Medical Image Processing

assoverwroughtAI and Robotics

Nov 6, 2013 (3 years and 11 months ago)

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Medical Image Processing

Federica Caselli


Department of Civil Engineering
University
of Rome Tor
Vergata

Corso

di

Modellazione

e
Simulazione

di

Sistemi

Fisiologici

Medical Imaging

X
-
Ray

CT

PET/SPECT

Ultrasound

MRI

Digital Imaging!

Medical Image

Processing


Image compression


Image
denoising


Image enhancement


Image segmentation


Image registration


Image fusion

What

kind
?

What

for
?


Image storage, retrieval,
transmission


Telemedicine


Quantitative analysis


Computer aided diagnosis,
surgery, treatment and
follow up

To

name

but

a
few
!

Image analysis software are becoming an essential
component of the medical instrumentation

Two examples

Mammographic

images

enhancement

and
denoising

for

breast

cancer

diagnosis

Delineation

of

target
volume
for

radiotheraphy

in
SPECT/PET

images

Mammographic image enhancement

MASSES

Disease

signs

in
mammograms
:

Shape

Boundary


EARLY DIAGNOSIS IS CRUCIAL FOR IMPROVING PROGNOSIS!

Mammographic image enhancement

26LM

EARLY DIAGNOSIS IS CRUCIAL FOR IMPROVING PROGNOSIS!

Morphology
,
size

(0.1
-

1 mm),
number

and
clusters

In
60
-
80
%

of

breast

cancers

at
hystological

examination

MICROCALCIFICATIONS

INTERPRETING MAMMOGRAMS IS AN EXTREMELY COMPLEX TASK

Disease

signs

in
mammograms
:

Transformed
-
domain processing

T

1)

Transform

Transformed

domain
representation

Image

T
-
1

3)

Inverse
Transform

Enhanced

image

RCC
IMAGE
2)

Transformed
-
domain

processing

Modified

image

in
transformed

domain

E(x)

Transformed
-
domain processing
: signal is processed in a
“suitable” domain. “Suitable” depends on the application

RCC
IMAGE






dt
e
t
f
F
t
i


)
(
)
(
Fourier
-
based processing

0.01
0.012
0.014
0.016
0.018
0.02
-3
-2
-1
0
1
2
3
Output Signal: Time Domain
Time (s)
0.01
0.012
0.014
0.016
0.018
0.02
-3
-2
-1
0
1
2
3
Input Signal: Time Domain
Time (s)
S + N

S: 200 Hz

N: 5000 Hz

0
2000
4000
6000
8000
10000
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Input Signal: Frequency Domain
Frequency (Hz)
Linear
|X
(
ω
)|

LPF

0
2000
4000
6000
8000
10000
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (Hz)
Linear
Filter Frequency Response
|H
(
ω
)|

0
2000
4000
6000
8000
10000
0
0.2
0.4
0.6
0.8
1
1.2
Output Signal: Frequency Domain
Frequency (Hz)
Linear
|Y
(
ω
)|

Is it suitable for
mammographic
image processing?

Fourier
-
based processing

?

Fourier is extremely
powerful for stationary
signals but

No time (or space)
localization

Short
-
Time Fourier Transform








dt
e
u
t
g
t
f
u
STFT
t
i


)
(
)
(
)
,
(
Frequency and time
domain information!

However a
compromise is
necessary...

Short
-
Time Fourier Transform

Short
-
Time Fourier Transform

Narrow window

Time

Frequency

Time

Frequency

Short
-
Time Fourier Transform

Medium window

Time

Frequency

Short
-
Time Fourier Transform

Large window

Once chosen
the

window,
time and frequency
resolution are fixed

Wavelet Transform:

more windows
, with
suitable

time and frequency resolution!

Wavelet Transform

“If you painted a picture with a sky, clouds, trees, and flowers,
you would use a different size brush depending on the size of
the features. Wavelet are like those brushes.”

I. Daubechies

)
(
t

Wavelet (db 10)
Wavelet (db 10)
u

Wavelet scalata
s









s
u
t
s
t
s
u


1
)
(
,
dt
s
u
t
s
t
f
s
u
Wf













1
)
(
)
,
(
Wavelet Transform

Wavelet (db 10)
“If you painted a picture with a sky, clouds, trees, and flowers,
you would use a different size brush depending on the size of
the features. Wavelet are like those brushes.”

I. Daubechies

dt
s
u
t
s
t
f
s
u
Wf













1
)
(
)
,
(
Wavelet Transform

Wavelet (db 10)
“If you painted a picture with a sky, clouds, trees, and flowers,
you would use a different size brush depending on the size of
the features. Wavelet are like those brushes.”

I. Daubechies

dt
s
u
t
s
t
f
s
u
Wf













1
)
(
)
,
(
Wavelet Transform

Wavelet (db 10)
“If you painted a picture with a sky, clouds, trees, and flowers,
you would use a different size brush depending on the size of
the features. Wavelet are like those brushes.”

I. Daubechies

dt
s
u
t
s
t
f
s
u
Wf













1
)
(
)
,
(
Wavelet Transform

Wavelet scalata
“If you painted a picture with a sky, clouds, trees, and flowers,
you would use a different size brush depending on the size of
the features. Wavelet are like those brushes.”

I. Daubechies

dt
s
u
t
s
t
f
s
u
Wf













1
)
(
)
,
(
Wavelet Transform

Wavelet scalata
I. Daubechies

“If you painted a picture with a sky, clouds, trees, and flowers,
you would use a different size brush depending on the size of
the features. Wavelet are like those brushes.”

dt
s
u
t
s
t
f
s
u
Wf













1
)
(
)
,
(
Many type of Wavelet
Transform (WT):
Continuous
WT and
Discrete

WT, each with
several choices for the
mother wavelet.

