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CHAPTER
23 Image Formation & Display
Images are a description of how a parameter varies over a surface. For example, standard visual
images result from light intensity variations across a two-dimensional plane. However, light is
not the only parameter used in scientific imaging. For example, an image can be formed of the
temperature of an integrated circuit, blood velocity in a patient's artery, x-ray emission from a
distant galaxy, ground motion during an earthquake, etc. These exotic images are usually
converted into conventional pictures (i.e., light images), so that they can be evaluated by the
human eye. This first chapter on image processing describes how digital images are formed and
presented to human observers.
Digital Image Structure
Figure 23-1 illustrates the structure of a digital image. This example image is
of the planet Venus, acquired by microwave radar from an orbiting space
probe. Microwave imaging is necessary because the dense atmosphere blocks
visible light, making standard photography impossible. The image shown is
represented by 40,000 samples arranged in a two-dimensional array of 200
columns by 200 rows. Just as with one-dimensional signals, these rows and
columns can be numbered 0 through 199, or 1 through 200. In imaging jargon,
each sample is called a pixel, a contraction of the phrase: picture element.
Each pixel in this example is a single number between 0 and 255. When the
image was acquired, this number related to the amount of microwave energy
being reflected from the corresponding location on the planet's surface. To
display this as a visual image, the value of each pixel is converted into a
grayscale, where 0 is black, 255 is white, and the intermediate values are
shades of gray.
Images have their information encoded in the spatial domain, the image
equivalent of the time domain. In other words, features in images are
represented by edges, not sinusoids. This means that the spacing and
number of pixels are determined by how small of features need to be seen,
The Scientist and Engineer's Guide to Digital Signal Processing 374
rather than by the formal constraints of the sampling theorem. Aliasing can
occur in images, but it is generally thought of as a nuisance rather than a major
problem. For instance, pinstriped suits look terrible on television because the
repetitive pattern is greater than the Nyquist frequency. The aliased
frequencies appear as light and dark bands that move across the clothing as the
person changes position.
A "typical" digital image is composed of about 500 rows by 500 columns. This
is the image quality encountered in television, personal computer applications,
and general scientific research. Images with fewer pixels, say 250 by 250, are
regarded as having unusually poor resolution. This is frequently the case with
new imaging modalities; as the technology matures, more pixels are added.
These low resolution images look noticeably unnatural, and the individual
pixels can often be seen. On the other end, images with more than 1000 by
1000 pixels are considered exceptionally good. This is the quality of the best
computer graphics, high-definition television, and 35 mm motion pictures.
There are also applications needing even higher resolution, requiring several
thousand pixels per side: digitized x-ray images, space photographs, and glossy
advertisements in magazines.
The strongest motivation for using lower resolution images is that there are
fewer pixels to handle. This is not trivial; one of the most difficult problems
in image processing is managing massive amounts of data. For example, one
second of digital audio requires about eight kilobytes. In comparison, one
second of television requires about eight Megabytes. Transmitting a 500 by
500 pixel image over a 33.6 kbps modem requires nearly a minute! Jumping
to an image size of 1000 by 1000 quadruples these problems.
It is common for 256 gray levels (quantization levels) to be used in image
processing, corresponding to a single byte per pixel. There are several reasons
for this. First, a single byte is convenient for data management, since this is
how computers usually store data. Second, the large number of pixels in an
image compensate to a certain degree for a limited number of quantization
steps. For example, imagine a group of adjacent pixels alternating in value
between digital numbers (DN) 145 and 146. The human eye perceives the
region as a brightness of 145.5. In other words, images are very dithered.
Third, and most important, a brightness step size of 1/256 (0.39%) is smaller
than the eye can perceive. An image presented to a human observer will not
be improved by using more than 256 levels.
However, some images need to be stored with more than 8 bits per pixel.
Remember, most of the images encountered in DSP represent nonvisual
parameters. The acquired image may be able to take advantage of more
quantization levels to properly capture the subtle details of the signal. The
point of this is, don't expect to human eye to see all the information contained
in these finely spaced levels. We will consider ways around this problem
during a later discussion of brightness and contrast.
The value of each pixel in the digital image represents a small region in the
continuous image being digitized. For example, imagine that the Venus
Chapter 23- Image Formation and Display 375
FIGURE 23-1
Digital image structure. This example
image is the planet Venus, as viewed in
reflected microwaves. Digital images
are represented by a two-dimensional
array of numbers, each called a pixel. In
this image, the array is 200 rows by 200
columns, with each pixel a number
between 0 to 255. When this image was
acquired, the value of each pixel
corresponded to the level of reflected
microwave energy. A grayscale image
is formed by assigning each of the 0 to
255 values to varying shades of gray.
183 183 181 184 177 200 200 189 159 135 94 105 160 174 191 196
186 195 190 195 191 205 216 206 174 153 112 80 134 157 174 196
194 196 198 201 206 209 215 216 199 175 140 77 106 142 170 186
184 212 200 204 201 202 214 214 214 205 173 102 84 120 134 159
202 215 203 179 165 165 199 207 202 208 197 129 73 112 131 146
203 208 166 159 160 168 166 157 174 211 204 158 69 79 127 143
174 149 143 151 156 148 146 123 118 203 208 162 81 58 101 125
143 137 147 153 150 140 121 133 157 184 203 164 94 56 66 80
164 165 159 179 188 159 126 134 150 199 174 119 100 41 41 58
173 187 193 181 167 151 162 182 192 175 129 60 88 47 37 50
172 184 179 153 158 172 163 207 205 188 127 63 56 43 42 55
156 191 196 159 167 195 178 203 214 201 143 101 69 38 44 52
154 163 175 165 207 211 197 201 201 199 138 79 76 67 51 53
144 150 143 162 215 212 211 209 197 198 133 71 69 77 63 53
140 151 150 185 215 214 210 210 211 209 135 80 45 69 66 60
135 143 151 179 213 216 214 191 201 205 138 61 59 61 77 63
150 155 160 165
Column
100 150 199 50 0
150 155 160 165
Column
Column
Row
55 50 65 60
50 55 60 65
100 0 50 150 199
Row
Row
probe takes samples every 10 meters along the planet's surface as it orbits
overhead. This defines a square sample spacing and sampling grid, with
each pixel representing a 10 meter by 10 meter area. Now, imagine what
happens in a single microwave reflection measurement. The space probe emits
The Scientist and Engineer's Guide to Digital Signal Processing 376
a highly focused burst of microwave energy, striking the surface in, for
example, a circular area 15 meters in diameter. Each pixel therefore
contains information about this circular area, regardless of the size of the
sampling grid.
