Outline

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Chapter 2
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Outline

• Linear filters
• Visual system (retina, LGN, V1)
• Spatial receptive fields
• V1
• LGN, retina
• Temporal receptive fields in V1
• Direction selectivity

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Linear filter model
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White noise stimulus
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Fourier transform
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H1 neuron in visual system of blowfly

• A Stimulus is velocity profile
• B response of H1 neuron of the fly visual
  system
• C rest(t) using the linear kernel D(t) (solid
  line) and actual neural rate r(t) agree when
  rates vary slowly.
• D(t) is constructed using white noise

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Deviation from linearity
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Early visual system Retina

• 5 types of cells
• Rods and cones photo-transduction into
  electrical signal
• Lateral interaction of Bipolar cells through
  Horizontal cells. No action potentials for local
  computation
• Action potentials in retinal ganglion cells
  coupled by Amacrine cells. Note
• G_1 off response
• G_2 on response

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Pathway from retina via LGN to V1

• Lateral geniculate nucleus (LGN) cells receive
  input from Retinal ganglion cells from both eyes.
• Both LGNs represent both eyes
• Neurons in retina, LGN and visual cortex have
  receptive fields
• Neurons fire only in response to higher/lower
  illumination within receptive field
• Neural response depends (indirectly) on
  illumination outside receptive field

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Simple and complex cells

• Cells in retina, LGN, V1 are simple or complex
• Simple cells
• Model as linear filter
• Complex cells
• Show invariance to spatial position within the
  receptive field
• Poorly described by linear model

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Retinotopic map

• Neighboring image points are mapped onto
  neighboring neurons in V1
• Visual world is centered on fixation point.
• The left/right visual world maps to the
  right/left V1
• Distance on the display (eccentricity) is
  measured in degrees by dividing by distance to
  the eye

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Retinotopic map
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Retinotopic map
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Visual stimuli
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Nyquist Frequency
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Spatial receptive fields
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V1 spatial receptive fields
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Gabor functions
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Response to grating
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Temporal receptive fields

• Space-time evolution of V1 cat receptive field
• ON/OFF boundary changes to OFF/ON boundary over
  time.
• Extrema locations do not change with time
  separable kernel.

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Space-time receptive fields
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Space-time receptive fields
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Space-time receptive fields
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Direction selective cells
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Complex cells
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Retina and LGN receptive fields
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Retina and LGN receptive fields
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Comparison model and data
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Constructing V1 receptive fields

• Oriented V1 spatial receptive fields can be
  constructed from LGN center surround neurons

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Summary

• Linear filters
• White noise stimulus for optimal estimation
• Visual system (retina, LGN, V1)
• Visual stimuli
• V1
• Spatial receptive fields
• Temporal receptive fields
• Space-time receptive fields
• Non-separable receptive fields, Direction
  selectivity
• LGN and Retina
• Non-separable ON center OFF surround cells
• V1 direction selective simple cells as sum of LGN
  simple cells