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

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

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

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

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

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, ...)

The Norwegian Radiumhospital Mammography Micro-calcifications Fourier Transformation

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

Wavelet Transform Morlet Wavelet Fourier / Wavelet

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

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

Wavelet Transform Mammography - Video

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

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

END