Per Henrik Hogstad Presentation - Mathematics - Statistics

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1 Per Henrik Hogstad Presentation - Mathematics - Statistics
- Physics (Main subject: Theoretical Nuclear Physics) - Computer Science - Programming / Objectorienting - Algorithms and Datastructures - Databases - Digital Image Processing - Supervisor Master Thesis Research - Mathematics of Wavelets + Computer Application Wavelets/Medicine - SimReal

2 Projects External Projects Internal Projects
Mathematics / Physics / Statistics / ICT Internal Projects SimReal+ (SimReal + SimVideo

3 Mathematics - Computer Science - Medicine
External Projects Mathematics - Computer Science - Medicine SINTEF Unimed Ultrasound in Trondheim The Norwegian Radiumhospital in Oslo Sørlandet hospital in Kristiansand / Arendal

4 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 The Norwegian Radiumhospital in Oslo Linear Accelerator
- Control of the Linear Accelerator - Databases (patient/employee/activity) - Computations of patient positions Patient Database Linear Accelerator Computer

6 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 … Wavelets er en relativt ny matematisk metode (har skutt fart først på 80- og 90-tallet). Wavelets har etter hvert fått mange anvendelsesområder. Navnet Wavelets benyttes ofte (slik som her) som navn på en bestemt matematisk metode. Imidlertid bør her nevnes at Wavelets også (mer korrekt) benyttes som navn på en spesiell gruppe såkalte basisfunksjoner i forbindelse med transformasjon av funksjoner. På bildet vises noen slike anvendelses-områder: - Detaljskalering av en datakilde (signal, bilde, ...) - Medisinsk bildebehandling (terskling og segmentering for bl.a. å fremheve detaljer) - Wavelets-tranformering av bilde (for komprimering eller gjenfinning av detaljer) - Seismologi (forutsi jordskjelv, studere forhold under havbunnen (lete etter olje, ...), ...) - ECG-diagram (bestemme eventuelle avvik, ...) - Røntgenbilde (bestemme eventuelle svulster, ...)

7 The Norwegian Radiumhospital Mammography Micro-calcifications Fourier Transformation

8 Definition of The Continuous Wavelet Transform CWT
The continuous-time wavelet transform (CWT) of f(x) with respect to a wavelet (x): L2(R )

9 Wavelet Transform Morlet Wavelet Fourier / Wavelet

10 Mammography The Norwegian Radiumhospital Mammography Micro-calcifications Wavelet Transformation Mexican Hat Seismic ECG

11 The Norwegian Radiumhospital Mammography Micro-calcifications
phantom Phantom information Diameter Relative contrast Number of microcalcifications Mathematical tranformation of the mammography imaging Transformed image

12 Wavelet Transform Mammography - Video

13 Osteroporosis External part External part E/I bone edge E/I bone edge
Morlet Osteroporosis External part External part E/I bone edge E/I bone edge

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

15 END