CS 450: Introduction to Digital Signal and Image Processing

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CS 450 Introduction to Digital Signal and Image
Processing

• Signal and Image Acquisition

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Acquisition Devices

• Aperture
• Scanning
• Sensor
• Quantizer
• Output storage medium

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Apertures

• Point measurements are impossible
• Have to make measurements using a (weighted)
  average over some aperture
• time window
• spatial area
• etc.

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Apertures

• Size of aperture determines resolution
• Smaller apertures better resolution
• Larger apertures worse resolution
• Lenses allow physically larger aperture w/
  effectively smaller one

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Lenses
Lens
Effective Aperture
Sensor
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Sensor

• Converts light (photons) to chemical and/or
  electrical response
• Examples
• Silver halide crystals (film)
• Photoreceptors in our eyes (rods, cones)
• Charge-coupled device (CCD), etc.

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Noise

• Unavoidable random fluctuations from correct
  value
• Can usually be modeled as a statistical
  distribution with mean at the correct value
• A measured sample will vary from that mean
  according to the distribution

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Signal-To-Noise Ratio

• Measure of how noise free the acquired signal
  is

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Sources of Noise

• Quantum noise
• Sensor inhomogeneity
• Electrical fluctuations
• Background noise

May not be random
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Quantum Noise

• Discrete nature of light
• Poisson distributed
• Signal-to-noise ratio increases with increased
  light

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Reducing Quantum Noise

• Turn up the source
• Larger aperture
• Collect for longer

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Noise vs. Resolution

• Smaller apertures
• Better resolution
• Less area -gt fewer photons -gt more noise
• Larger apertures
• Worse resolution
• More area -gt more photons -gt less noise

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Noise vs. Resolution

• Example 1 Camera settings
• F-stop aperture
• Shutter speed collection time
• Example 2 Film
• Larger crystals -gt less resolution but less time
  required (faster)
• Smaller crystals -gt more resolution but more time
  required (slower)

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Lenses
Physical (Collecting) Aperture
Lens
Effective Aperture
Sensor
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Ideal Sensor Response

• Multiplying the input by a constant multiplies
  the output by the same constant
• Adding two input signals causes their
  corresponding outputs to add

f(ax by) a f(x) b f(y)
Linearity
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Gain and Offset

• Gain proportionality of input to output
• Offset constant addition to output(also
  sometimes called bias)

slope gain
y-intercept offset
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Typical Intensity Responses

• Most approximately linear devices are linear
  over some range
• Below that range - little or no response
• Within that range - linear
• Above that range - saturation
• Example HD curve for film

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Transfer Function

• A way of measuring resolution
• Instead of using line-pairs, use sine waves
• Measure the contrast of the response as a
  function of frequency