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ForeleserForeleser. IntroductionIntroduction Per Henrik Hogstad -Mathematics -Statistics -Physics(Main subject: Theoretical Nuclear Physics) -Computer.

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Presentation on theme: "ForeleserForeleser. IntroductionIntroduction Per Henrik Hogstad -Mathematics -Statistics -Physics(Main subject: Theoretical Nuclear Physics) -Computer."— Presentation transcript:

1 ForeleserForeleser

2 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

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

4 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

5 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 …

6 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)

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

8 Fourier transformation

9 Wavelet Transform Morlet Wavelet Fourier/Wavelet Fourier Wavelet

10 The Norwegian Radiumhospital Mammography Diameter Relative contrast Number of microcalcifications

11 The Norwegian Radiumhospital Mammography - Mexican Hat - 2 Dim

12 The Norwegian Radiumhospital Mammography

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

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

15 ParAbel

16 End


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