This region of the continuous image that contributes to the pixel value is called
the sampling aperture. The size of the sampling aperture is often related to
the inherent capabilities of the particular imaging system being used. For
example, microscopes are limited by the quality of the optics and the
wavelength of light, electronic cameras are limited by random electron diffusion
in the image sensor, and so on. In most cases, the sampling grid is made
approximately the same as the sampling aperture of the system. Resolution in
the final digital image will be limited primary by the larger of the two, the
sampling grid or the sampling aperture. We will return to this topic in Chapter
25 when discussing the spatial resolution of digital images.
Color is added to digital images by using three numbers for each pixel,
representing the intensity of the three primary colors: red, green and blue.
Mixing these three colors generates all possible colors that the human eye can
perceive. A single byte is frequently used to store each of the color
intensities, allowing the image to capture a total of 256×256×256 = 16.8
million different colors.
Color is very important when the goal is to present the viewer with a true
picture of the world, such as in television and still photography. However, this
is usually not how images are used in science and engineering. The purpose
here is to analyze a two-dimensional signal by using the human visual system
as a tool. Black and white images are sufficient for this.
Cameras and Eyes
The structure and operation of the eye is very similar to an electronic camera,
and it is natural to discuss them together. Both are based on two major
components: a lens assembly, and an imaging sensor. The lens assembly
captures a portion of the light emanating from an object, and focus it onto the
imaging sensor. The imaging sensor then transforms the pattern of light into
a video signal, either electronic or neural.
Figure 23-2 shows the operation of the lens. In this example, the image of
an ice skater is focused onto a screen. The term focus means there is a oneto-
one match of every point on the ice skater with a corresponding point on
the screen. For example, consider a 1 mm × 1 mm region on the tip of the
toe. In bright light, there are roughly 100 trillion photons of light striking
this one square millimeter area each second. Depending on the
characteristics of the surface, between 1 and 99 percent of these incident
light photons will be reflected in random directions. Only a small portion
of these reflected photons will pass through the lens. For example, only
about one-millionth of the reflected light will pass through a one centimeter
diameter lens located 3 meters from the object.
Chapter 23- Image Formation and Display 377
lens
projected
image
FIGURE 23-2
Focusing by a lens. A lens gathers light expanding from a point source, and force it to return to a
point at another location. This allows a lens to project an image onto a surface.
Refraction in the lens changes the direction of the individual photons,
depending on the location and angle they strike the glass/air interface. These
direction changes cause light expanding from a single point to return to a single
point on the projection screen. All of the photons that reflect from the toe and
pass through the lens are brought back together at the "toe" in the projected
image. In a similar way, a portion of the light coming from any point on the
object will pass through the lens, and be focused to a corresponding point in the
projected image.
Figures 23-3 and 23-4 illustrate the major structures in an electronic camera
and the human eye, respectively. Both are light tight enclosures with a lens
mounted at one end and an image sensor at the other. The camera is filled
with air, while the eye is filled with a transparent liquid. Each lens system has
two adjustable parameters: focus and iris diameter.
If the lens is not properly focused, each point on the object will project to
a circular region on the imaging sensor, causing the image to be blurry. In
the camera, focusing is achieved by physically moving the lens toward or
away from the imaging sensor. In comparison, the eye contains two lenses,
a bulge on the front of the eyeball called the cornea, and an adjustable lens
inside the eye. The cornea does most of the light refraction, but is fixed in
shape and location. Adjustment to the focusing is accomplished by the inner
lens, a flexible structure that can be deformed by the action of the ciliary
muscles. As these muscles contract, the lens flattens to bring the object
into a sharp focus.
In both systems, the iris is used to control how much of the lens is exposed to
light, and therefore the brightness of the image projected onto the imaging
sensor. The iris of the eye is formed from opaque muscle tissue that can be
contracted to make the pupil (the light opening) larger. The iris in a camera
is a mechanical assembly that performs the same function.
The Scientist and Engineer's Guide to Digital Signal Processing 378
The parameters in optical systems interact in many unexpected ways. For
example, consider how the amount of available light and the sensitivity of
the light sensor affects the sharpness of the acquired image. This is
because the iris diameter and the exposure time are adjusted to transfer the
proper amount of light from the scene being viewed to the image sensor. If
more than enough light is available, the diameter of the iris can be reduced,
resulting in a greater depth-of-field (the range of distance from the camera
where an object remains in focus). A greater depth-of-field provides a
sharper image when objects are at various distances. In addition, an
abundance of light allows the exposure time to be reduced, resulting in less
blur from camera shaking and object motion. Optical systems are full of
these kinds of trade-offs.
An adjustable iris is necessary in both the camera and eye because the range
of light intensities in the environment is much larger than can be directly
handled by the light sensors. For example, the difference in light intensities
between sunlight and moonlight is about one-million. Adding to this that
reflectance can vary between 1% and 99%, results in a light intensity range of
almost one-hundred million.
The dynamic range of an electronic camera is typically 300 to 1000, defined
as the largest signal that can be measured, divided by the inherent noise of the
device. Put another way, the maximum signal produced is 1 volt, and the rms
noise in the dark is about 1 millivolt. Typical camera lenses have an iris that
change the area of the light opening by a factor of about 300. This results in
a typical electronic camera having a dynamic range of a few hundred thousand.
