ICON 2014
Brisbane, Australia
(How the thalamus changes) what the cat’s eye tells the cat’s brain
L. M. Martinez
M. Molano-Mazón
X. Wang
The Salk Institute for Biological Studies.
F. T. Sommer
Redwood Center for Theoretical Neuroscience.
University of California, Berkeley.
J. A. Hirsch
University of Southern California.
@
Retina
Fovea
Optic nerve
EYE
BRAIN
Kersten and Yuille (2003) Current Opinion in Neurobiology, 13:1–9
Highly correlated at the local level!
Kersten and Yuille (2003) Current Opinion in Neurobiology, 13:1–9
How does the visual system deal with these problems?
Large amount of information (and related energy cost)
Efficient coding (redundancy in natural images, finite capacity)
Optic nerve
Energy efficient
Image compression
Optic nerve
Biological efficiency
Energy efficient
Coding efficiency?
Image compression
Optic nerve
Wässle et al., 1981
Off Center cells
Light decrements
On Center cells
Light increments
The Visual Pathway
Cortex
?
Adapted from Felleman & Van Essen, 1991
Usrey et al., 1999.
How the thalamus changes the retinal output
?
Retinothalamic model
?
Retinothalamic model
Martinez et al 2014. Neuron 81:943-956.
Statistical wiring of thalamic receptive fields
Functional consequences of the thalamic relay
Retina
R
R
R
1:1
T
LGN
T
T
T
T
T
Functional consequences of the thalamic relay
Retina
R
R
R
3:1
T
LGN
T
T
T
T
T
Functional consequences of the thalamic relay
Diversity index
How different are the receptive fields of neighboring LGN relay cells?
Functional consequences of the thalamic relay
Diversity index
# inputs neuron 1
# inputs neuron 2
# common inputs
Diversity index
Average retinothalamic convergence
Functional consequences of the thalamic relay
Coverage index
How homogeneously do LGN relay cells cover visual space?
visual space coverage
Functional consequences of the thalamic relay
Average retinothalamic convergence
BAYESIAN DECODER
In short, we assume the response of each neuron follows a Gaussian
distribution centered on a point of the space:
yi  f i (x)  
where x is small localized point stimulus, with   N (0, ) being some sensor
 ( x  xi )2
noise and f i ( x)  max  e 2
the ideal response of the i-th neuron. We also
assume that the sensor noise is additive and independent in each channel.
Given a response pattern y, the decoder determines the stimulus x which
maximizes the posterior distribution:
2
^
x  max{log( p( x / y)}
x
With Gaussian sensor noise, the conditional probability of a neural response is:
p ( yi / x )  e
 ( yi  f i ( x )) 2
2 2
Since the responses of individual neurons are conditionally independent we
have:
p( y / x)   p( yi / x)
By virtue of Bayes theorem, we can now write the maximization of the posterior
probability as:
max{log( p( y / x)  p( x) / p( y)}
x
Note, p(y) acts only as a normalization constant as it is independent on the
stimulus. Thus, the previous equation simplifies to:
max{log( p( y / x)  p( x)}
x
which is equal to:
max{
x
1
2  2
(y
i
 f i ( x)) 2  log( p( x))}
i
If we finally assume a uniform or flat prior distribution (i.e., make no prior
assumptions about the location of the stimulus), we have to solve the following
maximization problem:
max{ ( yi  f i ( x)) 2 }
x
i
BAYESIAN DECODER
In short, we assume the response of each neuron follows a Gaussian
distribution centered on a point of the space:
yi  f i (x)  
where x is small localized point stimulus, with   N (0, ) being some sensor
 ( x  xi )2
noise and f i ( x)  max  e 2
the ideal response of the i-th neuron. We also
assume that the sensor noise is additive and independent in each channel.
Given a response pattern y, the decoder determines the stimulus x which
maximizes the posterior distribution:
2
^
x  max{log( p( x / y)}
x
With Gaussian sensor noise, the conditional probability of a neural response is:
p ( yi / x )  e
 ( yi  f i ( x )) 2
2 2
Since the responses of individual neurons are conditionally independent we
have:
p( y / x)   p( yi / x)
By virtue of Bayes theorem, we can now write the maximization of the posterior
probability as:
max{log( p( y / x)  p( x) / p( y)}
x
Note, p(y) acts only as a normalization constant as it is independent on the
stimulus. Thus, the previous equation simplifies to:
max{log( p( y / x)  p( x)}
x
which is equal to:
max{
x
1
2  2
(y
i
 f i ( x)) 2  log( p( x))}
i
If we finally assume a uniform or flat prior distribution (i.e., make no prior
assumptions about the location of the stimulus), we have to solve the following
maximization problem:
max{ ( yi  f i ( x)) 2 }
x
i
Bayesian decoder
Statistical wiring of thalamic RFs increases visual (interpolated) resolution
Martinez et al 2014. Neuron 81:943-956.
