The Topographic Primal Sketch

A complete mathematical treatment is given for describing the topographic primal sketch of the underlying gray tone intensity surface of a digital image. Each picture element is independently classified and assigned a unique descriptive label, invariant under monotonically increasing gray 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. A local, facet model, two-dimensional, cubic polynomial fit is done to estimate the image-intensity surface. Zero-crossings of the first directional derivative are identified as locations of interest in the image.