Bản chất của hình ảnh y sinh học (Phần 1)

1
The Nature of Biomedical Images
The human body is composed of many systems, such as the cardiovascular
system, the musculo-skeletal system, and the central nervous system. Each
system is made up of several subsystems that carry on many physiological processes. For example, the visual system performs the task of focusing visual or
pictorial information on to the retina, transduction of the image information
into neural signals, and encoding and transmission of the neural signals to the
visual cortex. The visual cortex is responsible for interpretation of the image
information. The cardiac system performs the important task of rhythmic
pumping of blood through the arterial network of the body to facilitate the
delivery of nutrients, as well as pumping of blood through the pulmonary system for oxygenation of the blood itself. The anatomical features of the organs
related to a physiological system often demonstrate characteristics that re ect
the functional aspects of its processes as well as the well-being or integrity of
the system itself.
Physiological processes are complex phenomena, including neural or hormonal stimulation and control inputs and outputs that could be in the form
of physical material or information and action that could be mechanical,
electrical, or biochemical. Most physiological processes are accompanied by
or manifest themselves as signals that re ect their nature and activities. Such
signals could be of many types, including biochemical in the form of hormones or neurotransmitters, electrical in the form of potential or current, and
physical in the form of pressure or temperature.
Diseases or defects in a physiological system cause alterations in its normal processes, leading to pathological processes that a ect the performance,
health, and general well-being of the system. A pathological process is typically associated with signals and anatomical features that are di erent in
some respects from the corresponding normal patterns. If we possess a good
understanding of a system of interest, it becomes possible to observe the corresponding signals and features and assess the state of the system. The task
is not di cult when the signal is simple and appears at the outer surface of
the body. However, most systems and organs are placed well within the body
and enclosed in protective layers (for good reason!). Investigating or probing
such systems typically requires the use of some form of penetrating radiation
or invasive procedure.
© 2005 by CRC Press LLC

1


2

Biomedical Image Analysis

1.1 Body Temperature as an Image
Most infections cause a rise in the temperature of the body, which may be
sensed easily, albeit in a relative and qualitative manner, via the palm of
one's hand. Objective or quantitative measurement of temperature requires
an instrument, such as a thermometer.
A single measurement f of temperature is a scalar, and represents the thermal state of the body at a particular physical location in or on the body
denoted by its spatial coordinates (x y z ) and at a particular or single instant of time t. If we record the temperature continuously in some form, such
as a strip-chart record, we obtain a signal as a one-dimensional (1D) function of time, which may be expressed in the continuous-time or analog form
as f (t). The units applicable here are o C (degrees Celsius) for the temperature variable, and s (seconds) for the temporal variable t. If some means
were available to measure the temperature of the body at every spatial position, we could obtain a three-dimensional (3D) distribution of temperature as
f (x y z). Furthermore, if we were to perform the 3D measurement at every
instant of time, we would obtain a 3D function of time as f (x y z t) this
entity may also be referred to as a four-dimensional (4D) function.
When oral temperature, for example, is measured at discrete instants of
time, it may be expressed in discrete-time form as f (nT ) or f (n), where n
is the index or measurement sample number of the array of values, and T
represents the uniform interval between the time instants of measurement. A
discrete-time signal that can take amplitude values only from a limited list of
quantized levels is called a digital signal this distinction between discrete-time
and digital signals is often ignored.
If one were to use a thermal camera and take a picture of a body, a twodimensional (2D) representation of the heat radiated from the body would
be obtained. Although the temperature distribution within the body (and
even on the surface of the body) is a 3D entity, the picture produced by the

camera is a 2D snapshot of the heat radiation eld. We then have a 2D spatial
function of temperature | an image | which could be represented as f (x y).
The units applicable here are o C for the temperature variable itself, and mm
(millimeters) for the spatial variables x and y. If the image were to be sampled in space and represented on a discrete spatial grid, the corresponding
data could be expressed as f (m x n y), where x and y are the sampling intervals along the horizontal and vertical axes, respectively (in spatial
units such as mm). It is common practice to represent a digital image simply
as f (m n), which could be interpreted as a 2D array or a matrix of values.
It should be noted at the outset that, while images are routinely treated as
arrays, matrices, and related mathematical entities, they are almost always
representative of physical or other measures of organs or of physiological pro© 2005 by CRC Press LLC


