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MatRICMatRIC
Hjertelig takk for invitasjontil
Høgskolen i Gjøvik
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)
MatRICMatRIC
MatRICMatRIC
Video LessonStreamingVideo SimulationInteractive SimulationExcercisesApplications
User GroupsMathematicsTeacher EducationMechatronicElectromagnetismICTMobile CommunicationEconomyMedicine…
Modeling Simulation Evaluation
MathematicsMathematics
List Understanding
Problems Technology EnthusiasmReal World
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
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 A RRP 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)
ENDEND