PresentationPresentation

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)

ProjectsProjects

External ProjectsMathematics / Physics / Statistics / ICT

Internal ProjectsSimReal+ (SimReal + SimVideo

External ProjectsExternal Projects

SINTEF Unimed Ultrasound in Trondheim

The Norwegian Radiumhospital in Oslo

Sørlandet hospital in Kristiansand / Arendal

Mathematics - Computer Science - Medicine

The Norwegian Radiumhospital in OsloThe 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 OsloLinear AcceleratorThe Norwegian Radiumhospital in OsloLinear Accelerator

- Control of the Linear Accelerator- Databases (patient/employee/activity)- Computations of patient positions

PatientDatabase

Computer

Linear Accelerator

WaveletsWaveletsNew New mathematical methodmathematical method with many interesting with many interesting applicationsapplications

WaveletsWaveletsNew New mathematical methodmathematical method with many interesting with many interesting applicationsapplications

Divide a function into parts with frequency and time/position information

Signal Processing - Image Processing - Astronomy/Optics/Nuclear PhysicsImage/Speech recognition - Seismologi - Diff.equations/Discontinuity

…

N=2

N=10

The Norwegian RadiumhospitalMammographyMicro-calcificationsFourier Transformation

The Norwegian RadiumhospitalMammographyMicro-calcificationsFourier Transformation

1

1

0

])12sin[(12

14

2sin

2cos

2)(

n

nnn

xnn

T

xnb

T

xna

axf

N

n

xnn

xf1

])12sin[(12

14)(

Definition of The Continuous Wavelet Transform CWTDefinition of The Continuous Wavelet Transform CWT

0 , )(, 2 aRbaRLf

The continuous-time wavelet transform (CWT)of f(x) with respect to a wavelet (x):

dxxfxfbafWbaW baba )()(),]([),( ,,

a

bxaxba

2/1, || )(

dadbxbaWaC

xf ba )(),(11

)( ,2

][ fW),]([ bafW

)(xf

)(xL2(R ))(0,1 x )(0,2 x )(1,2 x

Wavelet TransformMorlet WaveletFourier / Wavelet

Wavelet TransformMorlet WaveletFourier / Wavelet

Fourier

Wavelet

xex x

2ln

2cos)(

2

F[f]

[f]Wψ

f

1σ

2a 1a yx

The Norwegian RadiumhospitalMammographyMicro-calcificationsWavelet Transformation - Mexican Hat

The Norwegian RadiumhospitalMammographyMicro-calcificationsWavelet Transformation - Mexican Hat

2

2

2σ

x2

2π1 e

σ

x2Ψ(x)

brPbrT

a

T

y

brPbr

2

1

a2π

1b,a

e2)r(Ψx

y

xr

y

x

b

bb

y

x

a

aa

cosθsin θ

sin θcosθR

2

y

2x

a

10

0a

1

A ARRP T

ECG

MammographySeismic

The Norwegian RadiumhospitalMammographyMicro-calcifications

The Norwegian RadiumhospitalMammographyMicro-calcifications

DiameterRelative contrastNumber of microcalcifications

Mathematical tranformationof the mammography imaging

Mammographyphantom Phantom information

Transformed image

Wavelet TransformMammography - VideoWavelet TransformMammography - Video

OsteroporosisOsteroporosis

External part External part

[f]Wa

1ψ2

E/I bone edge E/I bone edge

a

bxaxba 2/1

, || )(

xex x

2ln

2cos)(

2

Morlet

Ultrasound Image - Edge detectionSINTEF – Unimed – Ultrasound - TrondheimUltrasound Image - Edge detectionSINTEF – Unimed – Ultrasound - Trondheim

- Ultrasound Images- Egde Detection

- Noise Removal- Egde Sharpening- Edge Detection

Prosthesis

Internal / External linksLessonsExercises / SolutionsVideo lessons / Streaming

Mastering Physics SimReal+

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 LessonStreamingVideo SimulationInteractive SimulationExerciseApplication

MathematicsParabel

Live Streaming

Different Chapters

Live Streaming

ContentsTime

Comments / ResultsComments / 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+ - ResearchSimReal+ - Research

Brekke : LICE conferenceLondon International Conferenceon Education

Brekke/Hogstad : JournalNew teaching methodsUsing computer technologyin physics and mathematics

Elira Curri : Master Thesis (UiA, Albania)Ninni Marie Hogstad : Master Thesis (UiA)

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