Table Of Contenti
An Introduction to Digital Image
Processing with Matlab
Notes for SCM2511 Image
Processing 1
Semester 1, 2004
Alasdair McAndrew
School of Computer Science and Mathematics
Victoria University of Technology
ii CONTENTS
Contents
1 Introduction 1
1.1 Images and pictures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 What is image processing? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Image Acquisition and sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Images and digital images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Some applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 Aspects of image processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.7 An image processing task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.8 Types of digital images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.9 Image File Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.10 Image perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.11 Greyscale images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.12 RGB Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.13 Indexed colour images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.14 Data types and conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.15 Basics of image display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.16 The imshow function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.17 Bit planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.18 Spatial Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2 Point Processing 37
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2 Arithmetic operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4 Lookup tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 Neighbourhood Processing 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 Filtering in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4 Frequencies; low and high pass (cid:28)lters . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.5 Edge sharpening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.6 Non-linear (cid:28)lters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4 The Fourier Transform 81
CONTENTS iii
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 The one-dimensional discrete Fourier transform . . . . . . . . . . . . . . . . . . . 81
4.4 The two-dimensional DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.5 Fourier transforms in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.6 Fourier transforms of images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.7 Filtering in the frequency domain . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5 Image Restoration (1) 109
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.2 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.3 Cleaning salt and pepper noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4 Cleaning Gaussian noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6 Image Restoration (2) 125
6.1 Removal of periodic noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.2 Inverse (cid:28)ltering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.3 Wiener (cid:28)ltering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7 Image Segmentation (1) 137
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.2 Thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.3 Applications of thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.4 Adaptive thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8 Image Segmentation (2) 145
8.1 Edge detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.2 Derivatives and edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.3 Second derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.4 The Hough transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
9 Mathematical morphology (1) 163
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.2 Basic ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.3 Dilation and erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
10 Mathematical morphology (2) 175
10.1 Opening and closing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
10.2 The hit-or-miss transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
10.3 Some morphological algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
iv CONTENTS
11 Colour processing 191
11.1 What is colour? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
11.2 Colour models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
11.3 Colour images in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
11.4 Pseudocolouring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
11.5 Processing of colour images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
12 Image coding and compression 215
12.1 Lossless and lossy compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
12.2 Hu(cid:27)man coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
12.3 Run length encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Bibliography 225
Index 226
Chapter 1
Introduction
1.1 Images and pictures
As we mentioned in the preface, human beings are predominantly visual creatures: we rely heavily
on our vision to make sense of the world around us. We not only look at things to identify and
classify them, but we can scan for di(cid:27)erences, and obtain an overall rough (cid:16)feeling(cid:17) for a scene with
a quick glance.
Humans have evolved very precise visual skills: we can identify a face in an instant; we can
di(cid:27)erentiate colours; we can process a large amount of visual information very quickly.
However, the world is in constant motion: stare at something for long enough and it will change
in some way. Even a large solid structure, like a building or a mountain, will change its appearance
dependingonthetimeofday(dayornight); amountofsunlight(clearorcloudy),orvariousshadows
falling upon it.
We are concerned with single images: snapshots, if you like, of a visual scene. Although image
processing can deal with changing scenes, we shall not discuss it in any detail in this text.
For our purposes, an image is a single picture which represents something. It may be a picture
of a person, of people or animals, or of an outdoor scene, or a microphotograph of an electronic
component, or the result of medical imaging. Even if the picture is not immediately recognizable,
it will not be just a random blur.
1.2 What is image processing?
Image processing involves changing the nature of an image in order to either
1. improve its pictorial information for human interpretation,
2. render it more suitable for autonomous machine perception.
We shall be concerned with digital image processing, which involves using a computer to change the
nature of a digital image (see below). It is necessary to realize that these two aspects represent two
separate but equally important aspects of image processing. A procedure which satis(cid:28)es condition
(1)(cid:22)a procedure which makes an image (cid:16)look better(cid:17)(cid:22)may be the very worst procedure for satis-
fying condition (2). Humans like their images to be sharp, clear and detailed; machines prefer their
images to be simple and uncluttered.
Examples of (1) may include:
1
2 CHAPTER 1. INTRODUCTION
(cid:0) Enhancing theedges ofanimage tomake itappearsharper; anexample isshown in(cid:28)gure1.1.
Note how the second image appears (cid:16)cleaner(cid:17); it is a more pleasant image. Sharpening edges
is a vital component of printing: in order for an image to appear (cid:16)at its best(cid:17) on the printed
page; some sharpening is usually performed.
(a) The original image (b) Result after (cid:16)sharperning(cid:17)
Figure 1.1: Image sharperning
(cid:0) Removing(cid:16)noise(cid:17) fromanimage; noisebeingrandomerrorsintheimage. Anexampleisgiven
in (cid:28)gure 1.2. Noise is a very common problem in data transmission: all sorts of electronic
components may a(cid:27)ect data passing through them, and the results may be undesirable. As
we shall see in chapter 5 noise may take many di(cid:27)erent forms;each type of noise requiring a
di(cid:27)erent method of removal.
(cid:0) Removing motion blur from an image. An example is given in (cid:28)gure 1.3. Note that in the
deblurred image (b) it is easier to read the numberplate, and to see the spikes on the fence
behind the car, as well as other details not at all clear in the original image (a). Motion blur
may occur when the shutter speed of the camera is too long for the speed of the object. In
photographs of fast moving objects: athletes, vehicles for example, the problem of blur may
be considerable.
