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)
Projects
External Projects
Internal Projects
Mathematics / Physics / Statistics / ICT
SimReal+ (SimReal + SimVideo
External Projects
Mathematics - Computer Science - Medicine
SINTEF Unimed Ultrasound in Trondheim
The Norwegian Radiumhospital in Oslo
Sørlandet hospital in Kristiansand / Arendal
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
Linear Accelerator
Computer
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
…
The Norwegian Radiumhospital
Mammography
Micro-calcifications
Fourier Transformation
a0  
2 nx
2 nx 
f ( x )     an cos
 bn sin
2 n 1 
T
T 

f ( x) 
4

1
sin[( 2 n  1)x ]

 n 1 2n  1
4 N 1
sin[( 2 n  1) x ]

 n 1 2 n  1
N=2
N=10
f ,   L2 ( R ) a , b  R a  0
Definition of The Continuous Wavelet Transform
CWT
The continuous-time wavelet transform (CWT)
of f(x) with respect to a wavelet (x):

W ( a , b )  W [ f ]( a , b )   a ,b f    a ,b ( x ) f ( x ) dx

1
f ( x) 
C
1
a
2
)  (x )
W ( a , b ) a ,b ( x ) dadb
  
W [ f ]
f (x )
L2(R
 
 xb
 a ,b ( x )  | a |1 / 2  

a


W  [ f ]( a , b )
 1, 0 ( x )
 2,0 ( x )
 2 ,1 ( x )
Wavelet Transform
Morlet Wavelet
Fourier / Wavelet
F[f]
Fourier
f
Wavelet


2
2
 ( x )  e  x cos 
 x 
 ln 2 
Wψ [f]
Mammography
The Norwegian Radiumhospital
Mammography
Micro-calcifications
Wavelet Transformation - Mexican Hat
Ψ(x) 
1
2π

Ψ (r) 

a, b
 x 
r 
 y
 x
2   
  σ 
1
2π a x a y
2

e

Seismic
ECG
x2
 2
2σ

σ 1
 
T  

2  r  b P r  b

 e


1  
r b
2
T P r  b 

  b x   a x 
b  a 
b y 
a y 
cosθ  sin θ 
R

 sin θ cosθ 
 1
a 2
A x
 0



0 

1 
2
a y 
P  R T AR
ax 1
ay  2
The Norwegian Radiumhospital
Mammography
Micro-calcifications
Mammography
phantom
Phantom information
Diameter
Relative contrast
Number of microcalcifications
Mathematical tranformation
of the mammography imaging
Transformed image
Wavelet Transform
Mammography - Video
Morlet
 xb
 a ,b ( x )  | a |1 / 2  

a


Osteroporosis
External part
E/I bone edge


2
2
 ( x )  e  x cos 
 x 
ln 2 

External part
E/I bone edge
1
Wψ [f]
a2
Ultrasound Image - Edge detection
SINTEF – Unimed – Ultrasound - Trondheim
- Ultrasound Images
- Egde Detection
- Noise Removal
- Egde Sharpening
- Edge Detection
Prosthesis
Subject Resources
Internal / External links
Lessons
Exercises / Solutions
Video lessons / Streaming
Mastering Physics
SimReal+
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
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.
SimReal+
Brekke
:
Brekke/Hogstad
:
Elira Curri
:
Ninni Marie Hogstad :
-
Research
LICE conference
London International Conference
on Education
Journal
New teaching methods
Using computer technology
in physics and mathematics
Master Thesis (UiA, Albania)
Master Thesis (UiA)
END