The Nature of Biomedical Images

3

cesses that impose practical limitations on the range, degrees of freedom, and
other properties of the image data.
Examples: In intensive-care monitoring, the tympanic (ear drum) temperature is often measured using an infrared sensor. Occasionally, when catheters
are being used for other purposes, a temperature sensor may also be introduced into an artery or the heart to measure the core temperature of the
body. It then becomes possible to obtain a continuous measurement of temperature, although only a few samples taken at intervals of a few minutes
may be stored for subsequent analysis. Figure 1.1 illustrates representations
of temperature measurements as a scalar, an array, and a signal that is a function of time. It is obvious that the graphical representation facilitates easier
and faster comprehension of trends in the temperature than the numerical
format. Long-term recordings of temperature can facilitate the analysis of
temperature-regulation mechanisms 15, 16].
Infrared (with wavelength in the range 3 000;5 000 nm) or thermal sensors
may also be used to capture the heat radiated or emitted from a body or a
part of a body as an image. Thermal imaging has been investigated as a
potential tool for the detection of breast cancer. A tumor is expected to be

more vascularized than its neighboring tissues, and hence could be at a slightly
higher temperature. The skin surface near the tumor may also demonstrate a
relatively high temperature. Temperature di erences of the order of 2o C have
been measured between surface regions near breast tumors and neighboring
tissues. Figure 1.2 shows thermal images of a patient with benign brocysts
and a patient with breast cancer the local increase in temperature due to a
tumor is evident in the latter case. Thermography can help in the diagnosis
of advanced cancer, but has limited success in the detection of early breast
cancer 17, 18]. Recent improvements in detectors and imaging techniques
have created a renewed interest in the application of thermography for the
detection of breast cancer 19, 20, 21, 22, 23].
Infrared imaging via a telethermographic camera has been applied to the
detection of varicocele, which is the most common cause of infertility in
men 24, 25, 26]. In normal men, the testicular temperature is about 3 ; 4 o C
below the core body temperature. In the case of varicocele, dilation of the testicular veins reduces the venous return from the scrotum, causes stagnation of
blood and edema, and leads to increased testicular temperature. In the experiments conducted by Merla et al. 25], a cold patch was applied to the subject's
scrotum, and the thermal recovery curves were analyzed. The results obtained
showed that the technique was successful in detecting subclinical varicocele.
Vlaisavljevic 26] showed that telethermography can provide better diagnostic
accuracy in the detection of varicocele than contact thermography.

© 2005 by CRC Press LLC


4

Biomedical Image Analysis
33.5 o C
(a)
Time

(hours)

08

10

12

14

16

18

20

22

24

Temperature 33.5 33.3 34.5 36.2 37.3 37.5 38.0 37.8 38.0
(o C )
(b)
39

Temperature in degrees Celsius

38

37

36

35

34

33

32

8

10

12

14

16
Time in hours

18

20

22

24

(c)

FIGURE 1.1

Measurements of the temperature of a patient presented as (a) a scalar with
one temperature measurement f at a time instant t (b) an array f (n) made
up of several measurements at di erent instants of time and (c) a signal f (t)
or f (n). The horizontal axis of the plot represents time in hours the vertical
axis gives temperature in degrees Celsius. Data courtesy of Foothills Hospital,
Calgary.

© 2005 by CRC Press LLC


The Nature of Biomedical Images

FIGURE 1.2

(a)

(b)

Body temperature as a 2D image f (x y) or f (m n). The images illustrate the distribution of surface temperature measured
using an infrared camera operating in the 3 000 ; 5 000 nm wavelength range. (a) Image of a patient with pronounced
vascular features and benign brocysts in the breasts. (b) Image of a patient with a malignant mass in the upper-outer
quadrant of the left breast. Images courtesy of P. Hoekstra, III, Therma-Scan, Inc., Huntington Woods, MI.
5

© 2005 by CRC Press LLC

6

Biomedical Image Analysis

The thermal images shown in Figure 1.2 serve to illustrate an important
distinction between two major categories of medical images:
anatomical or physical images, and
functional or physiological images.
The images illustrate the notion of body temperature as a signal or image.
Each point in the images in Figure 1.2 represents body temperature, which
is related to the ongoing physiological or pathological processes at the corresponding location in the body. A thermal image is, therefore, a functional
image. An ordinary photograph obtained with re ected light, on the other
hand, would be a purely anatomical or physical image. More sophisticated
techniques that provide functional images related to circulation and various
physiological processes are described in the following sections.

1.2 Transillumination

Transillumination, diaphanography, and diaphanoscopy involve the shining of
visible light or near-infrared radiation through a part of the body, and viewing
or imaging the transmitted radiation. The technique has been investigated
for the detection of breast cancer, the attractive feature being the use of
nonionizing radiation 27]. The use of near-infrared radiation appears to have
more potential than visible light, due to the observation that nitrogen-rich
compounds preferentially absorb (or attenuate) infrared radiation. The fat
and broglandular tissue in the mature breast contain much less nitrogen than
malignant tissues. Furthermore, the hemoglobin in blood has a high nitrogen
content, and tumors are more vascularized than normal tissues. For these
reasons, breast cancer appears as a relatively dark region in a transilluminated

image.
The e ectiveness of transillumination is limited by scatter and ine ective
penetration of light through a large organ such as the breast. Transillumination has been found to be useful in di erentiating between cystic ( uid- lled)
and solid lesions however, the technique has had limited success in distinguishing malignant tumors from benign masses 18, 28, 29].