Clearly, the same camera and lens assembly used in bright sunlight will be
useless on a dark night.
In comparison, the eye operates over a dynamic range that nearly covers the
large environmental variations. Surprisingly, the iris is not the main way that
this tremendous dynamic range is achieved. From dark to light, the area of the
pupil only changes by a factor of about 20. The light detecting nerve cells
gradually adjust their sensitivity to handle the remaining dynamic range. For
instance, it takes several minutes for your eyes to adjust to the low light after
walking into a dark movie theater.
One way that DSP can improve images is by reducing the dynamic range an
observer is required to view. That is, we do not want very light and very
dark areas in the same image. A reflection image is formed from two
image signals: the two-dimensional pattern of how the scene is illuminated,
multiplied by the two-dimensional pattern of reflectance in the scene. The
pattern of reflectance has a dynamic range of less than 100, because all
ordinary materials reflect between 1% and 99% of the incident light. This
is where most of the image information is contained, such as where objects
are located in the scene and what their surface characteristics are. In
comparison, the illumination signal depends on the light sources around the
objects, but not on the objects themselves. The illumination signal can have
a dynamic range of millions, although 10 to 100 is more typical within a
single image. The illumination signal carries little interesting information,
Chapter 23- Image Formation and Display 379
lens
focus iris
CCD
serial output
FIGURE 23-3
Diagram of an electronic camera. Focusing is
achieved by moving the lens toward or away
from the imaging sensor. The amount of
light reaching the sensor is controlled by the
iris, a mechanical device that changes the
effective diameter of the lens. The most
common imaging sensor in present day
cameras is the CCD, a two-dimensional array
of light sensitive elements.
optic
nerve
lens
liquid
muscle
ciliary
iris
cornea retina
fovea
clear
sclera TO EAR
TO NOSE
(top view)
FIGURE 23-4
Diagram of the human eye. The eye is a
liquid filled sphere about 3 cm in diameter,
enclosed by a tough outer case called the
sclera. Focusing is mainly provided by the
cornea, a fixed lens on the front of the eye.
The focus is adjusted by contracting muscles
attached to a flexible lens within the eye.
The amount of light entering the eye is
controlled by the iris, formed from opaque
muscle tissue covering a portion of the lens.
The rear hemisphere of the eye contains the
retina, a layer of light sensitive nerve cells
that converts the image to a neural signal in
the optic nerve.
but can degrade the final image by increasing its dynamic range. DSP can
improve this situation by suppressing the illumination signal, allowing the
reflectance signal to dominate the image. The next chapter presents an approach
for implementing this algorithm.
The light sensitive surface that covers the rear of the eye is called the retina.
As shown in Fig. 23-5, the retina can be divided into three main layers of
specialized nerve cells: one for converting light into neural signals, one for
image processing, and one for transferring information to the optic nerve
leading to the brain. In nearly all animals, these layers are seemingly
backward. That is, the light sensitive cells are in last layer, requiring light to
pass through the other layers before being detected.
There are two types of cells that detect light: rods and cones, named for their
physical appearance under the microscope. The rods are specialized in
operating with very little light, such as under the nighttime sky. Vision appears
very noisy in near darkness, that is, the image appears to be filled with a
continually changing grainy pattern. This results from the image signal being
very weak, and is not a limitation of the eye. There is so little light entering
The Scientist and Engineer's Guide to Digital Signal Processing 380
the eye, the random detection of individual photons can be seen. This is called
statistical noise, and is encountered in all low-light imaging, such as military
night vision systems. Chapter 25 will revisit this topic. Since rods cannot
detect color, low-light vision is in black and white.
The cone receptors are specialized in distinguishing color, but can only operate
when a reasonable amount of light is present. There are three types of cones
in the eye: red sensitive, green sensitive, and blue sensitive. This results from
their containing different photopigments, chemicals that absorbs different
wavelengths (colors) of light. Figure 23-6 shows the wavelengths of light that
trigger each of these three receptors. This is called RGB encoding, and is
how color information leaves the eye through the optic nerve. The human
perception of color is made more complicated by neural processing in the lower
levels of the brain. The RGB encoding is converted into another encoding
scheme, where colors are classified as: red or green, blue or yellow, and light
or dark.
RGB encoding is an important limitation of human vision; the wavelengths that
exist in the environment are lumped into only three broad categories. In
comparison, specialized cameras can separate the optical spectrum into
hundreds or thousands of individual colors. For example, these might be used
to classify cells as cancerous or healthy, understand the physics of a distant
star, or see camouflaged soldiers hiding in a forest. Why is the eye so limited
in detecting color? Apparently, all humans need for survival is to find a red
apple, among the green leaves, silhouetted against the blue sky.
Rods and cones are roughly 3 µm wide, and are closely packed over the entire
3 cm by 3 cm surface of the retina. This results in the retina being composed
of an array of roughly 10,000 × 10,000 = 100 million receptors. In
comparison, the optic nerve only has about one-million nerve fibers that
connect to these cells. On the average, each optic nerve fiber is connected to
roughly 100 light receptors through the connecting layer. In addition to
consolidating information, the connecting layer enhances the image by
sharpening edges and suppressing the illumination component of the scene.
This biological image processing will be discussed in the next chapter.
Directly in the center of the retina is a small region called the fovea (Latin for
pit), which is used for high resolution vision (see Fig. 23-4). The fovea is
different from the remainder of the retina in several respects. First, the optic
nerve and interconnecting layers are pushed to the side of the fovea, allowing
the receptors to be more directly exposed to the incoming light. This results in
the fovea appearing as a small depression in the retina. Second, only cones are
located in the fovea, and they are more tightly packed that in the remainder of
the retina. This absence of rods in the fovea explains why night vision is often
better when looking to the side of an object, rather than directly at it. Third,
each optic nerve fiber is influenced by only a few cones, proving good
localization ability. The fovea is surprisingly small. At normal reading
distance, the fovea only sees about a 1 mm diameter area, less than the size of
a single letter! The resolution is equivalent to about a 20×20 grid of pixels
within this region.
