Loading in 5 sec....

Neural Network Models in VisionPowerPoint Presentation

Neural Network Models in Vision

- 70 Views
- Uploaded on
- Presentation posted in: General

Neural Network Models in Vision

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Neural Network Models in Vision

Peter Andras

peter.andras@ncl.ac.uk

R

LGN

V1

V3

V2

Lower

V5

V4

Higher

Rod

Horizontal

Bipolar

Amacrine

Ganglion

The McCullogh-Pitts model

x1

x2

x3

…

xn-1

xn

w1

Output

w2

Inputs

y

w3

.

.

.

wn-1

wn

K+

Na+

Na+

Na+

The Hodgkin-Huxley Model

Na+

K+

K+

K+

Na+

K+

K+

K+

Na+

Na+

Na+

Na+

K+

Physiological measurements

Electrode

Response

Stimulus

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

Response characterisation in terms of stimulus properties

Stimulus

Models:

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

Models:

B. Macro-neural models: simplified model neurons organised in relatively simple networks, the overall input-output relationship of the full network is analysed;

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:

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.

Retina: ON and OFF centre ganglion cells

Bipolar cells

+1

-1

ON

OFF

Preferred stimulus

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

V1: Orientation selective cells

LGN cells

Preferred stimulus

Neural Network Models

V1: Orientation selective cells

Measurement

Model

Neural Network Models

V1: Ocular dominance patterns and orientation maps

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

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

V1: Contour detection

Stimulus

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

V5: Motion direction selective cells

Orientation selective cells

delay effect

-1

+1

Preferred stimulus

Neural Network Models

Visual object detection

Object

Invariant combination of features

- Features:
- colour;
- texture;
- edge distribution;
- contrast distribution;
- etc.

Object detection

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

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

Visual object detection

Method 3: Feature binding by synchronization.

- 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 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;

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)

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;

- 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.

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

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