1.3 Light Microscopy

Studies of the ne structure of biological cells and tissues require signi cant
magni cation for visualization of the details of interest. Useful magni cation
© 2005 by CRC Press LLC


The Nature of Biomedical Images

7

of up to 1 000 may be obtained via light microscopy by the use of combinations of lenses. However, the resolution of light microscopy is reduced by the
following factors 30]:

Di raction: The bending of light at edges causes blurring the image
of a pinhole appears as a blurred disc known as the Airy disc.

Astigmatism: Due to nonuniformities in lenses, a point may appear
as an ellipse.

Chromatic aberration: Electromagnetic (EM) waves of di erent wavelength or energy that compose the ordinarily used white light converge
at di erent focal planes, thereby causing enlargement of the focal point.
This e ect may be corrected for by using monochromatic light. See
Section 3.9 for a description of confocal microscopy.
Spherical aberration: The rays of light arriving at the periphery

of a lens are refracted more than the rays along the axis of the lens.
This causes the rays from the periphery and the axis not to arrive at a
common focal point, thereby resulting in blurring. The e ect may be
reduced by using a small aperture.

Geometric distortion: Poorly crafted lenses may cause geometric
distortion such as the pin-cushion e ect and barrel distortion.
Whereas the best resolution achievable by the human eye is of the order
of 0:1 ; 0:2 mm, light microscopes can provide resolving power up to about
0:2 m.
Example: Figure 1.3 shows a rabbit ventricular myocyte in its relaxed
state as seen through a light microscope at a magni cation of about 600.
The experimental setup was used to study the contractility of the myocyte
with the application of electrical stimuli 31].
Example: Figure 1.4 shows images of three-week-old scar tissue and fortyweek-old healed tissue samples from rabbit ligaments at a magni cation of
about 300. The images demonstrate the alignment patterns of the nuclei of
broblasts (stained to appear as the dark objects in the images): the threeweek-old scar tissue has many broblasts that are scattered in di erent directions, whereas the forty-week-old healed sample has fewer broblasts that are
well-aligned along the length of the ligament (the horizontal edge of the image). The appearance of the forty-week-old sample is closer to that of normal
samples than that of the three-week-old sample. Images of this nature have
been found to be useful in studying the healing and remodeling processes in
ligaments 32].
© 2005 by CRC Press LLC


8

Biomedical Image Analysis

FIGURE 1.3

A single ventricular myocyte (of a rabbit) in its relaxed state. The width
(thickness) of the myocyte is approximately 15 m. Image courtesy of R.
Clark, Department of Physiology and Biophysics, University of Calgary.

© 2005 by CRC Press LLC


The Nature of Biomedical Images

9

(a)

FIGURE 1.4

(b)

(a) Three-week-old scar tissue sample, and (b) forty-week-old healed tissue
sample from rabbit medial collateral ligaments. Images courtesy of C.B.
Frank, Department of Surgery, University of Calgary.

© 2005 by CRC Press LLC


10

1.4 Electron Microscopy

Biomedical Image Analysis

Accelerated electrons possess EM wave properties, with the wavelength
h , where h is Planck's constant, m is the mass of the electron,
given by = mv
and v is the electron's velocity this relationship reduces to = 1p:23
V , where
V is the accelerating voltage 30]. At a voltage of 60 kV , an electron beam
has an e ective wavelength of about 0:005 nm, and a resolving power limit
of about 0:003 nm. Imaging at a low kV provides high contrast but low
resolution, whereas imaging at a high kV provides high resolution due to
smaller wavelength but low contrast due to higher penetrating power. In
addition, a high-kV beam causes less damage to the specimen as the faster
electrons pass through the specimen in less time than with a low-kV beam.
Electron microscopes can provide useful magni cation of the order of 106 ,
and may be used to reveal the ultrastructure of biological tissues. Electron
microscopy typically requires the specimen to be xed, dehydrated, dried,
mounted, and coated with a metal.
Transmission electron microscopy: A transmission electron microscope
(TEM) consists of a high-voltage electron beam generator, a series of EM
lenses, a specimen holding and changing system, and a screen- lm holder, all
enclosed in vacuum. In TEM, the electron beam passes through the specimen,
is a ected in a manner similar to light, and the resulting image is captured
through a screen- lm combination or viewed via a phosphorescent viewing
screen.
Example: Figure 1.5 shows TEM images of collagen bers (in crosssection) in rabbit ligament samples. The images facilitate analysis of the
diameter distribution of the bers 33]. Scar samples have been observed to
have an almost uniform distribution of ber diameter in the range 60 ; 70 nm,
whereas normal samples have an average diameter of about 150 nm over a
broader distribution. Methods for the detection and analysis of circular objects are described in Sections 5.6.1, 5.6.3, and 5.8.
Example: In patients with hematuria, the glomerular basement membrane