Chapter 23- Image Formation and Display 381
optic
nerve
rods and
cones
connecting
layer
optic nerve sclera
to brain
light
FIGURE 23-5
The human retina. The retina contains three principle layers: (1) the rod and cone light receptors, (2) an
intermediate layer for data reduction and image processing, and (3) the optic nerve fibers that lead to the brain.
The structure of these layers is seemingly backward, requiring light to pass through the other layers before
reaching the light receptors.
FIGURE 23-6
Spectral response of the eye. The three types
of cones in the human eye respond to
different sections of the optical spectrum,
roughly corresponding to red, green, and
blue. Combinations of these three form all
colors that humans can perceive. The cones
do not have enough sensitivity to be used in
low-light environments, where the rods are
used to detect the image. This is why colors
are difficult to perceive at night.
violet
Wavelength (nm)
300 400 500 600 700
0
1
blue cones
green cones
red cones
rods
perception of
wavelength
red
orange
yellow
green
blue
Relative sensitivity
Human vision overcomes the small size of the fovea by jerky eye movements
called saccades. These abrupt motions allow the high resolution fovea to
rapidly scan the field of vision for pertinent information. In addition, saccades
present the rods and cones with a continually changing pattern of light. This
is important because of the natural ability of the retina to adapt to changing
levels of light intensity. In fact, if the eye is forced to remain fixed on the
same scene, detail and color begin to fade in a few seconds.
The most common image sensor used in electronic cameras is the charge
coupled device (CCD). The CCD is an integrated circuit that replaced most
vacuum tube cameras in the 1980s, just as transistors replaced vacuum tube
amplifiers twenty years before. The heart of the CCD is a thin wafer of
The Scientist and Engineer's Guide to Digital Signal Processing 382
silicon, typically about 1 cm square. As shown by the cross-sectional view in
Fig. 23-7, the backside is coated with a thin layer of metal connected to ground
potential. The topside is covered with a thin electrical insulator, and a
repetitive pattern of electrodes. The most common type of CCD is the three
phase readout, where every third electrode is connected together. The silicon
used is called p-type, meaning it has an excess of positive charge carriers
called holes. For this discussion, a hole can be thought of as a positively
charged particle that is free to move around in the silicon. Holes are
represented in this figure by the "+" symbol.
In (a), +10 volts is applied to one of the three phases, while the other two are
held at 0 volts. This causes the holes to move away from every third electrode,
since positive charges are repelled by a positive voltage. This forms a region
under these electrodes called a well, a shortened version of the physics term:
potential well.
Each well in the CCD is a very efficient light sensor. As shown in (b), a
single photon of light striking the silicon converts its energy into the formation
of two charged particles, one electron, and one hole. The hole moves away,
leaving the electron stuck in the well, held by the positive voltage on the
electrode. Electrons in this illustration are represented by the "-" symbol.
During the integration period, the pattern of light striking the CCD is
transferred into a pattern of charge within the CCD wells. Dimmer light
sources require longer integration periods. For example, the integration period
for standard television is 1/60th of a second, while astrophotography can
accumulate light for many hours.
Readout of the electronic image is quite clever; the accumulated electrons in
each well are pushed to the output amplifier. As shown in (c), a positive
voltage is placed on two of the phase lines. This results in each well expanding
to the right. As shown in (d), the next step is to remove the voltage from the
first phase, causing the original wells to collapse. This leaves the accumulated
electrons in one well to the right of where they started. By repeating this
pulsing sequence among the three phase lines, the accumulated electrons are
pushed to the right until they reach a charge sensitive amplifier. This is a
fancy name for a capacitor followed by a unity gain buffer. As the electrons
are pushed from the last well, they flow onto the capacitor where they produce
a voltage. To achieve high sensitivity, the capacitors are made extremely
small, usually less than 1 DF. This capacitor and amplifier are an integral part
of the CCD, and are made on the same piece of silicon. The signal leaving the
CCD is a sequence of voltage levels proportional to the amount of light that has
fallen on sequential wells.
Figure 23-8 shows how the two-dimensional image is read from the CCD.
After the integration period, the charge accumulated in each well is moved up
the column, one row at a time. For example, all the wells in row 15 are first
moved into row 14, then row 13, then row 12, etc. Each time the rows are
moved up, all the wells in row number 1 are transferred into the horizontal
register. This is a group of specialized CCD wells that rapidly move the
charge in a horizontal direction to the charge sensitive amplifier.
Chapter 23- Image Formation and Display 383
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a.
b.
c.
d.
output
amplifier
grounded back surface
p type silicon
well
electrode insulator
+
light photon
FIGURE 23-7
Operation of the charge coupled device (CCD). As shown in this cross-sectional view, a thin sheet of p-type silicon is
covered with an insulating layer and an array of electrodes. The electrodes are connected in groups of three, allowing
three separate voltages to be applied: N1, N2, and N3. When a positive voltage is applied to an electrode, the holes (i.e.,
the positive charge carriers indicated by the "+") are pushed away. This results in an area depleted of holes, called a well.
Incoming light generates holes and electrons, resulting in an accumulation of electrons confined to each well (indicated
by the "-"). By manipulating the three electrode voltages, the electrons in each well can be moved to the edge of the
silicon where a charge sensitive amplifier converts the charge into a voltage.
The Scientist and Engineer's Guide to Digital Signal Processing 384
horizontal
register
row 1
row 2
last row
column 1
column 2
last column
serial
video
output
FIGURE 23-8
Architecture of the CCD. The imaging wells of the CCD are arranged in columns. During readout, the charge
from each well is moved up the column into a horizontal register. The horizontal register is then readout into
the charge sensitive preamplifier.
Notice that this architecture converts a two-dimensional array into a serial data
stream in a particular sequence. The first pixel to be read is at the top-left
corner of the image. The readout then proceeds from left-to-right on the first
line, and then continues from left-to-right on subsequent lines. This is called
row major order, and is almost always followed when a two-dimensional
array (image) is converted to sequential data.
