Chapter 2
Outline
• Linear filters
• Visual system (retina, LGN, V1)
• Spatial receptive fields
– V1
– LGN, retina
• Temporal receptive fields in V1
– Direction selectivity
Linear filter model
White noise stimulus
Fourier transform
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
Deviation from linearity
Early visual system: Retina
• 5 types of cells:
– Rods and cones: phototransduction 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
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
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
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
Retinotopic map
Retinotopic map
Visual stimuli
Nyquist Frequency
Spatial receptive fields
V1 spatial receptive fields
Gabor functions
Response to grating
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.
Space-time receptive fields
Space-time receptive fields
Space-time receptive fields
Direction selective cells
Complex cells
Retina and LGN receptive fields
Retina and LGN receptive fields
Comparison model and data
Constructing V1 receptive fields
• Oriented V1 spatial receptive fields can be constructed
from LGN center surround neurons
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