of capillaries in the kidney is thinner (< 200 nm) than the normal thickness
of the order of 300 nm 34]. Investigation of this feature requires needle-core
biopsy of the kidney and TEM imaging. Figure 1.6 shows a TEM image
of a capillary of a normal kidney in cross-section. Figure 1.7 (a) shows an
image of a sample with normal membrane thickness Figure 1.7 (b) shows
an image of a sample with reduced and variable thickness. Although the
ranges of normal and abnormal membrane thickness have been established by
several studies 34], the diagnostic decision process is subjective methods for
objective and quantitative analysis are desired in this application.

© 2005 by CRC Press LLC


The Nature of Biomedical Images

11

(a)

FIGURE 1.5

(b)

TEM images of collagen bers in rabbit ligament samples at a magni cation
of approximately 30 000. (a) Normal and (b) scar tissue. Images courtesy
of C.B. Frank, Department of Surgery, University of Calgary.

© 2005 by CRC Press LLC

12

FIGURE 1.6

Biomedical Image Analysis

TEM image of a kidney biopsy sample at a magni cation of approximately
3 500. The image shows the complete cross-section of a capillary with normal membrane thickness. Image courtesy of H. Benediktsson, Department of
Pathology and Laboratory Medicine, University of Calgary.

© 2005 by CRC Press LLC


The Nature of Biomedical Images

(a)

(b)

FIGURE 1.7

© 2005 by CRC Press LLC

13

TEM images of kidney biopsy samples at a magni cation of approximately 8 000. (a) The sample shows normal capillary
membrane thickness. (b) The sample shows reduced and varying membrane thickness. Images courtesy of H. Benediktsson,
Department of Pathology and Laboratory Medicine, University of Calgary.

14

Biomedical Image Analysis

Scanning electron microscopy: A scanning electron microscope (SEM)
is similar to a TEM in many ways, but uses a nely focused electron beam
with a diameter of the order of 2 nm to scan the surface of the specimen. The
electron beam is not transmitted through the specimen, which could be fairly
thick in SEM. Instead, the beam is used to scan the surface of the specimen
in a raster pattern, and the secondary electrons that are emitted from the
surface of the sample are detected and ampli ed through a photomultiplier
tube (PMT), and used to form an image on a cathode-ray tube (CRT). An
SEM may be operated in di erent modes to detect a variety of signals emitted
from the sample, and may be used to obtain images with a depth of eld of
several mm.
Example: Figure 1.8 illustrates SEM images of collagen bers in rabbit
ligament samples (freeze-fractured surfaces) 35]. The images are useful in analyzing the angular distribution of bers and the realignment process during
healing after injury. It has been observed that collagen bers in a normal ligament are well aligned, that bers in scar tissue lack a preferred orientation,
and that organization and alignment return toward their normal patterns during the course of healing 36, 37, 35]. Image processing methods for directional
analysis are described in Chapter 8.

(a)

FIGURE 1.8

(b)

SEM images of collagen bers in rabbit ligament samples at a magni cation
of approximately 4 000. (a) Normal and (b) scar tissue. Reproduced with
permission from C.B. Frank, B. MacFarlane, P. Edwards, R. Rangayyan, Z.Q.

Liu, S. Walsh, and R. Bray, \A quantitative analysis of matrix alignment
in ligament scars: A comparison of movement versus immobilization in an
immature rabbit model", Journal of Orthopaedic Research, 9(2): 219 { 227,
1991. c Orthopaedic Research Society.
© 2005 by CRC Press LLC