Television Video Signals
Although over 50 years old, the standard television signal is still one of the
most common way to transmit an image. Figure 23-9 shows how the
television signal appears on an oscilloscope. This is called composite
video, meaning that there are vertical and horizontal synchronization (sync)
pulses mixed with the actual picture information. These pulses are used in
the television receiver to synchronize the vertical and horizontal deflection
circuits to match the video being displayed. Each second of standard video
contains 30 complete images, commonly called frames. A video engineer
would say that each frame contains 525 lines, the television jargon for what
programmers call rows. This number is a little deceptive because only 480
to 486 of these lines contain video information; the remaining 39 to 45 lines
are reserved for sync pulses to keep the television's circuits synchronized
with the video signal.
Standard television uses an interlaced format to reduce flicker in the
displayed image. This means that all the odd lines of each frame are
transmitted first, followed by the even lines. The group of odd lines is called
the odd field, and the group of even lines is called the even field. Since
Chapter 23- Image Formation and Display 385
0.25
0.50
0.75
-0.25
0.00
vertical
sync pulses line 1 line 3 line 5 line 2 line 4 line 485
horizontal sync pulses
vertical
sync pulses
ODD FIELD EVEN FIELD
Signal level (volts)
FIGURE 23-9
Composite video. The NTSC video signal consists of 30 complete frames (images) per second, with each
frame containing 480 to 486 lines of video. Each frame is broken into two fields, one containing the odd lines
and the other containing the even lines. Each field starts with a group of vertical sync pulses, followed by
successive lines of video information separated by horizontal sync pulses. (The horizontal axis of this figure
is not drawn to scale).
each frame consists of two fields, the video signal transmits 60 fields per
second. Each field starts with a complex series of vertical sync pulses
lasting 1.3 milliseconds. This is followed by either the even or odd lines of
video. Each line lasts for 63.5 microseconds, including a 10.2 microsecond
horizontal sync pulse, separating one line from the next. Within each line,
the analog voltage corresponds to the grayscale of the image, with brighter
values being in the direction away from the sync pulses. This places the
sync pulses beyond the black range. In video jargon, the sync pulses are
said to be blacker than black.
The hardware used for analog-to-digital conversion of video signals is called
a frame grabber. This is usually in the form of an electronics card that plugs
into a computer, and connects to a camera through a coaxial cable. Upon
command from software, the frame grabber waits for the beginning of the next
frame, as indicated by the vertical sync pulses. During the following two
fields, each line of video is sampled many times, typically 512, 640 or 720
samples per line, at 8 bits per sample. These samples are stored in memory as
one row of the digital image.
This way of acquiring a digital image results in an important difference
between the vertical and horizontal directions. Each row in the digital
image corresponds to one line in the video signal, and therefore to one row
of wells in the CCD. Unfortunately, the columns are not so straightforward.
In the CCD, each row contains between about 400 and 800 wells
(columns), depending on the particular device used. When a row of wells
is read from the CCD, the resulting line of video is filtered into a smooth
analog signal, such as in Fig. 23-9. In other words, the video signal does
not depend on how many columns are present in the CCD. The resolution
in the horizontal direction is limited by how rapidly the analog signal is
allowed to change. This is usually set at 3.2 MHz for color television,
resulting in a risetime of about 100 nanoseconds, i.e., about 1/500th of the
53.2 microsecond video line.
The Scientist and Engineer's Guide to Digital Signal Processing 386
When the video signal is digitized in the frame grabber, it is converted back
into columns. However, these columns in the digitized image have no relation
to the columns in the CCD. The number of columns in the digital image
depends solely on how many times the frame grabber samples each line of
video. For example, a CCD might have 800 wells per row, while the digitized
image might only have 512 pixels (i.e., columns) per row.
The number of columns in the digitized image is also important for another
reason. The standard television image has an aspect ratio of 4 to 3, i.e., it
is slightly wider than it is high. Motion pictures have the wider aspect ratio
of 25 to 9. CCDs used for scientific applications often have an aspect ratio
of 1 to 1, i.e., a perfect square. In any event, the aspect ratio of a CCD is
fixed by the placement of the electrodes, and cannot be altered. However, the
aspect ratio of the digitized image depends on the number of samples per line.
This becomes a problem when the image is displayed, either on a video monitor
or in a hardcopy. If the aspect ratio isn't properly reproduced, the image looks
squashed horizontally or vertically.
The 525 line video signal described here is called NTSC (National Television
Systems Committee), a standard defined way back in 1954. This is the system
used in the United States and Japan. In Europe there are two similar standards
called PAL (Phase Alternation by Line) and SECAM (Sequential
Chrominance And Memory). The basic concepts are the same, just the numbers
are different. Both PAL and SECAM operate with 25 interlaced frames per
second, with 625 lines per frame. Just as with NTSC, some of these lines
occur during the vertical sync, resulting in about 576 lines that carry picture
information. Other more subtle differences relate to how color and sound are
added to the signal.
The most straightforward way of transmitting color television would be to have
three separate analog signals, one for each of the three colors the human eye
can detect: red, green and blue. Unfortunately, the historical development of
television did not allow such a simple scheme. The color television signal was
developed to allow existing black and white television sets to remain in use
without modification. This was done by retaining the same signal for
brightness information, but adding a separate signal for color information. In
video jargon, the brightness is called the luminance signal, while the color is
the chrominance signal. The chrominance signal is contained on a 3.58 MHz
carrier wave added to the black and white video signal. Sound is added in this
same way, on a 4.5 MHz carrier wave. The television receiver separates these
three signals, processes them individually, and recombines them in the final
display.
