Hovedprojekt våren 2004 Bruk av Wavelets (en relativt ny matematisk metode) innen medisinsk bildebehandling.

Presentasjon om: "Hovedprojekt våren 2004 Bruk av Wavelets (en relativt ny matematisk metode) innen medisinsk bildebehandling."— Utskrift av presentasjonen:

1 Hovedprojekt våren 2004 Bruk av Wavelets (en relativt ny matematisk metode) innen medisinsk bildebehandling

2 Wavelets - Fagside http://fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htm

3 Prosjekter våren 2004 Matematisk behandling av medisinsk bilde-informasjon Ubegrenset sett av oppgaver av alle vanskelighetsgrader (fra ingen matematikk til avansert matematikk) - Bruk av Wavelets til å bestemme blodårekanter fra ultralydbilder. Oppdragsgiver: SINTEF Unimed Ultralyd i Trondheim. - Bruk av Wavelets til å bestemme brystkreftsvulster på tidlig stadium. Oppdragsgiver: Det Norske Radiumhospital i Oslo (DNR). - Bruk av Wavelets til å bestemme benmasse i kroppen. Oppdragsgiver: Sørlandet Sykehus i Kristiansand. - Bruk av Wavelets til å bestemme blodåretykkelse i lever. Oppdragsgiver: Sørlandet Sykehus i Kristiansand. - Bruk av bl.a. Wavelets innen diagnostikk vha IR. Oppdragsgiver: Sørlandet Sykehus i Arendal.

4 Tittel - Eksempel på oppgavedefinisjon DNR

5 Internasjonalt samarbeid Resterende sider (på engelsk) er utarbeidet i forbindelse med en invitasjon jeg fikk til en internasjonal matematikk-konferanse i Baltikum høsten 2003 for å holde foredrag om mitt arbeid med bruk av Wavelets (en relativt ny matematisk metode) innen matematisk behandling av medisinsk bildeinformsjon.

6 IntroductionIntroduction Per Henrik Hogstad Associate Professor Agder University College Faculty of Engineering and Science Dept of Computer Science Grooseveien 36, N-4876 Grimstad, Norway Telephone: +47 37253285Email: Per.Hogstad@hia.no

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8 IntroductionIntroduction Per Henrik Hogstad -Mathematics -Statistics -Physics(Main subject: Theoretical Nuclear Physics) -Computer Science -Programming / Objectorienting -Algorithms and Datastructures -Databases -Digital Image Processing -Supervisor Master Thesis -Research -PHH:Mathem of Wavelets + Computer Application Wavelets/Medicine -Students:Application + TestWavelets/Medicine

9 ResearchResearch SINTEF Unimed Ultrasound in Trondheim The Norwegian Radiumhospital in Oslo Sørlandet hospitalin Kristiansand / Arendal Mathematics - Computer Science - Medicine

10 Mathematical Image Operation - Application

11 Wavelets New mathematical method with many interesting applications Divide a function into parts with frequency and time/position information Signal Processing-Image Processing-Astronomy/Optics/Nuclear Physics Image/Speech recognition-Seismologi-Diff.equations/Discontinuity …

12 Definition of The Continuous Wavelet Transform CWT The continuous-time wavelet transform (CWT) of f(x) with respect to a wavelet  (x): L 2 (R)

13 Fourier-transformation of a square wave f(x) square wave (T=2) N=2 N=10 N=1

14 Fourier transformation

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18 CWT - Time and frequency localization Time Frequency Small a: CWT resolve events closely spaced in time. Large a: CWT resolve events closely spaced in frequency. CWT provides better frequency resolution in the lower end of the frequency spectrum. Wavelet a natural tool in the analysis of signals in which rapidly varying high-frequency components are superimposed on slowly varying low-frequency components (seismic signals, music compositions, pictures…).

19 Fourier - Wavelet t  a=1/2 a=1 a=2  t Signal Time Inf Fourier Freq Inf Wavelet Time Inf Freq Inf

20 Filtering / Compression Data compression Remove low W-values Lowpass-filtering Replace W-values by 0 for low a-values Highpass-filtering Replace W-values by 0 for high a-values

21 Wavelet Transform Morlet Wavelet Fourier/Wavelet Fourier Wavelet

22 Wavelet Transform Morlet Wavelet Fourier/Wavelet Fourier Wavelet

23 Wavelet Transform Morlet Wavelet - Visible Oscillation

24 Wavelet Transform Morlet Wavelet - Non-visible Oscillation [1/2]

25 Wavelet Transform Morlet Wavelet - Non-visible Oscillation [2/2]

26 Matcad Program Wavelet Transform

27 CWT - DWT CWT DWT Binary dilation Dyadic translation Dyadic Wavelets

28 Analysis /Synthesis Example J=5 Num of Samples: 2 J = 32

29 Analysis Synthesis J=5 Sampling: 2 5 = 32 j=4j=5j=3j=2j=1j=0

30 Discrete Wavelet-transformation

31 Compress 1:50 JPEGWavelet Original

32 Research The Norwegian Radiumhospital in Oslo -Control of the Linear Accelerator -Databases (patient/employee/activity) -Computations of patientpositions -Mathematical computations of medical image information -Different imageformat (bmp, dicom, …) -Noise Removal -Graylevel manipulation (Histogram, …) -Convolution, Gradientcomputation -Multilayer images -Transformations (Fourier, Wavelet, …) -Mammography -... Wavelet

33 The Norwegian Radiumhospital Mammography Diameter Relative contrast Number of microcalcifications

34 The Norwegian Radiumhospital Mammography - Mexican Hat - 2 Dim

35 The Norwegian Radiumhospital Mammography

36 Arthritis Measure of bone Morlet External part E/I bone edge

37 Ultrasound Image - Edge detection SINTEF – Unimed – Ultrasound - Trondheim -Ultrasound Images -Egde Detection -Noise Removal -Egde Sharpening -Edge Detection

38 Edge Detection Convolution

39 Edge detection Wavelet Mexican Hat

40 Edge Detection Wavelet - Scale Energy Wavelet Transform Inv Wavelet Transform Wavelet scale dependent spectrum Energy of the signal A measure of the distribution of energy of the signal f(x) as a function of scale.

41 Edge detection Wavelet - Max Energy Scale

42 Edge detection Wavelet - Different Edges

43 Noise Removal Thresholding HardSoftSemi-Soft

44 Noise Removal Syntetic Image 45 Wavelets - 500.000 test Original Original+ point spread function + white gaussian noise

45 Noise Removal Syntetic Image

46 Noise Removal Ultrasound Image Original Semi-soft Soft

47 Edge sharpening

48 Edge detection

49 Scalogram

50 Edge detection Scalogram

51 Edge detection

52 End