The Nature of Biomedical Images

15

1.5 X-ray Imaging

The medical diagnostic potential of X rays was realized soon after their discovery by Roentgen in 1895. (See Robb 38] for a review of the history of
X-ray imaging.) In the simplest form of X-ray imaging or radiography, a 2D
projection (shadow or silhouette) of a 3D body is produced on lm by irradiating the body with X-ray photons 4, 3, 5, 6]. This mode of imaging is
referred to as projection or planar imaging. Each ray of X-ray photons is
attenuated by a factor depending upon the integral of the linear attenuation
coe cient along the path of the ray, and produces a corresponding gray level
(or signal) at the point hit on the lm or the detecting device used.
Considering the ray path marked as AB in Figure 1.9, let Ni denote the
number of X-ray photons incident upon the body being imaged, within a
speci ed time interval. Let us assume that the X rays are mutually parallel,
with the X-ray source at a large distance from the subject or object being
imaged. Let No be the corresponding number of photons exiting the body.
Then, we have
Z
No = Ni exp ;
(x y) ds
(1.1)

or

rayAB

Z

rayAB

Ni :
(x y) ds = ln N
o

(1.2)

The equations above are modi ed versions of Beer's law (also known as the
Beer-Lambert law) on the attenuation of X rays due to passage through a
medium. The ray AB lies in the sectional plane PQRS the mutually parallel
rays within the plane PQRS are represented by the coordinates (t s) that are
at an angle with respect to the (x y) coordinates indicated in Figure 1.9,
with the s axis being parallel to the rays. Then, s = ;x sin + y cos . The
variable of integration ds represents the elemental distance along the ray, and
the integral is along the ray path AB from the X-ray source to the detector.
(See Section 9.1 for further details on this notation.) The quantities Ni and
No are Poisson variables it is assumed that their values are large for the
equations above to be applicable. The function (x y) represents the linear
attenuation coe cient at (x y) in the sectional plane PQRS. The value of
(x y) depends upon the density of the object or its constituents along the
ray path, as well as the frequency (or wavelength or energy) of the radiation
used. Equation 1.2 assumes the use of monochromatic or monoenergetic X
rays.

A measurement of the exiting X rays (that is, No , and Ni for reference) thus
gives us only an integral of (x y) over the ray path. The internal details of
the body along the ray path are compressed onto a single point on the lm
or a single measurement. Extending the same argument to all ray paths,
© 2005 by CRC Press LLC


16

Biomedical Image Analysis
z

z
Q’

R

Q

No
P’

P

B

ds

S

A

Ni

y
y

X rays
x

2D projection

3D object

FIGURE 1.9

An X-ray image or a typical radiograph is a 2D projection or planar image
of a 3D object. The entire object is irradiated with X rays. The projection
of a 2D cross-sectional plane PQRS of the object is a 1D pro le P'Q' of the
2D planar image. See also Figures 1.19 and 9.1. Reproduced, with permission, from R.M. Rangayyan and A. Kantzas, \Image reconstruction", Wiley
Encyclopedia of Electrical and Electronics Engineering, Supplement 1, Editor:
John G. Webster, Wiley, New York, NY, pp 249{268, 2000. c This material
is used by permission of John Wiley & Sons, Inc.
we see that the radiographic image so produced is a 2D planar image of the
3D object, where the internal details are superimposed. In the case that the
rays are parallel to the x axis (as in Figure 1.9), we have = 90o , s = ;x,
ds = ;dx, and the planar image

g(y z) =

Z

; (x y z) dx:

(1.3)

Ignoring the negative sign, we see that the 3D object is reduced to (or integrated into) a 2D planar image by the process of radiographic imaging.
The most commonly used detector in X-ray imaging is the screen- lm combination 5, 6]. The X rays exiting from the body being imaged strike a
uorescent (phosphor) screen made of compounds of rare-earth elements such
as lanthanum oxybromide or gadolinium oxysul de, where the X-ray photons
are converted into visible-light photons. A light-sensitive lm that is placed in
contact with the screen (in a light-tight cassette) records the result. The lm
contains a layer of silver-halide emulsion with a thickness of about 10 m.
The exposure or blackening of the lm depends upon the number of light
photons that reach the lm.
A thick screen provides a high e ciency of conversion of X rays to light,
but causes loss of resolution due to blurring (see Figure 1.10). The typical
thickness of the phosphor layer in screens is in the range 40 ; 100 m. Some
© 2005 by CRC Press LLC


The Nature of Biomedical Images

17

receiving units make use of a lm with emulsion on both sides that is sandwiched between two screens: the second screen (located after the lm along
the path of propagation of the X rays) converts the X-ray photons not affected by the rst screen into light, and thereby increases the e ciency of
the receiver. Thin screens may be used in such dual-screen systems to achieve
higher conversion e ciency (and lower dose to the patient) without sacri cing
resolution.

