower frequencies are closer and the higher frequencies are further from the observer.