Image Processing Reference
In-Depth Information
Chapter 1
Introduction
Classical signal and image processing uses linear processing techniques. These are
methods based in the familiar Fourier, Z, and Laplace transforms. These methods
assume that signal and image data may be processed by mapping them onto
lower-dimensional orthogonal spaces resulting in solutions designed by decom-
posing the input into sinusoidal components and processing them individually.
While mathematically elegant, this imposition of linearity results in a very limited
set of processing operations compared to the total set of solutions possible, i.e.,
both linear and nonlinear. For example, techniques based on rank ordering of val-
ues, logical and geometric processing approaches can give excellent results, partic-
ularly for image processing applications. This approach should not be viewed as an
alternative to the classical methods, but as a superset of techniques containing
many new novel techniques as well as the linear techniques listed above.
The model chosen to convey these concepts is that of digital logic. This is be-
cause it can quite literally capture any processing operation, linear or nonlinear,
that may be required. Many engineers and computer scientists are comfortable with
its notation and concepts. Minimization techniques and software tools are available
to reduce complex solutions into their simplest form, and the solutions translate
readily into electronic hardware or software implementations.
Every digital signal or image processing operation can be viewed at its most
basic level as the manipulation of a series of finite-length binary strings. Whether
the operation is implemented on a processor through software or in dedicated hard-
ware, the data and the algorithms are invariably mapped through electronic logic
components, which are inherently binary in nature.
Therefore, every digital signal and image processing task can be cast in terms
of a logical representation. It does not matter if the data is binary, grayscale, color,
or multiband, nor whether the operation is linear or nonlinear. If it can be pro-
grammed, then it can be placed in the context of a logical representation.
In nonlinear image and signal processing, the design of operators is carried out
by seeking the optimum mapping from one set of binary strings to another. This
contrasts with the linear approach which formulates a solution by optimizing coef-
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