Foreleser Introduction Per Henrik Hogstad Mathematics Statistics Physics

Foreleser

Introduction 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 + Test Wavelets/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/Speech recognition … - Image Processing - Astronomy/Optics/Nuclear Physics - Seismologi - Diff. equations/Discontinuity

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)

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 Fourier Wavelet

The Norwegian Radiumhospital Mammography Diameter Relative contrast Number of microcalcifications

The Norwegian Radiumhospital Mammography - Mexican Hat - 2 Dim

The Norwegian Radiumhospital Mammography

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

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

Par. Abel

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