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Presentation transcript:

Foreleser

Per Henrik Hogstad Introduction - 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 + Test Wavelets/Medicine

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

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

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, ...)

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

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

Fourier transformation

Wavelet Transform Morlet Wavelet Fourier/Wavelet

The Norwegian Radiumhospital Mammography Diameter Relative contrast Number of microcalcifications

The Norwegian Radiumhospital Mammography - Mexican Hat - 2 Dim

The Norwegian Radiumhospital Mammography

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

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

ParAbel

End

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