Statistical wiring of thalamic RFs increases visual (interpolated) resolution
Energy and coding efficient
Increasing visual acuity through RF interpolation
Increasing visual acuity through RF interpolation
LGN Receptive Fields. Push-pull inhibition
ON-center relay cell
ON_RF(x,y) =
OFF-center interneuron
LGN relay cells and interneurons form functional PUSH-PULL “pairs”
To CORTEX
THALAMUS
ON-center
relay cell
RETINA
+
+
OFF-center
interneuron
LGN relay cells and interneurons form functional PUSH-PULL “pairs”
Increase in dynamic range
of visual responses
To CORTEX
THALAMUS
ON-center
relay cell
+
+
OFF-center
interneuron
ON_RF(x,y) =
RETINA
Functional consequences of Push-Pull in the LGN
B
A
ON_RF(x,y) =
Histogram equalization by retinothalamic circuits
Original image
LCE through thalamic RFs
4
4
x 10
x 10
12
9
8
10
7
8
6
5
6
4
4
3
2
2
1
0
0
0
50
100
150
200
Corresponding histogram
250
0
50
100
150
200
Corresponding histogram
250
Statistical wiring of thalamic receptive fields
1. Increases visual resolution through interpolation.
2. Decreases local redundancy in the image.
3. Increases the dynamic range of the image (i.e. “flatens” its histogram)
4. Produces a very good local contrast enhancement performance
(without halos or visual artifacts)
5. Explains other visual perception phenomena
simultaneous contrast
ICON 2014
Brisbane, Australia
(How the thalamus changes) what the cat’s eye tells the cat’s brain
L. M. Martinez
M. Molano-Mazón
X. Wang
The Salk Institute for Biological Studies.
F. T. Sommer
Redwood Center for Theoretical Neuroscience.
University of California, Berkeley.
J. A. Hirsch
University of Southern California.
Original image
4
x 10
12
10
8
6
4
2
0
0
50
100
150
200
Corresponding histogram
250
Original image
Histogram equalization
4
4
x 10
x 10
12
6
10
5
8
4
6
3
4
2
2
1
0
0
0
50
100
150
200
Corresponding histogram
250
0
50
100
150
200
Corresponding histogram
250
Histogram equalization
LCE through thalamic RFs
4
4
x 10
x 10
9
6
8
7
5
6
4
5
3
4
3
2
2
1
1
0
0
0
50
100
150
200
Corresponding histogram
250
0
50
100
150
200
250
Corresponding histogram
Ferreiroa et al 2014. In preparation
PUSH-PULL “functional units”
To CORTEX
THALAMUS
OFF-center
interneuron
OFF-center
relay cell
+
+
ON-center
interneuron
ON-center
relay cell
-+
+
RETINA
Molano-Mazón, Alonso-Pablos et al 2014. Submitted
PUSH-PULL “functional units”
1. Increase the dynamic range of the image (i.e. “flatens” its histogram)
2. Have a very good local contrast enhancement performance
(without halos or visual artifacts)
3. Explain visual perception phenomena
simultaneous contrast
PUSH-PULL “functional units”
1. Increase the dynamic range of the image (i.e. “flatens” its histogram)
2. Have a very good local contrast enhancement performance
(without halos or visual artifacts)
3. Explain visual perception phenomena
Mach Bands
PUSH-PULL “functional units”
1. Increase the dynamic range of the image (i.e. “flatens” its histogram)
2. Have a very good local contrast enhancement performance
(without halos or visual artifacts)
3. Explain visual perception phenomena
Mach Bands
El Greco. Christ carrying the cross
INSTITUTO DE NEUROCIENCIAS
DE ALICANTE
Current members
Alexandra Gomis
Graciela Navarro (with Santiago Canals)
María del Carmen Navarro
Marie Popiel Jakobsen (with Claudio Mirasso)
Lucía Arena (undergrad)
Sergio Molina (undergrad)
http://thevisualanalogylab.wix.com/valab
Marcos Mirete (Undergrad)
http://about.me/luis.m.martinez
Alumni
External Colaborators
Diego Alonso-Pablos
Jose-Manuel Alonso (SUNY)
Isabel Benjumeda
Judith A. Hirsch (USC)
Joaquín Márquez
Joaquín Ibañez (UMH)
Manuel Molano-Mazón
Stephen L. Macknik (BNI)
Colaborators
Susana Martinez-Conde (BNI)
Victor Borrell
Claudio Mirasso (U. Illes Balears)
Santiago Canals
Rodrigo Quian Quiroga (U. Leicester)
Eloisa Herrera
Eduardo Sanchez (USC)
Guillermina López-Bendito
Mariano Sigman (U. Buenos Aires)
Miguel Maravall
Friedrich T. Sommer (UC Berkeley)
Oscar Marín
Beatriz Rico
Jordi Cami, Mago Koke, Tino Call, Miguel A. GEA