Neural Network Models in Vision

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Neural Network Models in Vision

• Peter Andras
• peter.andras_at_ncl.ac.uk

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The Visual System
R
LGN
V1
V3
V2
Lower
V5
V4
Higher
3
Neurons
Rod
Horizontal
Bipolar
Amacrine
Ganglion
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Neuron Models
The McCullogh-Pitts model
x1 x2 x3 xn-1 xn
w1
Output
w2
Inputs
y
w3
.
.
.
wn-1
wn
5
Neuron Models
K
Na
Na
Na
The Hodgkin-Huxley Model
Na
K
K
K
Na
K
K
K
Na
Na
Na
Na
K
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Modelling Methodology
Physiological measurements
Electrode
Response
Stimulus
Other methods EEG, MRI, PET, MEG, optical
recording, metabolic recording
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Modelling Methodology
Response characterisation in terms of stimulus
properties
Stimulus
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Modelling Methodology
Models
A. Statistical models large number of neurons,
with a few well-defined properties, the response
is analysed at the population level
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Modelling Methodology
Models
B. Macro-neural models simplified model neurons
organised in relatively simple networks, the
overall input-output relationship of the full
network is analysed
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Modelling Methodology
C. Micro-neural models the neurons are modelled
with many details and models of individual
neurons or networks of few detailed neurons are
analysed.
Models
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Modelling Methodology
Physiological measurements Response
characterisation Model selection OBJECTIVE 1
match the measured response properties by the
response properties of the model. OBJECTIVE 2
test the theories, generate predictions.
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Neural Network Models
Retina ON and OFF centre ganglion cells
Bipolar cells
1
-1
ON
OFF
Preferred stimulus
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Neural Network Models
Retina ON and OFF centre ganglion cells
Measured response of an ON cell
The response of a model ON cell
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Neural Network Models
V1 Orientation selective cells
LGN cells
Preferred stimulus
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Neural Network Models
V1 Orientation selective cells
Measurement
Model
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Neural Network Models
V1 Ocular dominance patterns and orientation maps
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Neural Network Models
V1 Ocular dominance patterns and orientation maps

• Neuron Feature vector
• orientation preference
• spatial frequency

• eye preference
• temporal frequency

• Training principles
• the neuron fires maximally when the stimulus
  matches its preferences set by the feature
  vector
• the neuron fires if its neighbours fire
• when the neuron fires it adapts its feature
  vector to the received stimulus.

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Neural Network Models
V1 Ocular dominance patterns and orientation maps
Mathematically
Neurons (wi , ci) wi feature vector ci
position vector Training set xt , training
vectors, they have the same dimensionality as the
feature vectors Training i index of the
neuron for which d(wi, xt) lt d(wi, xt), for
every i ? i wi (1-?) wi ? xt , for all
neurons with index i, for which d(ci, ci) lt ?.
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Neural Network Models
V1 Contour detection
Stimulus
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Neural Network Models
V1 Contour detection
Neural interactions specified by interconnection
weights. Mechanism constraint satisfaction by
mutual modification of the firing rates. Result
the neurons corresponding to the contour position
remain active and the rest of the neurons become
silent.
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Neural Network Models
V5 Motion direction selective cells
Orientation selective cells
delay effect
-1
1
Preferred stimulus
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Neural Network Models
Visual object detection
Object
Invariant combination of features

• Features
• colour
• texture
• edge distribution
• contrast distribution
• etc.

Object detection
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Neural Network Models
Visual object detection
Method 1 Hierarchical binary binding of features
Colour
Texture
Edges
This method leads to combinatorial explosion.
Contrast
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Neural Network Models
Visual object detection
Method 2 Non-linear segmentation of the feature
space.
Colour
Texture
Edges
Learning by back-propagation of the error signal
and modification of connection weights.
Contrast
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Neural Network Models
Visual object detection
Method 3 Feature binding by synchronization.
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Critical Evaluation

• Neural network models typically explain certain
  selected behavioural features of the modelled
  neural system, and they ignore most of the other
  aspects of neural activity.
• These models can be used to test theoretical
  assumptions about the functional organization of
  the neurons and of the nervous system. They
  provide predictions with which we can determine
  the extent of the validity of the model
  assumptions.
• One common error related to such models is to
  invert the causal relationship between the
  assumptions and consequences i.e., the fact that
  a model produces the same behavior as the
  modelled, does not necessarily mean that the
  modelled has exactly the same structure as the
  model.

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Revised View of the Neural Network Models

• Revised interpretation
• neurons anatomical / functional modules (e.g.,
  cortical columns or cortical areas)
• connections causal relationships (e.g.,
  activation of bits of LGN causes activation of
  bits of V1)
• activity function of a neuron conditional
  distribution of module responses, conditioned by
  the incoming stimuli

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Revised View of the Neural Network Models
Neural network model
Bayesian network model
x1
f1(x1)
P(y1x1)
y1
y1
x1
x2
y2
P(x1, x2, x3, x4)
f2(x2)
f(y1, y2, y3, y4)
y2
P(y2x2)
P(y y1, y2, y3, y4)
x2
y
y
y3
x3
y3
x3
f3(x3)
P(y3x3)
yi fi(xi) y f(y1, y2, y3, y4)
P(x1, x2, x3, x4) P(yi xi) P(y y1, y2, y3, y4)
y4
x4
y4
x4
f4(x4)
P(y4x4)
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Revised View of the Neural Network Models

• Advantages of the Bayesian interpretation
• relaxes structural restrictions
• makes the models conceptually open-ended
• allows easy upgrade of the model
• allows relaxed analytical search for minimal
  complexity models on the basis of data
• allows statistically sound testing

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Conclusions

• Neuron and neural network models can capture
  important aspects of the functioning of the
  nervous system. They allow us to test the extent
  of validity of the assumptions on which the
  models are based.
• A common mistake related to neural network
  models is to invert the causal relationship
  between assumptions and consequences. This can
  lead to far reaching conclusions about the
  organization of the nervous system on the basis
  of natural-like functioning of the neural network
  models that are invalid.
• The Bayesian reinterpretation of neural network
  models relaxes many constraints of such models,
  makes their upgrade and evaluation easier , and
  prevents to some extent incorrect interpretations.

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Seminar Papers
1. PNAS, 93, 623-627, Jan. 1996 2. PNAS, 96,
10530-10535, Aug. 1999