X rays

A
light

B

screen
film

FIGURE 1.10

Blur caused by a thick screen. Light emanating from point A in the screen is
spread over a larger area on the lm than that from point B.
A uoroscopy system uses an image intensi er and a video camera in place
of the lm to capture the image and display it on a monitor as a movie or
video 5, 6]. Images are acquired at a rate of 2 ; 8 frames=s (fps), with
the X-ray beam pulsed at 30 ; 100 ms per frame. In computed radiography
(CR), a photo-stimulable phosphor plate (made of europium-activated barium
uorohalide) is used instead of lm to capture and temporarily hold the image
pattern. The latent image pattern is then scanned using a laser and digitized.
In digital radiography (DR), the lm or the entire screen- lm combination is
replaced with solid-state electronic detectors 39, 40, 41, 42].
Examples: Figures 1.11 (a) and (b) show the posterior-anterior (PA, that
is, back-to-front) and lateral (side-to-side) X-ray images of the chest of a
patient. Details of the ribs and lungs, as well as the outline of the heart,
are visible in the images. Images of this type are useful in visualizing and
discriminating between the air- lled lungs, the uid- lled heart, the ribs, and
vessels. The size of the heart may be assessed in order to detect enlargement
of the heart. The images may be used to detect lesions in the lungs and

fracture of the ribs or the spinal column, and to exclude the presence of uid
in the thoracic cage. The use of two views assists in localizing lesions: use
of the PA view only, for example, will not provide information to decide if a
tumor is located toward the posterior or anterior of the patient.
© 2005 by CRC Press LLC


18

FIGURE 1.11

(b)

(a) Posterior-anterior and (b) lateral chest X-ray images of a patient. Images courtesy of Foothills Hospital, Calgary.

© 2005 by CRC Press LLC

Biomedical Image Analysis

(a)


The Nature of Biomedical Images

19

The following paragraphs describe some of the physical and technical considerations in X-ray imaging 4, 5, 6, 43, 44].

Target and focal spot: An electron beam with energy in the range
of 20 ; 140 keV is used to produce X rays for diagnostic imaging. The

typical target materials used are tungsten and molybdenum. The term
\focal spot" refers to the area of the target struck by the electron beam
to generate X rays however, the nominal focal spot is typically expressed in terms of its diameter in mm as observed in the imaging plane
(on the lm). A small focal spot is desired in order to obtain a sharp
image, especially in magni cation imaging. (See also Section 2.9 and
Figure 2.18.) Typical focal spot sizes in radiography lie in the range of
0:1 ; 2 mm. A focal spot size of 0:1 ; 0:3 mm is desired in mammography.
Energy: The penetrating capability of an X-ray beam is mainly determined by the accelerating voltage applied to the electron beam that
impinges the target in the X-ray generator. The commonly used indicator of penetrating capability (often referred to as the \energy" of the
X-ray beam) is kV p, standing for kilo-volt-peak. The higher the kV p,
the more penetrating the X-ray beam will be. The actual unit of energy of an X-ray photon is the electron volt or eV , which is the energy
gained by an electron when a potential of 1 V is applied to it. The kV p
measure relates to the highest possible X-ray photon energy that may
be achieved at the voltage used.
Low-energy X-ray photons are absorbed at or near the skin surface, and
do not contribute to the image. In order to prevent such unwanted
radiation, a lter is used at the X-ray source to absorb low-energy X
rays. Typical lter materials are aluminum and molybdenum.
Imaging of soft-tissue organs such as the breast is performed with lowenergy X rays in the range of 25 ; 32 kV p 45]. The use of a higher kV p
would result in low di erential attenuation and poor tissue-detail visibility or contrast. A few other energy levels used in projection radiography
are, for imaging the abdomen: 60 ; 100 kV p chest: 80 ; 120 kV p and
skull: 70 ; 90 kV p. The kV p to be used depends upon the distance
between the X-ray source and the patient, the size (thickness) of the
patient, the type of grid used, and several other factors.
Exposure: For a given tube voltage (kV p), the total number of X-ray
photons released at the source is related to the product of the tube current (mA) and the exposure time (s), together expressed as the product
mAs. As a result, for a given body being imaged, the number of photons that arrive at the lm is also related to the mAs quantity. A low
mAs results in an under-exposed lm (faint or light image), whereas a
high mAs results in an over-exposed or dark image (as well as increased

