Histogram model for 3D textures

Image texture can arise not only from surface albedo variations (2D texture) but also from surface height variations (3D texture). Since the appearance of 3D texture depends on the illumination and viewing direction in a complicated manner, such image texture can be called a bidirectional texture function. A fundamental representation of image texture is the histogram of pixel intensities. Since the histogram of 3D texture also depends on the illumination and viewing directions in a complex fashion, we refer to it as a bidirectional histogram. In this work, we present a concise analytical model for the bidirectional histogram of Lambertian, isotropic, randomly rough surfaces, which are common in real-world scenes. We demonstrate the accuracy of the histogram model by fitting to several samples from the Columbia-Utrecht texture database. The parameters obtained from the model fits are roughness measures which can be used in texture recognition schemes. In addition, the model has potential application in estimating illumination direction in scenes where surfaces of known tilt and roughness are visible. We demonstrate the usefulness of our model by employing it in a novel 3D texture synthesis procedure.