Moreover,
Discrete
-
Time

Wavelet Transform are
needed for discrete signals

Dyadic Wavelet Transform


(x)
r=1

(x)
r=2

(x)
p+r=1
p+r=2
p+r=3
p+r=4
S.
Mallat

and S.
Zhong
, “
Characterization

of

signals

from

multiscale

edge
”,
IEEE
Transactions

on Pattern
Analysis

and
Machine

Intelligence
, Vol. 14, No. 7, 1992.

Implementation

Decomposition

Discrete
-
time

transform

Algorithme à trous

Higher

scales

G
(2

)

H
(2

)

d
2

a
2

a
o

G
(

)

H
(

)

d
1

a
1

G
(4

)

H
(4

)

a
3

d
3

Wavelet (db 10)
Wavelet scalata
Wavelet scalata
Implementation

G
(

)

H
(

)

G
(2

)

H
(2

)

G
(4

)

H
(4

)

Decomposition

a
o

d
1

a
1

d
2

a
2

K
(4

)

H
(4

)

K
(

)

H
(

)

K
(2

)

H
(2

)

Reconstruction

a
2

a
1

a
o

Algorithme à trous

d
3

a
3

Higher

scales

Discrete
-
time

transform

Filters

0
0.5
1
1.5
2
2.5
3
-20
-10
0
10
G
omega
Ampiezza (dB)
0
0.5
1
1.5
2
2.5
3
80
100
120
140
160
180
omega
Fase (gradi)
0
0.5
1
1.5
2
2.5
3
-100
-50
0
H
omega
Ampiezza (dB)
0
0.5
1
1.5
2
2.5
3
0
20
40
60
80
100
omega
Fase (gradi)
G

Gradient

filter

r
= 1

Filters

0
0.5
1
1.5
2
2.5
3
-40
-20
0
20
G
omega
Ampiezza (dB)
0
0.5
1
1.5
2
2.5
3
100
150
200
250
omega
Fase (gradi)
0
0.5
1
1.5
2
2.5
3
-80
-60
-40
-20
0
H
omega
Ampiezza (dB)
0
0.5
1
1.5
2
2.5
3
-50
0
50
omega
Fase (gradi)
G

Laplacian

filter

r
= 2

1D Transform

50
100
150
200
250
300
350
-1
0
1
Gradiente
50
100
150
200
250
300
350
-0.5
0
0.5
50
100
150
200
250
300
350
-0.5
0
0.5
50
100
150
200
250
300
350
-0.5
0
0.5
50
100
150
200
250
300
350
-0.5
0
0.5
Laplaciano
50
100
150
200
250
300
350
-0.5
0
0.5
50
100
150
200
250
300
350
-0.5
0
0.5
50
100
150
200
250
300
350
-0.5
0
0.5
1
2
3
4
GRADIENTE

LAPLACIANO

Signal

Detail

coefficients

Scale

Denoising

100
200
300
400
500
600
700
800
900
-6
-4
-2
0
2
4
6
100
200
300
400
500
600
700
800
900
-4
-3
-2
-1
0
1
2
3
4
100
200
300
400
500
600
700
800
900
-4
-3
-2
-1
0
1
2
3
4
W

W
-
1

outlier

100
200
300
400
500
600
700
800
900
-2
-1
0
1
2
3
4
5
6
7
8
Segnale
rumoroso

100
200
300
400
500
600
700
800
900
-2
-1
0
1
2
3
4
5
6
7
8
Segnale ricostruito

Wavelet
Thresholding

-10
-8
-6
-4
-2
0
2
4
6
8
10
-10
-8
-6
-4
-2
0
2
4
6
8
10
funzione soglia netta (hard thresholding)
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10
-8
-6
-4
-2
0
2
4
6
8
10
funzione soglia dolce (soft thresholding)
Hard
thresholding

Soft
thresholding

Key
issue
:
thresholds

selection

d
v
1

G
(

y
)

G
(

x
)

H
(

x
)

H
(

y
)

G
(2

y
)

G
(2

x
)

H
(2

x
)

H
(2

y
)

H
(2

x
)

H
(2

y
)

L
(2

x
)

K
(2

y
)

K
(2

x
)

L
(2

y
)

H
(

x
)

H
(

y
)

L
(

x
)

K
(

y
)

K
(

x
)

L
(

y
)

Decomposition

Reconstruction

a
o

a
o

d
o
1

d
v
2

d
o
2

a
1

a
2

a
1

Algorithme à trous

Implementation

Discrete
-
time

transform

2D Transform

2D Transform

DDSM

5491 x 2761

12 bpp

Resolution
:
43.5

m

* University of South Florida,
http://marathon.csee.usf.edu/Mammography/Database.html

ROI 1024 x 1024

4.45 cm

Masses

2

1

3

4

d
v

d
o

m

Scale

Microcalcifications

2

1

3

4

d
v

d
o

m

W

1)

Decomposition

Wavelet
coefficients

Image

RCC
IMAGE
W
-
1

3)

Reconstruction

Enhanced

image

RCC
IMAGE
Enhancing

vertical

features

Linear
enhancement

Varying

the
gain

G=8

G=20

2)

Enhancement

Modified

coefficients

E(x)

Extremely

simple

and
powerful

tool

for

signal

prosessing
.
Many

many

applications
!

Wavelet
-
based

signal processing

Wavelet
-
based

signal processing

Key
issue
:
operator

and
thresholds

selection

Mammograms

have

low
contrast

Must

be

adaptive

and
automatic

-10
-8
-6
-4
-2
0
2
4
6
8
10
-25
-20
-15
-10
-5
0
5
10
15
20
25
G

E(x)

Saturation

region

Risk

region

T1

Amplification

region

T2