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Wavelets Medical Image Processing Projects

Wavelets Medical Image Processing Projects. Per Henrik Hogstad. - Mathematics - Statistics - Physics (Main subject: Theoretical Nuclear Physics) - Computer Science - Programming / Objectorienting - Algorithms and Datastructures - Databases - Digital Image Processing

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Wavelets Medical Image Processing Projects

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  1. WaveletsMedical Image ProcessingProjects

  2. Per HenrikHogstad - Mathematics - Statistics - Physics (Main subject: Theoretical Nuclear Physics) - Computer Science - Programming / Objectorienting - Algorithms and Datastructures - Databases - Digital Image Processing - Supervisor Master Thesis - Research - PHH : Mathem of Wavelets + Computer Application Wavelets/Medicine - Students : Application + Test Wavelets/Medicine

  3. Research Mathematics - Computer Science - Medicine SINTEF Unimed Ultrasound in Trondheim The Norwegian Radiumhospital in Oslo Sørlandet Hospital in Kristiansand / Arendal

  4. MathematicsComputer ScienceMedicine SINTEF Unimed Ultrasound in Trondheim - Detection of blood vessel in ultra sound image The Norwegian Radiumhospital in Oslo - Linear accelerator - Computing patient position - Databases - Image processing ( Wavelets) Sørlandet Hospital in Kristiansand - Bone thickness - Blood vessel thickness in liver Sørlandet Hospital in Arendal - IR diagnostic

  5. ResearchThe 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

  6. Linear Accelerator Databases Patient Position Image processing DNR

  7. Radiation Theraphy - Patient Position Referance picture Control picture

  8. Digital Image Processing Digital Image Processing Manipulation of images by computer Input Image Computer Output Image Digital Image Processing

  9. Image Tranformation Original Image Tranformed Image

  10. Histogram

  11. Histogram Equalization

  12. Convolution

  13. Fourier-transformation of a square wave f(x) square wave (T=2) N=1 N=2 N=10

  14. Image TransformationFourier Transformation (2-dim)

  15. WaveletsNew 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 …

  16. Interesting applicationsThe subject of Wavelets is expanding at a tremendous rate • Wavelet transform has been perhaps the most exciting development in the last decade to bring together researchers in several different fields: Seismic Geology Signal processing (frequency study, compression, …) Image processing (image compression, video compression, ...) Denoising data Communications Computer science Mathematics Electrical Engineering Quantum Physics Magnetic resonance Musical tones Diagnostic of cancer Economics …

  17. Introduction to Wavelets

  18. Wavelets = Building blocks At the present day it is almost impossible to give a precise definition of wavelets. The research field is growing so fast and novel contributions are made at such a rate that even if one manages to give a definition today, it might be obsolute tomorrow. One, very vague, way of thinking about wavelets could be: Wavelets are building blocks that can quickly decorrelate data. • Wavelets are building blocks for general functions. • Wavelets have space-frequency localization. • Wavelets have fast transform algorithms.

  19. Frequency / Transient signals / Discontinuity Adopting a whole new mindset or perspective in prosessing data Data • Wavelets are mathematical functions that can cut up data into different frequency components, and then study each component with a resolution matched to its scale. • Wavelets have advantages over traditional Fourier methods in analyzing physical situation where the signal is transient or contains discontinuities and sharp spikes.

  20. Wavelets - Different scales

  21. CWT - Time and frequency localization Time Frequency Small a: CWT resolve events closely spaced in time. Large a: CWT resolve events closely spaced in frequency. CWT provides better frequency resolution in the lower end of the frequency spectrum. Wavelet a natural tool in the analysis of signals in which rapidly varying high-frequency components are superimposed on slowly varying low-frequency components (seismic signals, music compositions, pictures…).

  22. Image TranformationDetails Details Image Original Image The rest of the Image

  23. Discrete Wavelet-transformation

  24. Original Compress 1:50 JPEG Wavelet

  25. Analysis /SynthesisExample J=5 Num of Samples: 2J = 32

  26. AnalysisSynthesisJ=5 Sampling: 25 = 32 j=5 j=4 j=3 j=2 j=1 j=0

  27. AnalysisSynthesisJ=5 Sampling: 25 = 32 j=5 j=4 j=3 j=2 j=1 j=0

  28. Filtering / Compression Data compression Remove low W-values Highpass-filtering Lowpass-filtering Replace W-values by 0 for high a-values Replace W-values by 0 for low a-values

  29. Wavelet TransformMorlet WaveletFourier/Wavelet Fourier Wavelet

  30. Wavelet TransformMorlet WaveletFourier/Wavelet Fourier Wavelet

  31. Wavelet TransformMorlet Wavelet - Visible Oscillation

  32. Wavelet TransformMorlet Wavelet - Non-visible Oscillation [1/2]

  33. Wavelet TransformMorlet Wavelet - Non-visible Oscillation [2/2]

  34. WaveletsBasic Knowledge - Informatics - Programming / Object oriented (Java / C++) - Mathematics - Lineær algebra (Vektor Space / Basis Functions / Matrices / … ) - Fourier Analysis - Statistics - Physics

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

  36. Wavelet Transform

  37. Wavelet TransformTumour

  38. The Norwegian RadiumhospitalMammography Diameter Relative contrast Number of microcalcifications

  39. The Norwegian RadiumhospitalMammography - Mexican Hat - 2 Dim

  40. The Norwegian RadiumhospitalMammography

  41. Morlet ArthritisMeasure of bone Krsand External part External part E/I bone edge E/I bone edge

  42. Morlet Thicknessof blood vesselin liver Krsand

  43. Krsand Mexican Hat Thickness

  44. ArendalDiagnostics - IR radiation

  45. Ultrasound Image - Edge detectionSINTEF – Unimed – Ultrasound - Trondheim • Ultrasound Images- Egde Detection- Noise Removal- Egde Sharpening- Edge Detection • - Edge Computation

  46. Ultrasound Image - Edge detectionSINTEF – Unimed – Ultrasound - Trondheim Ultra Sound Image Aorta with Prothesis

  47. Edge DetectionConvolution

  48. Edge detectionWavelet Mexican Hat

  49. Edge detection Scalogram

  50. Edge detectionOne beam

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