© 2005 by CRC Press LLC


20

Biomedical Image Analysis
X-ray dose to the patient). Typical exposure values lie in the range
of 2 ; 120 mAs. Most imaging systems determine automatically the
required exposure for a given mode of imaging, patient size, and kV p
setting. Some systems use an initial exposure of the order of 5 ms to
estimate the penetration of the X rays through the body being imaged,
and then determine the required exposure.
Beam hardening: The X rays used in radiographic imaging are typically not monoenergetic that is, they possess X-ray photons over a certain band of frequencies or EM energy levels. As the X rays propagate
through a body, the lower-energy photons get absorbed preferentially,
depending upon the length of the ray path through the body and the
attenuation characteristics of the tissues along the path. Thus, the X
rays that pass through the object at longer distances from the source
will possess relatively fewer photons at lower-energy levels than at the
point of entry into the object (and hence a relatively higher concentration of higher-energy photons). This e ect is known as beam hardening,
and leads to incorrect estimation of the attenuation coe cient in computed tomography (CT) imaging. The e ect of beam hardening may be
reduced by pre ltering or prehardening the X-ray beam and narrowing
its spectrum. The use of monoenergetic X rays from a synchrotron or a
laser obviates this problem.
Scatter and the use of grids: As an X-ray beam propagates through
a body, photons are lost due to absorption and scattering at each point
in the body. The angle of the scattered photon at a given point along the
incoming beam is a random variable, and hence the scattered photon
contributes to noise at the point where it strikes the detector. Furthermore, scattering results in the loss of contrast of the part of the
object where X-ray photons were scattered from the main beam. The
noise e ect of the scattered radiation is signi cant in gamma-ray emission imaging, and requires speci c methods to improve the quality of

the image 4, 46]. The e ect of scatter may be reduced by the use of
grids, collimation, or energy discrimination due to the fact that the scattered (or secondary) photons usually have lower energy levels than the
primary photons.
A grid consists of an array of X-ray absorbing strips that are mutually
parallel if the X rays are in a parallel beam, as in chest imaging (see
Figures 1.12 and 1.13), or are converging toward the X-ray source in the
case of a diverging beam (as in breast imaging, see Figure 1.15). Lattice
or honeycomb grids with parallel strips in criss-cross patterns are also
used in mammography. X-ray photons that arrive via a path that is not
aligned with the grids will be stopped from reaching the detector.
A typical grid contains thin strips of lead or aluminum with a strip density of 25 ; 80 lines=cm and a grid height:strip width ratio in the range

© 2005 by CRC Press LLC


The Nature of Biomedical Images

21

parallel X rays

A
F

B

E

C

parallel grid
screen-film

A’

D

FIGURE 1.12

Use of parallel grids to reduce scatter. X rays that are parallel to the grids
reach the lm for example, line AA'. Scattered rays AB, AC, and AE have
been blocked by the grids however, the scattered ray AD has reached the lm
in the illustration.
of 5:1 to 12:1. The space between the grids is lled with low-attenuation
material such as wood. A stationary grid produces a line pattern that is
superimposed upon the image, which would be distracting. Figure 1.13
(a) shows a part of an image of a phantom with the grid artifact clearly
visible. (An image of the complete phantom is shown in Figure 1.14.)
Grid artifact is prevented in a reciprocating grid, where the grid is moved
about 20 grid spacings during exposure: the movement smears the grid
shadow and renders it invisible on the image. Figure 1.13 (b) shows
an image of the same object as in part (a), but with no grid artifact.
Low levels of grid artifact may appear in images if the bucky that holds
the grid does not move at a uniform pace or starts moving late or ends
movement early with respect to the X-ray exposure interval. A major
disadvantage of using grids is that it requires approximately two times
the radiation dose required for imaging techniques without grids. Furthermore, the contrast of ne details is reduced due to the smeared
shadow of the grid.

Photon detection noise: The interaction between an X-ray beam

and a detector is governed by the same rules as for interaction with
any other matter: photons are lost due to scatter and absorption, and
some photons may pass through una ected (or undetected). The small
size of the detectors in DR and CT imaging reduces their detection

© 2005 by CRC Press LLC


22

Biomedical Image Analysis
e ciency. Scattered and undetected photons cause noise in the measurement for detailed analysis of noise in X-ray detection, refer to Barrett and Swindell 3], Macovski 5], and Cho et al. 4]. More details on
noise in medical images and techniques to remove noise are presented in
Chapter 3.

Ray stopping by heavy implants: If the body being imaged contains

extremely heavy parts or components, such as metal screws or pins in
bones and surgical clips that are nearly X-ray-opaque and entirely stop
the incoming X-ray photons, no photons would be detected at the corresponding point of exit from the body. The attenuation coe cient for
the corresponding path would be inde nite, or within the computational
context, in nity. Then, a reconstruction algorithm would not be able
to redistribute the attenuation values over the points along the corresponding ray path in the reconstructed image. This leads to streaking
artifacts in CT images.
Two special techniques for enhanced X-ray imaging | digital subtraction
angiography (DSA) and dual-energy imaging | are described in Sections 4.1
and 4.2, respectively.

