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MatRICMatRIC
Hjertelig takk for invitasjontil
Høgskolen i Gjøvik
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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)
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MatRICMatRIC
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MatRICMatRIC
Video LessonStreamingVideo SimulationInteractive SimulationExcercisesApplications
User GroupsMathematicsTeacher EducationMechatronicElectromagnetismICTMobile CommunicationEconomyMedicine…
Modeling Simulation Evaluation
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MathematicsMathematics
List Understanding
Problems Technology EnthusiasmReal World
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MathematicsComputational MathematicsMathematicsComputational 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
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ProjectsProjects
External ProjectsMathematics / Physics / Statistics / ICT
Internal ProjectsSimReal+ (SimReal + SimVideo)
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External ProjectsExternal Projects
SINTEF Unimed Ultrasound in Trondheim
The Norwegian Radiumhospital in Oslo
Sørlandet hospital in Kristiansand / Arendal
Mathematics - Computer Science - Medicine
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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
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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
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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
…
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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)(
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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
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Wavelet TransformMorlet WaveletFourier / Wavelet
Wavelet TransformMorlet WaveletFourier / Wavelet
Fourier
Wavelet
xex x
2ln
2cos)(
2
F[f]
[f]Wψ
f
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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 A RRP T
ECG
MammographySeismic
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The Norwegian RadiumhospitalMammographyMicro-calcifications
The Norwegian RadiumhospitalMammographyMicro-calcifications
DiameterRelative contrastNumber of microcalcifications
Mathematical tranformationof the mammography imaging
Mammographyphantom Phantom information
Transformed image
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Wavelet TransformMammography - VideoWavelet TransformMammography - Video
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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
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Ultrasound Image - Edge detectionSINTEF – Unimed – Ultrasound - TrondheimUltrasound Image - Edge detectionSINTEF – Unimed – Ultrasound - Trondheim
- Ultrasound Images- Egde Detection
- Noise Removal- Egde Sharpening- Edge Detection
Prosthesis
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Internal / External linksLessonsExercises / SolutionsVideo lessons / Streaming
Mastering Physics SimReal+
Subject Resources
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SimReal+ = SimReal + SimVideo
SimReal+
SimReal SimVideo
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SimReal+Interactice Learning Tool in Mathematics / Physics / Statistics / Computer Science Video Lesson / Live Streaming / Video Simulation / Interactive Simulation / Exercise / Applicaction
Video LessonStreamingVideo SimulationInteractive SimulationExerciseApplication
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MathematicsParabel
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Live Streaming
Different Chapters
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Live Streaming
ContentsTime
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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
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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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