Examples of (2) may include:
(cid:0) Obtaining the edges of an image. This may be necessary for the measurement of objects in
an image; an example is shown in (cid:28)gures 1.4. Once we have the edges we can measure their
spread, and the area contained within them. We can also use edge detection algorithms as a
(cid:28)rst step in edge enhancement, as we saw above.
1.2. WHAT IS IMAGE PROCESSING? 3
(a) The original image (b) After removing noise
Figure 1.2: Removing noise from an image
(a) The original image (b) After removing the blur
Figure 1.3: Image deblurring
4 CHAPTER 1. INTRODUCTION
From the edge result, we see that it may be necessary to enhance the original image slightly,
to make the edges clearer.
(a) The original image (b) Its edge image
Figure 1.4: Finding edges in an image
(cid:0) Removing detail from an image. For measurement or counting purposes, we may not be
interestedinallthedetailinanimage. Forexample,amachineinspecteditemsonanassembly
line, the only matters of interest may be shape, size or colour. For such cases, we might want
to simplify the image. Figure 1.5 shows an example: in image (a) is a picture of an African
bu(cid:27)alo, and image (b) shows a blurred version in which extraneous detail (like the logs of
wood in the background) have been removed. Notice that in image (b) all the (cid:28)ne detail is
gone; what remains is the coarse structure of the image. We could for example, measure the
size and shape of the animal without being (cid:16)distracted(cid:17) by unnecessary detail.
1.3 Image Acquisition and sampling
Sampling refers to the process of digitizing a continuous function. For example, suppose we take
the function
(cid:0)(cid:2)(cid:1)(cid:4)(cid:3)(cid:6)(cid:5)(cid:8)(cid:7)(cid:10)(cid:9)(cid:12)(cid:11)(cid:14)(cid:13)(cid:10)(cid:15)(cid:17)(cid:16) (cid:3)(cid:19)(cid:5)(cid:20)(cid:7)(cid:10)(cid:9) (cid:18) (cid:11)(cid:14)(cid:13)(cid:22)(cid:21)
(cid:18)
and sample it at ten evenly spaced values of (cid:11) only. The resulting sample points are shown in
(cid:28)gure 1.6. This shows an example of undersampling, where the number of points is not su(cid:30)cient to
reconstruct the function. Suppose we sample the function at 100 points, as shown in (cid:28)gure 1.7. We
can clearly now reconstruct the function; all its properties can be determined from this sampling.
In order to ensure that we have enough sample points, we require that the sampling period is not
greater than one-half the (cid:28)nest detail in our function. This is known as the Nyquist criterion, and
can be formulated more precisely in terms of (cid:16)frequencies(cid:17), which are discussed in chapter 4. The
Nyquist criterion can be stated as the sampling theorem, which says, in e(cid:27)ect, that a continuous
function can be reconstructed from its samples provided that the sampling frequency is at least
twice the maximum frequency in the function. A formal account of this theorem is provided by
Castleman [1].
1.3. IMAGE ACQUISITION AND SAMPLING 5
(a) The original image (b) Blurring to remove detail
Figure 1.5: Blurring an image
(cid:0) (cid:0)
(cid:0) (cid:0)
(cid:0)
(cid:0)
(cid:0)
(cid:0)
(cid:0)
(cid:0)
Figure 1.6: Sampling a function(cid:22)undersampling
(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
(cid:1) (cid:1) (cid:1)
(cid:1) (cid:1) (cid:1)
(cid:1) (cid:1) (cid:1)
(cid:1) (cid:1) (cid:1)
(cid:1) (cid:1)
(cid:1) (cid:1)
(cid:1) (cid:1)
(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
Figure 1.7: Sampling a function with more points
6 CHAPTER 1. INTRODUCTION
Sampling an image again requires that we consider the Nyquist criterion, when we consider an
imageasacontinuous functionoftwovariables, andwewishtosampleittoproduceadigitalimage.
An example is shown in (cid:28)gure 1.8 where an image is shown, and then with an undersampled
version. The jagged edges in the undersampled image are examples of aliasing. The sampling rate
Correct sampling; no aliasing An undersampled version with aliasing
Figure 1.8: E(cid:27)ects of sampling
will of course a(cid:27)ect the (cid:28)nal resolution of the image; we discuss this below. In order to obtain a
sampled (digital) image, we may start with a continuous representation of a scene. To view the
scene, we record the energy re(cid:29)ected from it; we may use visible light, or some other energy source.
Using light
Light is the predominant energy source for images; simply because it is the energy source which
human beings can observe directly. We are all familiar with photographs, which are a pictorial
record of a visual scene.
Many digital images are captured usingvisible light asthe energy source; this hasthe advantage
ofbeingsafe,cheap, easilydetectedandreadilyprocessedwithsuitablehardware. Twoverypopular
methods of producing a digital image are with a digital camera or a (cid:29)at-bed scanner.
CCD camera. Such a camera has, in place of the usual (cid:28)lm, an array of photosites; these are
silicon electronic devices whose voltage output is proportional to the intensity of light falling
on them.
For a camera attached to a computer, information from the photosites is then output to a
suitable storage medium. Generally this is done on hardware, as being much faster and more
e(cid:30)cient than software, using a frame-grabbing card. This allows a large number of images to
be captured in a very short time(cid:22)in the order of one ten-thousandth of a second each. The
images can then be copied onto a permanent storage device at some later time.
This is shown schematically in (cid:28)gure 1.9.
The output will be an array of values; each representing a sampled point from the original
scene. The elements of this array are called picture elements, or more simply pixels.
