Neural network models in vision
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Neural Network Models in Vision. Peter Andras [email protected] The Visual System. R. LGN. V1. V3. V2. Lower. V5. V4. Higher. Neurons. Rod. Horizontal. Bipolar. Amacrine. Ganglion. Neuron Models. The McCullogh-Pitts model. x 1 x 2 x 3 … x n-1 x n. w 1. Output.

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Neural Network Models in Vision

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Neural network models in vision

Neural Network Models in Vision

Peter Andras

[email protected]


The visual system

The Visual System

R

LGN

V1

V3

V2

Lower

V5

V4

Higher


Neurons

Neurons

Rod

Horizontal

Bipolar

Amacrine

Ganglion


Neuron models

Neuron Models

The McCullogh-Pitts model

x1

x2

x3

xn-1

xn

w1

Output

w2

Inputs

y

w3

.

.

.

wn-1

wn


Neuron models1

Neuron Models

K+

Na+

Na+

Na+

The Hodgkin-Huxley Model

Na+

K+

K+

K+

Na+

K+

K+

K+

Na+

Na+

Na+

Na+

K+


Modelling methodology

Modelling Methodology

Physiological measurements

Electrode

Response

Stimulus

Other methods: EEG, MRI, PET, MEG, optical recording, metabolic recording


Modelling methodology1

Modelling Methodology

Response characterisation in terms of stimulus properties

Stimulus


Modelling methodology2

Modelling Methodology

Models:

A. Statistical models: large number of neurons, with a few well-defined properties, the response is analysed at the population level;


Modelling methodology3

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;


Modelling methodology4

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:


Neural network models in vision

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.


Neural network models

Neural Network Models

Retina: ON and OFF centre ganglion cells

Bipolar cells

+1

-1

ON

OFF

Preferred stimulus


Neural network models in vision

Neural Network Models

Retina: ON and OFF centre ganglion cells

Measured response of an ON cell

The response of a model ON cell


Neural network models in vision

Neural Network Models

V1: Orientation selective cells

LGN cells

Preferred stimulus


Neural network models in vision

Neural Network Models

V1: Orientation selective cells

Measurement

Model


Neural network models in vision

Neural Network Models

V1: Ocular dominance patterns and orientation maps


Neural network models in vision

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.


Neural network models in vision

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) < d(wi, xt), for every i  i*;

wi = (1-) wi +  xt , for all neurons with index i, for which d(ci, ci*) < .


Neural network models in vision

Neural Network Models

V1: Contour detection

Stimulus


Neural network models in vision

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.


Neural network models in vision

Neural Network Models

V5: Motion direction selective cells

Orientation selective cells

delay effect

-1

+1

Preferred stimulus


Neural network models in vision

Neural Network Models

Visual object detection

Object

Invariant combination of features

  • Features:

    • colour;

    • texture;

    • edge distribution;

    • contrast distribution;

    • etc.

Object detection


Neural network models in vision

Neural Network Models

Visual object detection

Method 1: Hierarchical binary binding of features

Colour

Texture

Edges

This method leads to combinatorial explosion.

Contrast


Neural network models in vision

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


Neural network models in vision

Neural Network Models

Visual object detection

Method 3: Feature binding by synchronization.


Critical evaluation

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.


Revised view of the neural network models

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;


Neural network models in vision

Revised View of the Neural Network Models

Neural network model

Bayesian network model

x1

f1(x1)

P(y1|x1)

y1

y1

x1

x2

y2

P(x1, x2, x3, x4)

f2(x2)

f(y1, y2, y3, y4)

y2

P(y2|x2)

P(y | y1, y2, y3, y4)

x2

y

y

y3

x3

y3

x3

f3(x3)

P(y3|x3)

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(y4|x4)


Neural network models in vision

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;


Conclusions

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.


Seminar papers

Seminar Papers

1. PNAS, 93, 623-627, Jan. 1996

2. PNAS, 96, 10530-10535, Aug. 1999


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