1. Medical Image Processing Federica Caselli Department of Civil Engineering University of Rome Tor Vergata Corso di Modellazione e Simulazione di Sistemi Fisiologici

2. Medical Imaging X-Ray CT PET/SPECT Ultrasound MRI Digital Imaging!

3. 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

4. Two examples Mammographic images enhancement and denoising for breast cancer diagnosis Delineation of target volume for radiotheraphy in SPECT/PET images

5. Mammographic image enhancement MASSES Disease signs in mammograms: ShapeBoundary EARLY DIAGNOSIS IS CRUCIAL FOR IMPROVING PROGNOSIS!

6. Mammographic image enhancement 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:

7. Transformed-domain processing T 1) Transform Transformed domain representation Image T -1 3) Inverse Transform Enhanced 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

8. Fourier-based processing S + N S: 200 Hz N: 5000 Hz |X(ω)| LPF |H(ω)| |Y(ω)| Is it suitable for mammographic image processing?

9. Fourier-based processing ? Fourier is extremely powerful for stationary signals but No time (or space) localization

10. Short-Time Fourier Transform Frequency and time domain information! However a compromise is necessary...

11. Short-Time Fourier Transform

12. Narrow window Time Frequency

13. Time Frequency Short-Time Fourier Transform Medium window

14. 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!

15. 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 u s

16. 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

17. 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

18. 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

19. 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

20. Wavelet Transform 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.” 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

21. Dyadic Wavelet Transform S. Mallat and S. Zhong, “Characterization of signals from multiscale edge”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 7, 1992.

22. Implementation Decomposition Discrete-time transform Algorithme à trous Higher scales G(2  ) H(2  ) d2d2 a2a2 aoao G()G() H()H() d1d1 a1a1 G(4  ) H(4  ) a3a3 d3d3

23. Implementation G()G() H()H() G(2  ) H(2  ) G(4  ) H(4  ) Decomposition aoao d1d1 a1a1 d2d2 a2a2 K(4  ) H(4  ) K()K() H()H() K(2  ) H(2  ) Reconstruction a2a2 a1a1 aoao Algorithme à trous d3d3 a3a3 Higher scales Discrete-time transform

24. Filters G Gradient filter r = 1

25. Filters G Laplacian filter r = 2

26. 1D Transform GRADIENTELAPLACIANO Signal Detail coefficients Scale

27. Denoising W W -1 outlier Segnale rumoroso Segnale ricostruito

28. Wavelet Thresholding Hard thresholdingSoft thresholding Key issue: thresholds selection

29. dv1dv1 G(y)G(y) G(x)G(x) H(x)H(x)H(y)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(x)H(y)H(y) L(x)L(x)K(y)K(y) K(x)K(x)L(y)L(y) DecompositionReconstruction aoao aoao do1do1 dv2dv2 do2do2 a1a1 a2a2 a1a1 Algorithme à trous Implementation Discrete-time transform

30. 2D Transform

32. 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

33. Masses 2 1 3 4 dvdv dodo m Scale

34. Microcalcifications 2 1 3 4 dvdv dodo m

35. W 1) Decomposition Wavelet coefficients Image W -1 3) Reconstruction Enhanced image Enhancing vertical features Linear enhancement Varying the gain G=8G=20 2) Enhancement Modified coefficients E(x) Extremely simple and powerful tool for signal prosessing. Many many applications! Wavelet-based signal processing

36. Key issue: operator and thresholds selection Mammograms have low contrast Must be adaptive and automatic G E(x) Saturation region Risk region T1 Amplification region T2