Image Processing Reference
In-Depth Information
2
Fundamentals of Digital
Image Processing
2.1 INTRODUCTION
This chapter is devoted to providing an overview of fundamentals of digital imaging,
including topics such as digital image formation, imaging systems, image sampling,
quantization,
y covers image
formation and systems. Section 2.3 covers optical and modulation transfer functions.
Section 2.4 discusses image sampling and quantization. Section 2.5 deals with image
transforms, and image
filtering, and image transformation. Section 2.2 brie
filtering is covered in Section 2.6. Issues such as image resizing
and its practical implementation are addressed in Section 2.7. Image enhancement is
covered in Section 2.8. Image degradation and restoration are brie
y discussed in
Section 2.9. Finally, basic image halftoning techniques are described in Section 2.10.
2.2 DIGITAL IMAGE FORMATION AND SYSTEMS
Linear system theory provides a powerful tool for the modeling and analysis of
various imaging systems [1
3]. A linear system is characterized as a system that
obeys the superposition principle, that is, if the input I
1
to a system results in the
output O
1
, and the input I
2
to the system results in the output O
2
, then the input
aI
1
þ
bI
2
results in the output aO
1
þ
bO
2
for any I
1
, I
2
signal and scale factors a and
b. A linear system provides a convenient model for an imaging system. Unfortu-
nately, none of the imaging systems encountered in the real world are completely
linear. However, such systems are almost always approximated by linear systems to
make their analysis mathematically tractable. Conventional and digital cameras,
scanners, printers, and the human visual system (HVS) are among many examples
of imaging systems that are modeled and analyzed by using linear system theory. A
two-dimensional
-
(2-D)
linear
imaging system is characterized by a function
h
(
x, y;
l
1
,
l
2
)
, referred to as the point spread function (PSF) of the imaging system
that speci
es the output of the system when the input is a point (impulse) at location
(l
1
,
l
2
)
in the input image plane as shown in Figure 2.1. To
find the output of an
imaging system g
(
x, y
)
to a given input f
(
x, y
)
,
first the input is broken up into sum of
weighted impulses (points)
1
1
f
(
x, y
) ¼
f
(l
1
,
l
2
)d(
x
l
1
, y
l
2
)dl
1
dl
2
(
2
:
1
)
1
1
19
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