energy, stereoscopic depth, and correlations
DESCRIPTION
Energy, Stereoscopic Depth, and Correlations. 1m. CNS. 10cm. Sub-Systems. 1cm. Areas / „Maps“ . 1mm. Local Networks. Levels of Information Processing in the Nervous System. 100 m m. Neurons. 1 m m. Synapses. 0.01 m m. Molecules. But first we need complex numbers…. Correlations. - PowerPoint PPT PresentationTRANSCRIPT
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Energy, Stereoscopic Depth, and Correlations
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Molecules
Levels of Information Processing in the Nervous System
0.01mm
Synapses1mm
Neurons100mm
Local Networks1mm
Areas / „Maps“ 1cm
Sub-Systems10cm
CNS1m
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3
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)()2
)(exp(21)(
20
kxtrigxxxg
trig=sin trig=cos
Note:2-dim. Gabor
function are elongated.Thus, cells responses
are orientationselective.Top view: .
trig=cos
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But first we need complex numbers…
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𝐗𝟏
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The response profile of a cortical s im ple cellhas the shape of a Gabor function.
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Correlations
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)()()()()()()( xfxgxgxfduuxgufxh
)()()()()()()( xgxfxfxgduxugufxh
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3) determine motion and sound perceptions
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Motion is correlation in time and space:
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Motion is correlation in time and space:
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Motion is correlation in time and space:
This point is on at time t
This point is on at time t + t
We see motion when two neighbouring spatial positions are stimulated with a temporal delay.
First, however, we will do
this with spikes (by hand)
before we come back to this
example !
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Intuition: To correlate two signals means to shift one signal backand forth with respect to the other and to check how similar thetwo signals are (for each of these shifts).
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Motion is correlation in time and space:
This point is on at time t
This point is on at time t + t
We see motion when two neighbouring spatial positions are stimulated with a temporal delay.
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Motion is detected by comparing the responses of two photoreceptors
The signal of the first photoreceptor is delayed by - t
Then the comparison stage detects whether both signals arrive at the same time
Motion detection by correlation:
Delay ( - t )
Compare
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Sound coming from a particular location in space reaches the two ears at different times.
From the interaural time difference the azimuth of the sound direction can be estimated.
Example:
Interaural Time Difference (ITD):
tcS
msec3.0m/s330cm10
tcS
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When a sound wave of a particular frequency reaches the (left) ear, a certain set of hair cells (those that encode this frequency) become excited.
Transformation of sound to spikes:
These hair cells generate spikes. These spikes always appear at the same phase of the wave.They are „phase-locked“.
The same sound wave reaches the right ear a little later. This gives a phase shift between left and right ear. Spikes are again phase-locked to the sound wave.
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When a sound wave of a particular frequency reaches the (left) ear, a certain set of hair cells (those that encode this frequency) become excited.
Transformation of sound to spikes:
These hair cells generate spikes. These spikes always appear at the same phase of the wave.They are „phase-locked“.
The same sound wave reaches the right ear a little later. This gives a phase shift between left and right ear. Spikes are again phase-locked to the sound wave.
Difference in spike times ~ sound azimuth !
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Each neuron receives input from both ears.
Due to the lengths of the two axons, the inputs arrive at different times.
The neuron acts as a „coincidence detector“ and only fires if two spikes arrive at the same time.
Delay line correlator:
=> Each neuron encodes a specific interaural time difference.
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Delay lines in the owl brain:
Ear -> Auditory nerve -> NM -> NL -> LS -> ICx
Input
Coincidence detector
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Correlation:
Left spike train
)(tL )(tRRight spike train
)( ttRTime delay
)(*)( ttRtLCoincidence detection
Average over time dttRtL )(*)( t