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BME1450 – Biomedical Engineering 2002. Basic Image Display and Processing Linear Systems and Imaging Optical Microscopy X-ray Magnetic Resonance Imaging Ultrasound Nuclear Medical Electron Microscopy Scanning Probe Microscopy.

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BME1450 – Biomedical Engineering 2002

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BME1450 – Biomedical Engineering 2002

Basic Image Display and Processing

Linear Systems and Imaging

Optical Microscopy

X-ray

Magnetic Resonance Imaging

Ultrasound

Nuclear Medical

Electron Microscopy

Scanning Probe Microscopy

BME 1450 - 2002


Basic Image Display Greyscale

  • Measurements displayed as colors or shades of gray.

  • Pixels or voxels.

  • Axes unusual

  • Colour maps

BME1450 - 2002


Basic Image DisplayPseudo Colour

  • Max 105 :white

  • Min 0 :black

  • (R, G, B)

  • Contrast

  • Histogram

  • 4x104 :white

  • 2.5x104 :black

BME1450 - 2002


Basic Image DisplayContrast enhanced

  • Note colour bar range 2.5e4 to 4e4.

  • Higher contrast

  • More noise

BME1450 - 2002


Basic Image DisplayMedian Filtered

  • Median Filter

  • Less spatial resolution

BME1450 - 2002


Basic Image DisplayNoise

  • Find the disk objects.

  • 32x32 pixels

  • R = 3 pixels

  • 100 photons /pixels

  • + - 10

  • Poisson

BME1450 - 2002


Basic Image DisplayRose’s Criterion

  • Rose’s hypothesis is that the human will do as well as the best machine when both human and machine are given the same task and a priori information.

  • N equals sum of the pixels in the region where the disk may be.

  • The machine knows average N = NBG if the disk is present and NOB if it is absent.

BME1450 - 2002


Basic Image DisplayMachine Detection

  • N equals sum of the pixels in the region where the disk may be.

  • The machine knows average N = NBG if the disk is present and NOB if it is absent.

  • The machine says "present" if N > (NOB + NBG)/2 and "absent" otherwise.

  • I chose cases for which the machine's probability of false positive is the same.

BME1450 - 2002


Basic Image DisplayEqually Visible?

  • Now R = 7 pixels.

  • Disks have same visibility to the machine.

  • Their contrast is reduced.

  • Are they as easy to spot as the R=3?

BME1450 - 2002


BME1450 – Biomedical Engineering 2002

Basic Image Display and Processing

Linear Systems and Imaging

Optical Microscopy

X-ray

Magnetic Resonance Imaging

Ultrasound

Nuclear Medical

Electron Microscopy

Scanning Probe Microscopy

BME 1450 - 2002


Linear Systems and ImagingLinearity

  • Linear

BME1450 - 2002


Linear Systems and ImagingSpatial Invariance

  • Spatially Invariant

BME1450 - 2002


Linear Systems and ImagingConvolution Integral

The convolution integral

  • h(x,y) is the “point response function”

  • It is the image of a delta function.

  • It is translated by (a,b), weighed by f(a,b) and added to g(x,y).

BME1450 - 2002


Linear Systems and ImagingFourier Theory

  • Fourier Transform

  • Convolution Theorem

  • H is the transfer function of the system

BME1450 - 2002


Fourier Domain = K Space

BME1450 - 2002


Linear Systems and Imaging Effects of filtering

Filter

Width

32 pix

In K space

Of

256x256

BME1450 - 2002


Linear Systems and ImagingSpectral Components

  • Real part of the FFT of pixel Kx,Ky =3

  • Other pixels 0

BME1450 - 2002


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