Other Image Acquisition and Display
Not all images are acquired an entire frame at a time. Another very common
way is by line scanning. This involves using a detector containing a onedimensional
array of pixels, say, 2048 pixels long by 1 pixel wide. As an
object is moved past the detector, the image is acquired line-by-line. Line
Chapter 23- Image Formation and Display 387
scanning is used by fax machines and airport x-ray baggage scanners. As a
variation, the object can be kept stationary while the detector is moved. This
is very convenient when the detector is already mounted on a moving object,
such as an aircraft taking images of the ground beneath it. The advantage of
line scanning is that speed is traded for detector simplicity. For example, a fax
machine may take several seconds to scan an entire page of text, but the
resulting image contains thousands of rows and columns.
An even more simplified approach is to acquire the image point-by-point.
For example, the microwave image of Venus was acquired one pixel at a
time. Another example is the scanning probe microscope, capable of
imaging individual atoms. A small probe, often consisting of only a single
atom at its tip, is brought exceedingly close to the sample being imaged.
Quantum mechanical effects can be detected between the probe and the
sample, allowing the probe to be stopped an exact distance from the
sample's surface. The probe is then moved over the surface of the sample,
keeping a constant distance, tracing out the peaks and valleys. In the final
image, each pixel's value represents the elevation of the corresponding
location on the sample's surface.
Printed images are divided into two categories: grayscale and halftone.
Each pixel in a grayscale image is a shade of gray between black and white,
such as in a photograph. In comparison, each pixel in a halftone image is
formed from many individual dots, with each dot being completely black or
completely white. Shades of gray are produced by alternating various numbers
of these black and white dots. For example, imagine a laser printer with a
resolution of 600 dots-per-inch. To reproduce 256 levels of brightness between
black and white, each pixel would correspond to an array of 16 by 16 printable
dots. Black pixels are formed by making all of these 256 dots black.
Likewise, white pixels are formed making all of these 256 dots white. Midgray
has one-half of the dots white and one-half black. Since the individual
dots are too small to be seen when viewed at a normal distance, the eye is
fooled into thinking a grayscale has been formed.
Halftone images are easier for printers to handle, including photocopy
machines. The disadvantage is that the image quality is often worse than
grayscale pictures.
Brightness and Contrast Adjustments
An image must have the proper brightness and contrast for easy viewing.
Brightness refers to the overall lightness or darkness of the image. Contrast
is the difference in brightness between objects or regions. For example, a
white rabbit running across a snowy field has poor contrast, while a black
dog against the same white background has good contrast. Figure 23-10
shows four possible ways that brightness and contrast can be misadjusted.
When the brightness is too high, as in (a), the whitest pixels are saturated,
destroying the detail in these areas. The reverse is shown in (b), where the
brightness is set too low, saturating the blackest pixels. Figure (c) shows
The Scientist and Engineer's Guide to Digital Signal Processing 388
b. Brightness too low a. Brightness too high
c. Contrast too high d. Contrast too low
FIGURE 23-10
Brightness and contrast adjustments. Increasing the brightness makes every pixel in the image becomes
lighter. In comparison, increasing the contrast makes the light areas become lighter, and the dark areas become
darker. These images show the effect of misadjusting the brightness and contrast.
the contrast set to high, resulting in the blacks being too black, and the whites
being too white. Lastly, (d) has the contrast set too low; all of the pixels are
a mid-shade of gray making the objects fade into each other.
Figures 23-11 and 23-12 illustrate brightness and contrast in more detail. A
test image is displayed in Fig. 23-12, using six different brightness and
contrast levels. Figure 23-11 shows the construction of the test image, an
array of 80×32 pixels, with each pixel having a value between 0 and 255.
The backgound of the test image is filled with random noise, uniformly
distributed between 0 and 255. The three square boxes have pixel values of
75, 150 and 225, from left-to-right. Each square contains two triangles with
pixel values only slightly different from their surroundings. In other
Chapter 23- Image Formation and Display 389
146
154
71
79
221
229
75 150 225
random 0 to 255
80 pixels
32 pixels
FIGURE 23-11
Brightness and contrast test image. This
is the structure of the digital image used
in Fig. 23-12. The three squares form
dark, medium, and bright objects, each
containing two low contrast triangles.
This figure indicates the digital numbers
(DN) of the pixels in each region.
words, there is a dark region in the image with faint detail, this is a medium
region in the image with faint detail, and there is a bright region in the image
with faint detail.
Figure 23-12 shows how adjustment of the contrast and brightness allows
different features in the image to be visualized. In (a), the brightness and
contrast are set at the normal level, as indicated by the B and C slide bars
at the left side of the image. Now turn your attention to the graph shown with
each image, called an output transform, an output look-up table, or a
gamma curve. This controls the hardware that displays the image. The value
of each pixel in the stored image, a number between 0 and 255, is passed
through this look-up table to produces another number between 0 and 255.
This new digital number drives the video intensity circuit, with 0 through 255
being transformed into black through white, respectively. That is, the look-up
table maps the stored numbers into the displayed brightness.
Figure (a) shows how the image appears when the output transform is set to do
nothing, i.e., the digital output is identical to the digital input. Each pixel in
the noisy background is a random shade of gray, equally distributed between
black and white. The three boxes are displayed as dark, medium and light,
clearly distinct from each other. The problem is, the triangles inside each
square cannot be easily seen; the contrast is too low for the eye to distinguished
these regions from their surroundings.
Figures (b) & (c) shows the effect of changing the brightness. Increasing
the brightness shifts the output transform to the left, while decreasing the
brightness shifts it to the right. Increasing the brightness makes every
pixel in the image appear lighter. Conversely, decreasing the brightness
makes every pixel in the image appear darker. These changes can improve
the viewability of excessively dark or light areas in the image, but will
saturate the image if taken too far. For example, all of the pixels in the far
right square in (b) are displayed with full intensity, i.e., 255. The opposite
effect is shown in (c), where all of the pixels in the far left square are
displayed as blackest black, or digital number 0. Since all the pixels in
these regions have the same value, the triangles are completely wiped out.
Also notice that none of the triangles in (b) and (c) are easier to see than
in (a). Changing the brightness provides little (if any) help in distinguishing
low contrast objects from their surroundings.
