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26 Chapter 2 ■ Edge-Detection Techniques

Although the ideal step edge and ramp edge models were generally used
to devise new edge detectors in the past, the model was recognized to be a
simplification, and newer edge-detection schemes incorporate noise into the
model and are tested on staircases and noisy edges.

2.2.2 Noise

All image-acquisition processes are subject to noise of some type, so there is
little point in ignoring it; the ideal situation of no noise never occurs in practice.
Noise cannot be predicted accurately because of its random nature, and cannot
even be measured accurately from a noisy image, since the contribution to the
grey levels of the noise can’t be distinguished from the pixel data. However,
noise can sometimes be characterized by its effect on the image and is usually
expressed as a probability distribution with a specific mean and standard
deviation.
Two types of noise are of specific interest in image analysis:

Signal-independent noise
Signal-dependent noise
Signal-independent noise is a random set of grey levels, statistically indepen-
dent of the image data, added to the pixels in the image to give the resulting
noisy image. This kind of noise occurs when an image is transmitted electron-
ically from one place to another. If A is a perfect image and N is the noise that
occurs during transmission, then the final image B is:
B = A + N (EQ 2.2)

A and N are unrelated to each other. The noise image N could have any
statistical properties, but a common assumption is that it follows the normal
(Gaussian) distribution with a mean of zero and some measured or presumed
standard deviation.
It is a simple matter to create an artificially noisy image having known
characteristics, and such images are very useful tools for experimenting with
edge-detection algorithms. Figure 2.5 shows an image of a chessboard that has
been subjected to various degrees of artificial noise. For a normal distribution
with a mean of zero, the amount of noise is specified by the standard deviation;
values of 10, 20, 30, and 50 are shown in the figure.
For these images, it is possible to obtain an estimate of the noise. The scene
contains a number of small regions that should have a uniform grey level —
the squares on the chessboard. If the noise is consistent over the entire image,
the noise in any one square will be a sample of the noise in the whole image,
and since the level is constant over the square, illumination being constant,
anyvariation canbeassumedtobecausedbythe noisealone.Inthiscase, the
mean and standard deviation of the grey levels in any square can be computed;