H A N D B O O K O F
MEDICAL IMAGING
Editorial Advisory Board
Dr. William Brody Dr. Elias Zerhouni
President Chairman, Department of Radiology
Johns Hopkins Un...
H A N D B O O K O F
MEDICAL IMAGING
P R O C E S S I N G A N D A N A LY S I S
Editor-in-Chief
Isaac N. Bankman, PhD
Applied...
This book is printed on acid-free paper. ?s
Copyright # 2000 by Academic Press
All rights reserved.
No part of this public...
To Lisa, Judy, and Danny
Contents
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
30 Validation of Registration Accuracy Roger P. Woods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
Foreword
The development of medical imaging over the past three
decades has been truly revolutionary. For example, in card...
Preface
The discoveries of seminal physical phenomena such as X-rays,
ultrasound, radioactivity, and magnetic resonance, a...
V Visualization
Visualization is a relatively new area that is contributing
signi®cantly to medicine and biology. While au...
Contributors
M. Stella Atkins
School of Computing Science
Simon Fraser University
Burnaby, BC V5A 1S6, Canada
Chapter 11
N...
Nobuhiko Hata
Surgical Planning Lab
Department of Radiology
Brigham & Women's Hospital
Harvard Medical School
Boston, MA 0...
Tim McInerney
Department of Computer Science
University of Toronto
Toronto, ON M5S 3H5, Canada
Chapter 8
Michael B. Millis...
Michael Unser
Swiss Federal Institute of Technology-
Lausanne
EPFL/DMT/IOA/Biomedical Imaging Group
CH-1015 Lausanne, Swit...
I
Enhancement
1 Fundamental Enhancement Techniques Raman B. Paranjape . . . . . . . . . . . . . . . . . . 3
2 Adaptive Ima...
The ®rst chapter, by Paranjape, provides an introduction to basic techniques, including histogram
manipulation, mean and m...
1
Fundamental Enhancement
Techniques
Raman B. Paranjape
University of Regina
1 Introduction . . . . . . . . . . . . . . . ...
sampled at regular intervals and the intensity is quantized to a
®nite number of levels. Each element of the array is refe...
g…m; n† ˆ T…e…m; n††%CÀ1
…C…f …m; n†††
g…m; n†%f …m; n†;
where T…† is a nonlinear operator which is approximately equal
to...
3.3 Histogram Equalization
Although intensity scaling can be very effective in enhancing
image information present in spec...
pro®le of the image, each bin of the histogram should have a
pixel count of …M à N†=P.
It is, in general, possible to move...
(c)
(b)
(d)
(a)
FIGURE 3 (a) Original image where gray levels are not uniformly distributed. Many image details are not we...
(g)
(f )
(h)
(e)
FIGURE 3 (Continued).
1 Fundamental Enhancement Techniques 9
enhanced. The edge-enhanced images may be combined with
the original image in order to preserve the context.
Horizontal ed...
image can result in an output image with both positive and
negative values. An enhanced image with only positive pixels
ca...
convolving the original image with the kernel after adding 1
to its central coef®cient. Edge enhancement appears to
provid...
(d)
(a) (b)
(c)
FIGURE 6 (a) Absolute value of output image after convolution of wH1
with the image in Fig. 3a. (b) Absolu...
(a) (b)
(c)
(d) (f )(e)
FIGURE 7 (a) Sum of original image in Fig. 3a and its convolution with
wH1, (b) with wV1, and (c) ...
the image. The method formulated as shown next is applied at
each pixel …m; n† of the input image.
hLA…m; n†…i† ˆ
ˆK
kˆÀK
...
b…m; n† ˆ f1…m; n† À f2…m; n†
g…m; n† ˆ fmax ?
b…m; n† À minfb…m; n†g
maxfb…m; n†g À minfb…m; n†g
 
where fmax is the maxi...
enhance image information. After these algorithms have been
applied and adjusted for best outcome, additional image
enhanc...
4. Gonzalez, R. C., and Wintz, P., Digital Image Processing.
Addison-Wesley, Reading, MA, 1987.
5. Gonzalez, R. C., and Wo...
2
Adaptive Image Filtering
Carl-Fredrik Westin
Ron Kikinis
Harvard Medical School
Hans Knutsson
LinkoÈping University
1 In...
latter case. A multidimensional sinusoidal function can be
written as
f ˆ cos…xT
^e†; …1†
where x is the spatial position ...
2.2 Filtering
Linear ®ltering of a signal can be seen as a controlled scaling of
the signal components in the frequency do...
g ˆ 1, the ®lter is the identity map, flp ‡ fhp ˆ flp
‡…f À flp† ˆ f , and the output image equals the input image.
For g4...
are two main categories of such adaptive ®lters, ®lters for image
enhancement and ®lters for image restoration. The two
ca...
A random process n…x† is called a white noise process if
Rnn…s† ˆ s2
nd…s†: …17†
From Eq. (16), the power spectrum of a wh...
signal variance. A local mean operator can be implemented by
a normalized lowpass ®lter where the support region of the
®l...
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053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
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053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
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053 handbook of medical imaging processing and analysis   isaac bankman
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053 handbook of medical imaging processing and analysis   isaac bankman
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053 handbook of medical imaging processing and analysis   isaac bankman
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053 handbook of medical imaging processing and analysis   isaac bankman
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053 handbook of medical imaging processing and analysis   isaac bankman
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053 handbook of medical imaging processing and analysis   isaac bankman
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053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
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053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
053 handbook of medical imaging processing and analysis   isaac bankman
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