The Scientist and Engineer's Guide to Digital Signal Processing 390
Figure (d) shows the display optimized to view pixel values around digital
number 75. This is done by turning up the contrast, resulting in the output
transform increasing in slope. For example, the stored pixel values of 71 and
75 become 100 and 116 in the display, making the contrast a factor of four
greater. Pixel values between 46 and 109 are displayed as the blackest black,
to the whitest white. The price for this increased contrast is that pixel values
0 to 45 are saturated at black, and pixel values 110 to 255 are saturated at
white. As shown in (d), the increased contrast allows the triangles in the left
square to be seen, at the cost of saturating the middle and right squares.
Figure (e) shows the effect of increasing the contrast even further, resulting in
only 16 of the possible 256 stored levels being displayed as nonsaturated. The
brightness has also been decreased so that the 16 usable levels are centered on
digital number 150. The details in the center square are now very visible;
however, almost everything else in the image is saturated. For example, look
at the noise around the border of the image. There are very few pixels with an
intermediate gray shade; almost every pixel is either pure black or pure white.
This technique of using high contrast to view only a few levels is sometimes
called a grayscale stretch.
The contrast adjustment is a way of zooming in on a smaller range of pixel
values. The brightness control centers the zoomed section on the pixel values
of interest. Most digital imaging systems allow the brightness and contrast to
be adjusted in just this manner, and often provide a graphical display of the
output transform (as in Fig. 23-12). In comparison, the brightness and contrast
controls on television and video monitors are analog circuits, and may operate
differently. For example, the contrast control of a monitor may adjust the gain
of the analog signal, while the brightness might add or subtract a DC offset.
The moral is, don't be surprised if these analog controls don't respond in the
way you think they should.
Grayscale Transforms
The last image, Fig. 23-12f, is different from the rest. Rather than having a
slope in the curve over one range of input values, it has a slope in the curve
over two ranges. This allows the display to simultaneously show the triangles
in both the left and the right squares. Of course, this results in saturation of
the pixel values that are not near these digital numbers. Notice that the slide
bars for contrast and brightness are not shown in (f); this display is beyond
what brightness and contrast adjustments can provide.
Taking this approach further results in a powerful technique for improving the
appearance of images: the grayscale transform. The idea is to increase the
contrast at pixel values of interest, at the expense of the pixel values we don't
care about. This is done by defining the relative importance of each of the 0
to 255 possible pixel values. The more important the value, the greater its
contrast is made in the displayed image. An example will show a systematic
way of implementing this procedure.
Chapter 23- Image Formation and Display 391
Input value
0 50 100 150 200 250
0
50
100
150
200
250
B
C
a. Normal
B
C
b. Increased brightness
B
C
c. Decreased brightness
B
C
d. Slightly increased
contrast at DN 75
B
C
e. Greatly increased
contrast at DN 150
FIGURE 23-12
f. Increased contrast at
both DN 75 and 225
B
C
Input value
0 50 100 150 200 250
0
50
100
150
200
250
Input value
0 50 100 150 200 250
0
50
100
150
200
250
Input value
0 50 100 150 200 250
0
50
100
150
200
250
Input value
0 50 100 150 200 250
0
50
100
150
200
250
Input value
0 50 100 150 200 250
0
50
100
150
200
250
Output value Output value Output value Output value Output value Output value
The Scientist and Engineer's Guide to Digital Signal Processing 392
FIGURE 23-13
Grayscale processing. Image (a) was acquired with an infrared camera in total darkness. Brightness in the
image is related to the temperature, accounting for the appearance of the warm human body and the hot truck
grill. Image (b) was processed with the manual grayscale transform shown in Fig. 23-14c.
a. Original IR image b. With grayscale transform
The image in Fig. 23-13a was acquired in total darkness by using a CCD
camera that is sensitive in the far infrared. The parameter being imaged is
temperature: the hotter the object, the more infrared energy it emits and the
brighter it appears in the image. This accounts for the background being very
black (cold), the body being gray (warm), and the truck grill being white (hot).
These systems are great for the military and police; you can see the other guy
when he can't even see himself! The image in (a) is difficult to view because
of the uneven distribution of pixel values. Most of the image is so dark that
details cannot be seen in the scene. On the other end, the grill is near white
saturation.
The histogram of this image is displayed in Fig. 23-14a, showing that the
background, human, and grill have reasonably separate values. In this
example, we will increase the contrast in the background and the grill, at the
expense of everything else, including the human body. Figure (b) represents
this strategy. We declare that the lowest pixel values, the background, will
have a relative contrast of twelve. Likewise, the highest pixel values, the grill,
will have a relative contrast of six. The body will have a relative contrast of
one, with a staircase transition between the regions. All these values are
determined by trial and error.
The grayscale transform resulting from this strategy is shown in (c), labeled
manual. It is found by taking the running sum (i.e., the discrete integral) of the
curve in (b), and then normalizing so that it has a value of 255 at the
Chapter 23- Image Formation and Display 393
Value of pixel
0 50 100 150 200 250
0
200
400
600
800
1000
1200
1400
1600
a. Histogram
human body
background
grill
Value of pixel
0 50 100 150 200 250
0
2
4
6
8
10
12
14
16
b. Desired contrast
Input value
0 50 100 150 200 250
0
50
100
150
200
250
manual
from histogram
c. Output transform
Display value Desired contrast
Number of pixels
FIGURE 23-14
Developing a grayscale transform. Figure (a) is
the histogram of the raw image in Fig. 23-13a. In
(b), a curve is manually generated indicating the
desired contrast at each pixel value. The LUT for
the output transform is then found by integration
and normalization of (b), resulting in the curve
labeled manual in (c). In histogram equalization,
the histogram of the raw image, shown in (a), is
integrated and normalized to find the LUT,
shown in (c).
right side. Why take the integral to find the required curve? Think of it this
way: The contrast at a particular pixel value is equal to the slope of the output
transform. That is, we want (b) to be the derivative (slope) of (c). This means
that (c) must be the integral of (b).
