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Chapter 2 ■ Edge-Detection Techniques 23

the edge pixel values to a specific grey level or color so that they can be easily
seen. In addition, edge tracing is the process of following the edges, usually
collecting the edge pixels into a list. This is done in a consistent direction,
either clockwise or counter-clockwise around the objects. Chain coding is one
example of a specific algorithm for edge tracing. The result is a non-raster
representation of the objects that can be used to compute shape measures or
otherwise identify or classify the object.
The remainder of this chapter discusses the theory of edge detection,
including a collection of traditional methods. This includes the Canny edge
detector and the Shen-Castan, or ISEF, edge detector. Both are based solidly on
theoretical considerations, and both claim a degree of optimality; that is, both
claim to be the best that can be done under certain specified circumstances.
These claims will be examined, both in theory and in practice.

2.2 Traditional Approaches and Theory

Most good algorithms begin with a clear statement of the problem to be solved,
and a cogent analysis of the possible methods of solution and the conditions
under which the methods will operate correctly. Using this paradigm, to define
an edge-detection algorithm means first defining what an edge is, and then
using this definition to suggest methods of enhancement and identification.
As usual, there are a number of possible definitions of an edge, each being
applicable in various specific circumstances. One of the most common and
most general definitions is the ideal step edge, illustrated in Figure 2.3.
In this one-dimensional example, the edge is simply a change in grey level
occurring at one specific location. The greater the change in level, the easier
the edge is to detect (although in the ideal case, any level change can be seen
quite easily).
The first complication occurs because of digitization. It is unlikely that the
image will be sampled in such a way that all the edges happen to correspond
exactly with a pixel boundary. Indeed, the change in level may extend across
some number of pixels (Figures 2.3b–d). The actual position of the edge is
considered to be the center of the ramp connecting the low grey level to the
high one. This is a ramp in the mathematical world only, since after the image
has been made digital (sampled), the ramp has the jagged appearance of a
staircase.
The second complication is the ubiquitous problem of noise.Due to a
great many factors such as light intensity, type of camera and lens, motion,
temperature, atmospheric effects, dust, and others, it is very unlikely that two
pixels that correspond to precisely the same grey level in the scene will have
the same level in the image. Noise is a random effect and can be characterized
only statistically. The result of noise on the image is to produce a random