medical image processing federica caselli department of civil engineering university of rome tor...

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...


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 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

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

medical image processing federica caselli department of civil engineering university of rome tor...

Documents

different size brush

suitable time

wavelet transformif

mammographic image processing

time domain information

image storage

suitable domain

fixedwavelet transform