Passing the image in Fig. 23-13a through this manually determined grayscale
transform produces the image in (b). The background has been made lighter,
the grill has been made darker, and both have better contrast. These
improvements are at the expense of the body's contrast, producing a less
detailed image of the intruder (although it can't get much worse than in the
original image).
Grayscale transforms can significantly improve the viewability of an image.
The problem is, they can require a great deal of trial and error. Histogram
equalization is a way to automate the procedure. Notice that the histogram
in (a) and the contrast weighting curve in (b) have the same general shape.
Histogram equalization blindly uses the histogram as the contrast weighing
curve, eliminating the need for human judgement. That is, the output transform
is found by integration and normalization of the histogram, rather than a
manually generated curve. This results in the greatest contrast being given to
those values that have the greatest number of pixels.
The Scientist and Engineer's Guide to Digital Signal Processing 394
Histogram equalization is an interesting mathematical procedure because it
maximizes the entropy of the image, a measure of how much information is
transmitted by a fixed number of bits. The fault with histogram equalization
is that it mistakes the shear number of pixels at a certain value with the
importance of the pixels at that value. For example, the truck grill and human
intruder are the most prominent features in Fig. 23-13. In spite of this,
histogram equalization would almost completely ignore these objects because
they contain relatively few pixels. Histogram equalization is quick and easy.
Just remember, if it doesn't work well, a manually generated curve will
probably do much better.
Warping
One of the problems in photographing a planet's surface is the distortion
from the curvature of the spherical shape. For example, suppose you use a
telescope to photograph a square region near the center of a planet, as
illustrated in Fig. 23-15a. After a few hours, the planet will have rotated
on its axis, appearing as in (b). The previously photographed region
appears highly distorted because it is curved near the horizon of the planet.
Each of the two images contain complete information about the region, just
from a different perspective. It is quite common to acquire a photograph
such as (a), but really want the image to look like (b), or vice versa. For
example, a satellite mapping the surface of a planet may take thousands of
images from straight above, as in (a). To make a natural looking picture of
the entire planet, such as the image of Venus in Fig. 23-1, each image must
be distorted and placed in the proper position. On the other hand, consider
a weather satellite looking at a hurricane that is not directly below it.
There is no choice but to acquire the image obliquely, as in (b). The image
is then converted into how it would appear from above, as in (a).
These spatial transformations are called warping. Space photography is the
most common use for warping, but there are others. For example, many
vacuum tube imaging detectors have various amounts of spatial distortion. This
includes night vision cameras used by the military and x-ray detectors used in
the medical field. Digital warping (or dewarping if you prefer) can be used to
correct the inherent distortion in these devices. Special effects artists for
motion pictures love to warp images. For example, a technique called
morphing gradually warps one object into another over a series of frames.
This can produces illusions such as a child turning into an adult, or a man
turning into a werewolf.
Warping takes the original image (a two-dimensional array) and generates
a warped image (another two-dimensional array). This is done by looping
through each pixel in the warped image and asking: What is the proper
pixel value that should be placed here? Given the particular row and
column being calculated in the warped image, there is a corresponding row
and column in the original image. The pixel value from the original image
is transferred to the warped image to carry out the algorithm. In the jargon
of image processing, the row and column that the pixel comes from in the
Chapter 23- Image Formation and Display 395
N
S
N
S
a. Normal View
b. Oblique View
FIGURE 23-15
Image warping. As shown in (a), a normal view of a small section of a planet appears relatively distortion free.
In comparison, an oblique view presents significant spatial distortion. Warping is the technique of changing
one of these images into the other.
original image is called the comes-from address. Transferring each pixel
from the original to the warped image is the easy part. The hard part is
calculating the comes-from address associated with each pixel in the warped
image. This is usually a pure math problem, and can become quite involved.
Simply stretching the image in the horizontal or vertical direction is easier,
involving only a multiplication of the row and/or column number to find the
comes-from address.
One of the techniques used in warping is subpixel interpolation. For
example, suppose you have developed a set of equations that turns a row and
column address in the warped image into the comes-from address in the original
The Scientist and Engineer's Guide to Digital Signal Processing 396
91
210
95
162
row
col
column
14 15
14.5
91 210
95 162
150.5
128.5
139.5
FIGURE 23-16
Subpixel interpolation. Subpixel interpolation for image warping is usually accomplished with bilinear
interpolation. As shown in (a), two intermediate values are calculated by linear interpolation in the horizontal
direction. The final value is then found by using linear interpolation in the vertical direction between the
intermediate values. As shown by the three-dimensional illustration in (b), this procedure uniquely defines all
values between the four known pixels at each of the corners.
a. b.
value
row
20.2
20 21
image. Consider what might happen when you try to find the value of the pixel
at row 10 and column 20 in the warped image. You pass the information: row
= 10, column = 20, into your equations, and out pops: comes-from row =
20.2, comes-from column = 14.5. The point being, your calculations will
likely use floating point, and therefore the comes-from addresses will not be
integers. The easiest method to use is the nearest neighbor algorithm, that
is, simply round the addresses to the nearest integer. This is simple, but can
produce a very grainy appearance at the edges of objects where pixels may
appear to be slightly misplaced.
Bilinear interpolation requires a little more effort, but provides significantly
better images. Figure 23-16 shows how it works. You know the value of the
four pixels around the fractional address, i.e., the value of the pixels at row 20
& 21, and column 14 and 15. In this example we will assume the pixels values
are 91, 210, 162 and 95. The problem is to interpolate between these four
values. This is done in two steps. First, interpolate in the horizontal direction
between column 14 and 15. This produces two intermediate values, 150.5 on
line 20, and 128.5 on line 21. Second, interpolate between these intermediate
values in the vertical direction. This produces the bilinear interpolated pixel
value of 139.5, which is then transferred to the warped image. Why interpolate
in the horizontal direction and then the vertical direction instead of the reverse?
It doesn't matter; the final answer is the same regardless of which order is
used.