A Computational Approach to Edge Detection

Inside the paper

The problem

Edge detectors help vision systems locate image boundaries, but noise can cause missed edges, misplaced edges, or several responses to a single boundary. Choosing a detector requires balancing these competing errors.

The idea

Canny expresses desirable detection behavior as mathematical criteria and derives filters under a model of noisy edges. The paper then develops practical methods for finding and combining edges at different scales.

How it works

• For a one-dimensional edge in Gaussian noise, the analysis defines criteria for detection strength and localization accuracy.
• A further constraint limits multiple responses near a single edge, which the first two criteria alone do not adequately prevent.
• For step edges, the analysis derives an optimal filter shape and relates its width to the tradeoff between detection and localization.
• A practical approximation smooths the image with a Gaussian and marks local maxima of gradient magnitude, with thresholding used to select edge contours.

What it showed

The paper shows a tradeoff between detection and localization for its noisy step-edge model and illustrates the detector on images. It also studies using multiple widths and directional operators to improve detection in more varied conditions.

Read it for

Figure 1 and Section II introduce the criteria; Section V connects the derivation to an implementable detector. Skim the optimization in Sections III–IV on a first pass, then return to it for the assumptions behind the result.

Written in our own words from the paper itself. A draft the editors have not yet reviewed.