Transcript Document

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
February 10, 2002
BME 1450 - 2002
Slide # 1
Basic Image Display
Greyscale
 Measurements
displayed as
colors or
shades of gray.
 Pixels or
voxels.
 Axes unusual
 Colour maps
February 10, 2002
BME1450 - 2002
Slide 2
Basic Image Display
Pseudo Colour
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Max 105 :white
Min 0 :black
(R, G, B)
Contrast
Histogram
4x104 :white
2.5x104 :black
February 10, 2002
BME1450 - 2002
Slide 3
Basic Image Display
Contrast enhanced
 Note colour bar
range 2.5e4 to
4e4.
 Higher contrast
 More noise
February 10, 2002
BME1450 - 2002
Slide 4
Basic Image Display
Median Filtered
 Median Filter
 Less spatial resolution
February 10, 2002
BME1450 - 2002
Slide 5
Basic Image Display
Noise
 Find the
disk objects.
 32x32 pixels
 R = 3 pixels
 100 photons
/pixels
 + - 10
 Poisson
February 10, 2002
BME1450 - 2002
Slide 6
Basic Image Display
Rose’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.
February 10, 2002
BME1450 - 2002
Slide 7
Basic Image Display
Machine 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.
February 10, 2002
BME1450 - 2002
Slide 8
Basic Image Display
Equally 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?
February 10, 2002
BME1450 - 2002
Slide 9
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
February 10, 2002
BME 1450 - 2002
Slide # 10
Linear Systems and Imaging
Linearity
 Linear
if
Input
produces
f1(x, y)
and
then
February 10, 2002
Output
g1(x, y)
g2(x, y)
f1(x, y) +
f2(x, y)
BME1450 - 2002
g1(x, y) +
g2(x, y)
Slide 11
Linear Systems and Imaging
Spatial Invariance
 Spatially Invariant
Input
produces
Output
if
f(x, y)
g(x, y)
then
f(x-a, y-b)
f(x-a, y-b)
February 10, 2002
BME1450 - 2002
Slide 12
Linear Systems and Imaging
Convolution 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).
February 10, 2002
BME1450 - 2002
Slide 13
Linear Systems and Imaging
Fourier Theory
 Fourier Transform
 Convolution Theorem
 H is the transfer function of the system
February 10, 2002
BME1450 - 2002
Slide 14
Fourier Domain = K Space
February 10, 2002
BME1450 - 2002
Slide 15
Linear Systems and Imaging
Effects of filtering
Filter
Width
32 pix
In K
space
Of
256x256
February 10, 2002
BME1450 - 2002
Slide 16
Linear Systems and Imaging
Spectral Components
 Real
part of
the FFT
of pixel
Kx,Ky
=3
 Other
pixels 0
February 10, 2002
BME1450 - 2002
Slide 17