1. Mathematics - ICT - Medicine1

2. Per Henrik Hogstad Presentation University of Agder - 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)

3. Mathematics Bachelor / Master
Fourier / Wavelets
Transformation Theory
Vector Field Vector Calculus
Linear Algebra Vector Space
Matrix
Derivation / Integration
Trigonometry
Vector
Algebra
Basic Mathematics
University 3

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

5. 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
Studier av svingninger (spesielt resonans)
for å hindre at f.eks. bruer kollapser under påvirkning av vindkast. 5

6. Comments / Results Survey Exam - Physics Comments from the students
- 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.

7. 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)

8. Mathematics Parabel Studier av svingninger (spesielt resonans)
for å hindre at f.eks. bruer kollapser under påvirkning av vindkast. 8

9. SimReal+ Calculator - Graph - Function Analysis - Built in Function
Studier av svingninger (spesielt resonans)
for å hindre at f.eks. bruer kollapser under påvirkning av vindkast.

10. SimReal+ Calculator - Regression Analysis
Studier av svingninger (spesielt resonans)
for å hindre at f.eks. bruer kollapser under påvirkning av vindkast.

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

12. Mathematical Applications12

13. 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

14. 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

15. 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

16. Mathematical Transformation of Medical Images

17. Detector
Metal Detector
Mathematics

18. Image Transformation

19. Transformation
Car Repair
Hospital
Home

20. Transformation Computing - Addition
Room 1
Room 2 4 + 16 = 20 2 + 8 = 10
Transformation

21. Transformation Computing - Logarithm
Rom 1 y
Rom 2 x 8 * 32 =
256 3 + 5 = 8
Transformasjon

22. Music - Digital Ren tone Reell tone Digitalisering Tabell
Analog
Digital
Ren tone
Reell tone
Digitalisering Tabell
FourierTransform Sammensetn av rene toner
Integrasjon
Derivasjon

23. Transformation Theory
F(u) = T[f(x)]
Transformasjon
f(x)
F(u)
Room 1
Room 2
f(x) = T-1(F(u))

24. Transformation Theory
Integral Transformation
F(…) = T[f(…)]
f(…)
F(…)
Room 1
Room 2
f(…) = T-1(F(…))

25. Transformation Theory
Integral Transformation
Wavelet Laplace Fourier
Wavelet
Laplace
f(…)
F(…)
Fourier

26. Fourier Transformation Fourier Serie

27. Analog - Digital Fourier Transformation

28. Transformation Theory
T[f(x)]
f(x)
F(a,b)
T-1[F(a,b)] b x a

29. Wavelet Transform Morlet Wavelet - Non-visible Oscillation

30. 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, ...)

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

32. Wavelet Transform Morlet Wavelet Fourier / Wavelet

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

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

35. Wavelet Transform Mammography - Video

36. 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

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

38. Ultrasound 38

39. Doppler-effekt Lytter L beveger seg mot / fra lyd-kilden S
samtidig som
S også beveger seg.

40. Svevning To lyd-kilder med litt avvikende frekvens gir opphav til en
resultant-bølge som inneholder
varierende amplitude.
Frekvensen som
resultant-amplituden
varierer med kalles
svevnings-frekvensen.
Svevningsfrekvensen
er differensen mellom enkelt-frekvensene

41. Svevning Piano To stk piano spiller samme a-tone med frekvens 440 Hz.
Ved å la det ene pianoet endre
sin a-tone-frekvens til henholdvis
441 Hz, 442 Hz og 443 Hz,
hører vi en svevningstone
med økende frekvens.
Svevningstonens frekvens
er lik differensen mellom frekvensene
til de to pianofrekvensene.

42. Microcosmos Different parts of microcosmos in our daily life
Mobile
phone
Electricity TV
Medicine
Magnetic resonance
New energy
Induction
Semiconductor 42

43. Microcosmos LHC - Large Hadron Collider43

44. MRI Magnetic Resonance Imaging44

45. PET Emission of Positrons
PET radiotracer (18F fluorodeoxyglucose (FDG))
+ radioactive fluorine.
Natural decay includes emmission of positrons
that reach with electrons (annihilaation) in the body
produces energy in the form of a pair of photons.
The PET skanner, which is able to detect these photons,
creates three-dimensional images that show
how the FDG is distributed in the area of the body.
Areas where a large amount of FDG accumulates,
called ’hot spots’ because they appear more intense
than surrounding tissue, indicate that a high level of
chemical activity or metabolism is occuring there. 45

46. Infrared camera - Wavelets46

47. Calculator in Medicine Safety Calculator47

48. Heart Circulation 48

49. Surgery Simulator 49

50. END