The Topographic Primal Sketch

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Abstract
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.

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