Is shading a linear filter?

The decomposition of an input image into its materialdependent “intrinsic” properties and its light-dependent shading properties is useful for many computer vision tasks such as image segmentation, object recognition, and geometric inference. For example, image segmentation and edge detection can be performed by grouping sets of pixels by reflectance values; object recognition will be more robust to differences in lighting if shading is removed; and information about the 3D geometry of a scene can be determined from patterns in shading alone. The decomposition is expressed as I(x) = s(x)R(x), where I(·) is the observed intensity and S(·) and R(·) represent the light-dependent and material-dependent properties respectively at any pixel x. A computationally efficient algorithm for recovering S and R from any image I could possibly increase the efficiency of many common higherlevel tasks in computer vision.