MatRIC Hjertelig takk for invitasjon til Høgskolen i Gjøvik

Presentation 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 -Mathematics of Wavelets + Computer Application Wavelets/Medicine -SimReal+(SimReal + SimVideo)

MatRIC

Video Lesson Streaming Video Simulation Interactive Simulation Excercises Applications User Groups Mathematics Teacher Education Mechatronic Electromagnetism ICT Mobile Communication Economy Medicine … Modeling  Simulation  Evaluation

Mathematics List Understanding Problems Technology Enthusiasm Real World

Mathematics Computational Mathematics Development and analysis of mathematical models Numerical techniques Method oriented software Science, technology, biology, medicine, … Programming (C, C++, Java, Actionscript, Python, Matlab, Mathematica, … Template

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

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

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 Computer Linear Accelerator

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 …

N=2 N=10 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): L 2 (R )

Wavelet Transform Morlet Wavelet Fourier / Wavelet Fourier Wavelet

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

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

Wavelet Transform Mammography - Video

Osteroporosis External part E/I bone edge Morlet

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

Internal / External links Lessons Exercises / Solutions Video lessons / Streaming Mastering PhysicsSimReal+ Subject Resources

SimReal+ = SimReal + SimVideo SimReal+ SimReal SimVideo

SimReal+ Interactice Learning Tool in Mathematics / Physics / Statistics / Computer Science Video Lesson / Live Streaming / Video Simulation / Interactive Simulation / Exercise / Applicaction Video Lesson Streaming Video Simulation Interactive Simulation Exercise Application

Mathematics Parabel

Live Streaming Different Chapters

Live Streaming Contents Time

Comments / Results - A great supplement, and very good academic contents - A great way to repeat past lectures - I wish this could be used in all my courses - Enables me to get a better understanding of the subject - Extremely impressive that you have spent all this time to create such a fantastic tool. Survey Exam - Physics Comments from the students

SimReal+ - Research Brekke: LICE conference London International Conference on Education Brekke/Hogstad:Journal New teaching methods Using computer technology in physics and mathematics Elira Curri:Master Thesis (UiA, Albania) Ninni Marie Hogstad:Master Thesis (UiA)

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