Theory of edge detection

A theory of edge detection is presented. The analysis proceeds in two parts. (1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales. An appropriate filter for this purpose a t a given scale is found to be the second derivative of a Gaussian, and it is shown that, provided some simple conditions are satisfied, these primary filters need not be orientation-dependent. Thus, intensity changes a t a given scale are best detected by finding the zero values of V2G(x, y)* I(x, y) for image I, where G(x, y) is a two-dimen­ sional Gaussian distribution and V2 is the Laplacian. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given th a t this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination bound­ aries, and these all have the property tha t they are spatially localized. Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. This description is called the raw primal sketch. The theory explains several basic psychophysical findings, and the opera­ tion of forming oriented zero-crossing segments from the output of centre-surround V2G filters acting on the image forms the basis for a physiological model of simple cells (see Marr & Ullman 1979).