Image Processing Reference
In-Depth Information
2
MODELS OF IMAGES AND IMAGE
OPERATIONS
2.1 Introduction
In order to study methods of image processing, theoretically we need to first
make clear what the
image
to be processed is and what is meant by
processing
an image
. In this chapter we present a theoretical model of digitized images
and the processing of these images. For the convenience of explanation, let us
start our discussion with a two-dimensional image.
In Section 2.2, we define both a (two-dimensional or 2D) continuous image
and a (2D) digitized image as a function of two variables and a 2D array,
respectively. Relationships between images, such as
equality
and
greater than
,
are introduced later in Subsection 2.2.6.
In Section 2.3, we give the formal description of image processing using
the definitions of images above. Application of an image process algorithm
is defined as
mapping
from one image space onto another. In other words, a
process that generates a new image from an input image is formulated as a
kind of operator on an image space. Relationships between image operators
are defined based on the relationships between images. Operations between
two or more image operations are then introduced in the similar way to those
among images. Two different types of compositions of image operations, called
parallel composition
and
serial composition
, are explained in detail.
In the last section, Section 2.4, image operations are classified based on
their features. We will discuss several important families of operations (or
types of algorithms) such as sequential type, parallel type, local operations,
iterative operations, and shift invariant operations. Concepts and methods to
treat images and image process algorithms discussed here will be used very
effectively in the following chapters to study characteristics of each algorithm
theoretically and to extend their applications to wider area of practical image
processing problems.
Search WWH ::
Custom Search