Theory of edge detection

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 a t a given scale is found to be the second derivative of a Gaussian, and it is shown th a t, provided some simple conditions are satisfied, these prim ary 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 th a 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 .

Color vision and image intensities: When are changes material?

“…The operator's largest response occurs when it is slightly offset from the material change boundary. This is reminiscent of properites of the V 2 G convolution operator' 6 for luminance discontinuities (Marr & Hildreth, 1980).…”

Interaction of ON and OFF pathways for visual contrast measurement

“…In classical proposals, such as, for example, in Rodieck (1965) or Marr and Hildreth (1980), the center and surround contributions combine linearly to determine the cell's response. Other approaches have speci®ed visual adaptation processes that render responses sensitive to luminance ratios.…”

“…A discontinuity in a visual stimulus signals a causally related change in at least one physical scene parameter (Marr 1982). The development of ®lters to detect such discontinuities has been substantially in¯uenced by neurophysiological investigations concerning the shape of receptive ®eld (RF) pro®les of retinal and cortical neurons.…”

“…The development of ®lters to detect such discontinuities has been substantially in¯uenced by neurophysiological investigations concerning the shape of receptive ®eld (RF) pro®les of retinal and cortical neurons. Marr and Hildreth (1980) proposed that the RF pro®le of mammalian retinal ganglion cells can be modeled by a Laplacian-of-Gaussian or di erence of circular symmetric Gaussians, both implementing an isotropic secondorder derivative ®ltering stage (Marr 1982). More recently, oriented linear ®lters built from Gabor or Gaussian derivative functions have been employed (Daugman 1985;Koenderink and van Doorn 1990).…”

“…Following this theoretical analysis, we show results of computer simulations in which we selectively investigate key functionalities of the proposed processing scheme. Finally, we relate the present model to other proposals that also have made use of non-linear or AND-gating processing for edge detection, most notably those of Marr and Hildreth (1980) and Iverson and Zucker (1995).…”