A complete mathematical treatment is given for describing the topographic primal sketch of the underlying grey tone intensity surface of a digital image. Each picture element is independently classified and assigned a unique descriptive label, invariant under monotonically increasing grey tone transformations, from the set {peak, pit, ridge, ravine, saddle, flat, and hillside}, with hillside having subcategories {inflection point, slope, convex hill, concave hill, and saddle hill}. The topographic classification is based on the first and second directional derivatives of the estimated image intensity surface. Three different sets of basis functions, bicubic polynomial (local facet model), generalized splines, and the discrete cosine basis, are used to estimate the image intensity surface using a least squares technique. Zero-crossings of the first directional derivative are identified as locations of interest in the image. / M.S.