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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
dtetfF ti )()(
Fourier-based processing
0.01 0.012 0.014 0.016 0.018 0.02-3
-2
-1
0
1
2
3Output Signal: Time Domain
Time (s)0.01 0.012 0.014 0.016 0.018 0.02-3
-2
-1
0
1
2
3Input Signal: Time Domain
Time (s)
S + NS: 200 HzN: 5000 Hz
0 2000 4000 6000 8000 100000
0.2
0.4
0.6
0.8
1
1.2
1.4Input Signal: Frequency Domain
Frequency (Hz)
Lin
ea
r
|X(ω)|
LPF
0 2000 4000 6000 8000 100000
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (Hz)
Line
ar
Filter Frequency Response
|H(ω)|
0 2000 4000 6000 8000 100000
0.2
0.4
0.6
0.8
1
1.2
Output Signal: Frequency Domain
Frequency (Hz)
Lin
ea
r
|Y(ω)|
Is it suitable for mammographic
image processing?
Fourier-based processing
?
Fourier is extremely powerful for stationary
signals butNo time (or space)
localization
Short-Time Fourier Transform
dteutgtfuSTFT ti )()(),(
Frequency and time domain information!
However a compromise is
necessary...
Short-Time Fourier Transform
Short-Time Fourier Transform
Narrow window
Time
Freq
uenc
y
Time
Freq
uenc
yShort-Time Fourier Transform
Medium window
Time
Freq
uenc
yShort-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
)(tWavelet (db 10) Wavelet (db 10)
u
Wavelet scalata
s
s
ut
stsu 1)(,
dts
ut
stfsuWf
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
dts
ut
stfsuWf
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
dts
ut
stfsuWf
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
dts
ut
stfsuWf
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
dts
ut
stfsuWf
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.”
dts
ut
stfsuWf
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)
d2
a2
ao
G()
H()
d1
a1
G(4)
H(4)
a3
d3
Wavelet (db 10)
Wavelet scalata
Wavelet scalata
Implementation
G()
H()
G(2)
H(2)
G(4)
H(4)
Decomposition
ao
d1
a1
d2
a2
K(4)
H(4)
K()
H()
K(2)
H(2)
Reconstruction
a2
a1
ao
Algorithme à trous
d3
a3
Higher scales
Discrete-time transform
Filters
0 0.5 1 1.5 2 2.5 3-20
-10
0
10G
omega
Am
pie
zza
(d
B)
0 0.5 1 1.5 2 2.5 380
100
120
140
160
180
omega
Fa
se (
gra
di)
0 0.5 1 1.5 2 2.5 3-100
-50
0H
omega
Am
pie
zza
(d
B)
0 0.5 1 1.5 2 2.5 30
20
40
60
80
100
omega
Fa
se (
gra
di)
G Gradient filter
r = 1
Filters
0 0.5 1 1.5 2 2.5 3-40
-20
0
20G
omega
Am
pie
zza
(d
B)
0 0.5 1 1.5 2 2.5 3
100
150
200
250
omega
Fa
se (
gra
di)
0 0.5 1 1.5 2 2.5 3-80
-60
-40
-20
0H
omega
Am
pie
zza
(d
B)
0 0.5 1 1.5 2 2.5 3
-50
0
50
omega
Fa
se (
gra
di)
G Laplacian filter
r = 2
1D Transform
50 100 150 200 250 300 350-1
0
1Gradiente
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
0.5Laplaciano
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
outlier100 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
10funzione 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
10funzione soglia dolce (soft thresholding)
Hard thresholding Soft thresholding
Key issue: thresholds selection
dv1
G(y)
G(x)
H(x) H(y) G(2y)
G(2x)
H(2x) H(2y) H(2x) H(2y)
L(2x) K(2y)
K(2x) L(2y)
H(x) H(y)
L(x) K(y)
K(x) L(y)
Decomposition Reconstruction
ao ao
do1
dv2
do2
a1
a2
a1
Algorithme à trous
Implementation
Discrete-time transform
2D Transform
2D Transform
DDSM
5491 x 276112 bppResolution: 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
dv do m
Scale
Microcalcifications
2
1
3
4
dv do m
W
1)
Decomposition
Wavelet coefficients
Image
RCC
IMAGE
W-1
3)
Reconstruction
Enhanced image
RCC
IMAGE
Enhancing vertical features
Linear enhancement
Varying the gainG=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