1.5.1 Breast cancer and mammography

Breast cancer: Cancer is caused when a single cell or a group of cells

escapes from the usual controls that regulate cellular growth, and begins to
multiply and spread. This activity results in a mass, tumor, or neoplasm.
Many masses are benign that is, the abnormal growth is restricted to a single,
circumscribed, expanding mass of cells. Some tumors are malignant that is,
the abnormal growth invades the surrounding tissues and may spread, or
metastasize, to distant areas of the body. Although benign masses may lead
to complications, malignant tumors are usually more serious, and it is for
these tumors that the term \cancer" is used. The majority of breast tumors
will have metastasized before reaching a palpable size.
Although curable, especially when detected at early stages, breast cancer
is a major cause of death in women. An important factor in breast cancer
is that it tends to occur earlier in life than other types of cancer and other
major diseases 47, 48]. Although the cause of breast cancer has not yet
been fully understood, early detection and removal of the primary tumor are
essential and e ective methods to reduce mortality, because, at such a point
in time, only a few of the cells that departed from the primary tumor would
have succeeded in forming secondary tumors 49]. When breast tumors are
detected by the a ected women themselves (via self-examination), most of the
tumors would have metastasized 50].
If breast cancer can be detected by some means at an early stage, while it is
clinically localized, the survival rate can be dramatically increased. However,
© 2005 by CRC Press LLC


The Nature of Biomedical Images

23

(a)

(b)

FIGURE 1.13

X-ray images of a part of a phantom: (a) with, and (b) without grid artifact.
Image courtesy of L.J. Hahn, Foothills Hospital, Calgary. See also Figure 1.14.

© 2005 by CRC Press LLC


24

FIGURE 1.14

Biomedical Image Analysis

X-ray image of the American College of Radiology (ACR) phantom for mammography. The pixel-value range 117 210] has been linearly stretched to the
display range 0 255] to show the details. Image courtesy of S. Bright, Sunnybrook & Women's College Health Sciences Centre, Toronto, ON, Canada.
See also Figure 1.13.

© 2005 by CRC Press LLC


The Nature of Biomedical Images

25

such early breast cancer is generally not amenable to detection by physical examination and breast self-examination. The primary role of an imaging technique is thus the detection of lesions in the breast 29]. Currently, the most
e ective method for the detection of early breast cancer is X-ray mammography. Other modalities, such as ultrasonography, transillumination, thermography, CT, and magnetic resonance imaging (MRI) have been investigated for
breast cancer diagnosis, but mammography is the only reliable procedure for
detecting nonpalpable cancers and for detecting many minimal breast cancers
when they appear to be curable 18, 28, 29, 51]. Therefore, mammography
has been recommended for periodic screening of asymptomatic women. Mammography has gained recognition as the single most successful technique for
the detection of early, clinically occult breast cancer 52, 53, 54, 55, 56].
X-ray imaging of the breast: The technique of using X rays to obtain images of the breast was rst reported by Warren in 1930, after he had
examined 100 women using sagital views 57]. Because of the lack of a reproducible method for obtaining satisfactory images, this technique did not
make much progress until 1960, when Egan 58] reported on high-mA and
low-kV p X-ray sources that yielded reproducible images on industrial lm. It
was in the mid-1960s that the rst modern X-ray unit dedicated to mammography was developed. Since then, remarkable advances have led to a striking
improvement in image quality and a dramatic reduction in radiation dose.
A major characteristic of mammograms is low contrast, which is due to
the relatively homogeneous soft-tissue composition of the breast. Many efforts have been focused on developing methods to enhance contrast. In an
alternative imaging method known as xeromammography, a selenium-coated
aluminum plate is used as the detector 6]. The plate is initially charged
to about 1 000 V . Exposure to the X rays exiting the patient creates a
charge pattern on the plate due to the liberation of electrons and ions. The
plate is then sprayed with an ionized toner, the pattern of which is transferred to plastic-coated paper. Xeromammograms provide wide latitude and
edge enhancement, which lead to improved images as compared to screen- lm
mammography. However, xeromammography results in a higher dose to the
subject, and has not been in much use since the 1980s.
A typical mammographic imaging system is shown schematically in Figure 1.15. Mammography requires high X-ray beam quality (a narrow-band
or nearly monochromatic beam), which is controlled by the tube target material (molybdenum) and beam ltration with molybdenum. E ective breast
compression is an important factor in reducing scattered radiation, creating
as uniform a density distribution as possible, eliminating motion, and separating mammary structures, thereby increasing the visibility of details in the
image. The use of grids speci cally designed for mammography can further
reduce scattered radiation and improve subject contrast, which is especially
signi cant when imaging thick, dense breasts 59].

Generally, conventional screen- lm mammography is performed with the
breast directly in contact with the screen- lm cassette, producing essentially
© 2005 by CRC Press LLC