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Research · February 1980

Edges as zero crossings, at several scales

In February 1980 David Marr and Ellen Hildreth published a theory of edge detection. An image is convolved with a Laplacian of a Gaussian and an edge is marked where the result crosses zero. The filter is applied at several widths — the paper shows w = 6, 12 and 24 pixels — and zero crossings count as an edge when they coincide across channels of adjacent sizes.

Why it matters

Edge detection acquired a statement in which the operator is derived from requirements rather than picked. Until then edges were found with a collection of kernels chosen by eye, each kernel its own decision. Here there is one kernel, its width is a parameter, and the rule for combining several scales into one answer is stated outright and can be checked.

The operator is the Laplacian of a Gaussian. Its half-power bandwidth is about 1.2 octaves and its half-sensitivity bandwidth about 1.75 octaves. The experimental images are 320 by 320 picture elements. The paper states that the minimum number of channels required is two, and that computer vision operators of the time examined 10 to 20 image points, against the smallest human foveal channel covering over 500 cones. The record does not claim four scales. The four channels the paper names are the psychophysical channels of Wilson and Bergen, measured on people; the paper's own examples use three widths. It does not claim edge localisation to within one pixel either: no such figure appears in the paper. The paper is marked "Received 22 February 1979" and appeared in the February 1980 issue.

Event record

Event date
February 1980
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Sources gathered automatically · September 21, 2026
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evt-0486

The issue of Proceedings of the Royal Society of London B, volume 207, number 1167. The publisher deposit at Crossref gives the day as 29 February 1980; the paper itself prints only the year, so the record keeps the month.

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