Theory of edge detection

TLDR

Intensity changes in images arise from surface discontinuities or reflectance/illumination boundaries and are spatially localized. The paper presents a theory of edge detection. The theory analyzes images in two stages: first detecting intensity changes at multiple scales using the Laplacian of Gaussian zero‑crossings, then combining the resulting zero‑crossing segments across scales into a unified description. The method demonstrates that the Laplacian of Gaussian filter is effective and orientation‑independent, that zero‑crossing segments provide a complete representation, and that the resulting raw primal sketch explains basic psychophysical findings and underlies a physiological model of simple cells.

Abstract

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 at 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 at a given scale are best detected by finding the zero values of ∇ 2 G(x, y) * I(x, y) for image I, where G(x, y) is a two-dimen­sional Gaussian distribution and ∇ 2 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 that this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination bound­aries, and these all have the property that 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 opera­tion of forming oriented zero-crossing segments from the output of centre-surround ∇ 2 G filters acting on the image forms the basis for a physiological model of simple cells (see Marr & Ullman 1979).