Spatial Frequency

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PSY 3520 Sensation and Perception
Spatial Frequency
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Spatial Frequency Lecture Outline

• Contrast
• The Effects of Spatial Frequency on Contrast
  Perception
• A. The Grating Stimulus
• B. The Contrast Sensitivity Function
• 1. Spatial Frequency Channels in the Visual
  System
• 2. Contrast Sensitivity and Visual Acuity
• Spatial Fourier Analysis/Fourier Synthesis

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I. Contrast

• Contrast can be defined in two ways
• Perceptual Contrast the perception of the
  difference in intensity of two areas (focus of
  our discussion)
• Physical Contrast the actual physical
  difference in the intensity between two areas

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II. The Effect of Spatial Frequency on Contrast
Perception

• Spatial frequency the number of cycles per unit
  distance across the grating

Grating Stimulus
One Cycle 1 black bar 1 white bar
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The Grating Stimulus

• The properties of a grating stimulus can be
  specified in terms of
• Waveform
• Physical contrast
• Spatial frequency

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• Waveform the shape of the gratings intensity
  distribution

Contour narrow region which visually separates
one area/object from another
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• Physical Contrast equal to the amplitude (A)
  divided by the mean intensity (M)

Mean
Both of these gratings have the same mean
intensity but the grating with the larger
amplitude has higher contrast.
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Physical Contrast

• Another way to describe physical contrast is the
  Michaelson Contrast Ratio
• Michaelson
• Contrast Ratio (LMAX-LMIN) / (LMAXLMIN)
• LMAX the maximum luminance of the visual image
• LMIN the minimum luminance of the visual image

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Spatial Frequency

• The of cycles per unit distance across the
  grating

4 ½ Cycles
This grating has 4 ½ cycles
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Spatial Frequency andVisual Angle
a 1.0o
3 ½ cycles per 1o of visual angle
a 0.5o
3 ½ cycles per 0.5o of visual angle
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Spatial Frequency

• By describing spatial frequency in terms of
  visual angle you know how much space is taken
  up on the retina by a particular grating

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The Contrast Sensitivity Function

• Contrast Sensitivity Function (CSF) -allows us
  to assess the sensitivity of the visual system to
  spatial frequencies
• To measure the CSF
• Start with a grating that has a low spatial
  frequency (wide bars) and low physical contrast
  (light gray on white)
• Start at a point where the whole grating looks
  gray (can not perceive the individual bars)

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• The observer increases the physical contrast of
  the grating stimulus until they can just detect
  the bars
• This procedure is continued with gratings of
  increased spatial frequency (narrower bars)
• A plot is made of the contrast sensitivity values
  as a function of spatial frequency

High spatial frequency
Low spatial frequency
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The Contrast Sensitivity Function

• Most sensitive to sine-wave gratings above 3 cpd
• Our ability to detect a grating depends on the
  gratings spatial frequency

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The Contrast Sensitivity Function

• The contrast sensitivity function covers a broad
  range of spatial frequencies
• Because of the broad coverage it was
  hypothesized that a number of detectors for
  spatial frequency must exist
• These detectors make up the spatial frequency
  channels

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Spatial Frequency Channels
CSF
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Spatial Frequency Channels

• To test for spatial frequency channels a
  selective adaptation procedure was used.
• Example of a typical study
• Determine CSF
• Adapt observer to a certain spatial freq. stare
  at a grating for 1-2 min.
• Redetermine the CSF

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Selective Adaptation
Contrast Sensitivity
CSF
Adapted CSF
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Selective Adaptation

• If the selective adaptation experiments repeated
  with a different adapting stimulus you will get
  similar results
• The results of selective adapatation studies
  support the idea that the CSF is made up of a
  number of spatial frequency channels
• These channels are sensitive to a narrow range of
  frequencies

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Spatial Frequency Channels

• There are many researchers that believe these
  spatial frequency channels correspond to neurons
  in the cortex
• When selective adaptation occurs it is because
  neurons tuned to a specific frequency become
  fatigued

This is the Blakemore-Sutton Effect
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Selectively Tuned Cells

• Maffei Fiorentini (1973) were the first to find
  these selectively tuned cells in the cortex
• They moved gratings of different spatial
  frequencies across the receptive fields of simple
  cortical cells
• They found tuning curves for 3 simple cortical
  cells

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Contrast Sensitivity and Visual Acuity

• Measure visual acuity using a grating stimulus
• Assess what is the finest spatial frequency a
  person can detect
• Usually the gratings have high spatial frequency
  and high contrast (like the E-chart)

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Contrast Sensitivity and Visual Acuity

• What is really being measured is the resolving
  power of the foveal region to stimuli with high
  physical contrast and high spatial frequency

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Contrast Sensitivity and Visual Acuity

• The problem with using this method to measure
  visual performance
• Ignores a wide range of spatial frequencies
• Ignores the range of physical contrasts we
  experience in our environment
• Examples?
• High spatial frequency
• Low spatial frequency
• High spatial frequency/high contrast
• Low spatial frequency/low contrast

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Contrast Sensitivity and Visual Acuity

• Sekuler, Hutman Owsley (1980) study
• 2 groups of observers
• Gave observers standard acuity tests
• 73 yr. olds
• 18 yr. olds
• Then observers contrast sensitivity functions
  were measured

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III. Spatial Fourier Analysis/Fourier Synthesis

• Baron Jean Fourier (1822) French physicist
  developed what is known as Fouriers theorem
• Fourier Analysis any repeating waveform can be
  broken down into a number of sine-wave components
• Fourier Synthesis any waveform can be
  synthesized by adding together its sine-wave
  components

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Spatial Fourier Analysis/Fourier Synthesis
Fundamental Frequency
Harmonics