Ch 3 last set of notes

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Ch 3 (last set of notes)

• Psyc 317A

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Lab One Feedback

• Evaluation of Lab One is now complete Grades on
  course website.
• Those who have not completed the lab must arrange
  to do so with TA Travis Baker (teb_at_uvic.ca) ASAP
  in order to pass the course.
• Other Tips
• Do not include raw data (research ethics requires
  it be kept for a brief period and then destroyed.
  Why?). Summarize data in a table (e.g. matrix)
• Make your tables and charts look nice. Appearance
  is important making it self-explanatory is your
  goal. Use clear and effective labeling that is
  uncluttered. Format tables to appropriate size.
  Create a professional look.
• Dont show all your calculations, but enough to
  show how calculations were carried out (e.g., by
  graph, by formulae, by website tool?)
• Say only what you need to say. Use best judgment
  in selection. How?
• Imagine your audience, not as your professor but
  as a community of peers (scientific community)
• Conserve paper dont use title pages (name and
  number all pages)

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Fourier Theorem in Perception Research

• Fourier Analysis a set of mathematical
  algorithms for expressing complex wave phenomena
  as and equation of simpler waves functions
  (trigonometric functions like sine(x), cos(x),
  etc.).
• Application of Fourier Analysis in visual
  perception
• Any spatial pattern of luminance can be
  represented as an equation (e.g. a sum) of sine
  waves.
• Any complex pattern of light across space can be
  analyzed inot a seies of simpler sine waves.
• Fourier Synthesis is the building of complex
  representations of complex phenomenon out of
  simpler sin wave representations.
• It is important to distinguish mathematical
  possibility (existence proofs, proof procedures)
  from neural implementation
• Just because a square wave grating can be
  approximated (or represented) by a sum of sine
  waves does not mean that the brain is somehow
  doing (or approximating) Fourier Analysis in
  order to perceive that grating
• this is an empirical question, not one provable
  by mathematics (or a priori)
• mathematical representation is not
  (automatically) cognitive representation

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Sine Wave Grating with Graph
SOURCE

• Gradually fading bars can be graphically
  represented by single sine wave (mapping position
  onto luminance)
• Such a grating is therefore called a sine wave
  grating
• It can be used to adapt subjects to specific
  spatial frequencies it is indispensable for
  measure the contrast sensitivity function (CSF)

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Spatial Frequencies and Illusory Contrast

• High spatial frequencies cause less apparent
  contrast.
• high spatial frequencies cause an illusion of
  reduced contrast
• therefore, contrast sensitivity varies with
  spatial frequencies, especially near thresholds
• What would a graph of spatial frequency onto
  contrast sensitivity look like?
• Let x-axis be spatial frequency
• Let y-axis be contrast sensitivity (which is the
  reciprocal of the contrast threshold).
• How would you measure it?

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Square Wave Grating with Graph

• Solid distinct bars can be mapped with square
  waves (in red).
• Such patterns are therefore called square-wave
  gratings
• The amplitude on the graph represents the range
  of luminance in the display measured.
• Visualize a sine graph superimposed on the above
  square graph. Visualize the height difference for
  each x between the two curves. How might that
  difference be expressed mathematically?

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First and Third Harmonic Superimposed

• The smaller curve cycles three times for every
  one time the fundamental cycles. Its amplitude
  is only 1/3.
• Imagine these two summed up

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Fourier Analysis components of a square wave
Fig. B2 Appendix, page 592
The square wave (a) can be considered the sum of
its fundamental frequency sign-wave (b) plus its
nth harmonics (for all odd n). (e) bcd.
(a)bcd Any spatial pattern of luminance can
be broken down and expressed as a sum of sine
waves. Fourier analysis is useful for studying
properties of visual systems, but it should not
be assumed to be a model of visual processing.
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Fourier Synthesis

• Creating a high contrast square sqave grating
  from continuous signals
• A graphical representation of a given square wave
  can be created by adding the fundamental wave (a
  sine wave with amplitude and frequency equal to
  the square wave) to the odd harmonics

The n-th harmonic is a wave with n-times the
frequency and 1/n-th the amplitude.
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Contrast SensitivityFunction
Why are sine wave gratings used to measure CSF?
The solid curve is a CSF psychophysical mapping
of spatial frequencies onto contrast sensitivity.

• Higher contrast sensitivity means lower threshold
  of resolution, generally around 4-6 cpd.
• The dotted curve shows reduced contrast
  sensitivity after adaptation to a 7.1 cpd
  sine-wave grating.

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