modeling the visual cortex area 1(v1) for pattern …scc/seminars/neuro_atanendu_s_mandal... ·...

Modeling the Visual Cortex Area 1(V1) for Pattern Recognition

ByAtanendu Sekhar MandalIC Design GroupCentral Electronics Engineering Research InstitutePilani – 333031Rajasthan.Email : [email protected]

• Introduction

• Development of Corticocortical Lateral Connections

• Simulation Results

• Role of Lateral Connections

• Axon Growth Model

• Conclusion and Future Works

• Pattern Recognition

Order of Presentation

Neuro Vision : Introduction

Bhagabhan Buddha


The Visual System


A Simplified Model of the Visual Pathway


Receptive Fields


Visual Information Processing


Cell organizations


Characteristics of Cortical Cells of V1

1. Orientation Specificity

2. Orientation Tuning

φ

Neuro Vision : Introduction LC

The Orientation Map (Bosking et. al, 1997)


Characteristics of Horizontal Connections

1. Orientation Specificity

2. Axial Specificity


Importance of Horizontal Connections

1. Elongated Receptive Fields of Layer 6 Simple Cells

2. Integration of Information by a Neuronal Cell

3. Receptive Field Surround Effects

4. Cortical Plasticity


Our Objective :

1. Development of Orientations Maps

2. Development of Horizontal Connections

3. Study of Horizontal Connections in the Development Orientation Tuning

Neuro Vision

Developed Orientation Map :

(200 – 700)

The Model

(Development of Horizontal Connections)

Modeling the Horizontal Connections

• The Three Layer Model of the Visual System

Cortex : 50x50

RF : 13x13

LGN : 42x42

VS : 195x195


• The Model

- Initial Response Generation : Three Layer Model

- Cortical Weight development : One Layer Model

- Cortical Response Generation : Three Layer Model


• The Model

- Initial Response Generation :

( ) ( )( ) ( )( )( )( )

∑ ∑ ∑∈ Γ∈ ∈

+−+−=i

fi i i

fjFt j Ft

Pf

jijijf

iii RttWtttu )1(εη

( ) ( )2expexp ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−−−⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ−−=

s

ax

m

ax

ijsssττ

ε

( )

where

( )3exp ⎟⎠⎞

⎜⎝⎛−−=

τϑη ssi

EPSP

t


• The Models

- Cortical Weight Development : Model1

.

( )( ) ( ) ( )3,exp21

2

1' jifWYYWWW distR

ijTT

ijj

ji⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−

−−=φφ

γγ

- Cortical Weight Development : Model2

( )( ) ( ) ( )4,21'jidistij

TTij OOjifWYYWWW −−= γγ

• Bhaumik B. and Mandal A.S. (2003) An Integrated Feedforward and Recurrent Model for layer 4 Cortical Cells in the Visual Cortex, Proceedings International Symposium: Building the Brain, NBRC, Manesar, Dec. 15-17.


• The Model

- Cortical Response Generation :

( ) ( )( ) ( )( )( )( )

( )( )( )( ) ( )

( )∑ ∑

∑∑ ∑ ∑

Γ∈ ∈

Γ∈∈ Γ∈ ∈

+−

+−+−+−=

i jf

j

iif

i i jf

j

j Ftp

fjij

ciij

i

j

fjij

ceij

e

Ft j Ft

fjij

lij

lfiii

RttW

ttWttWtttu

72

21

εβ

εβεβη

where( ) functionrefractoryti :η

potentialrestingRp :

Simulation Results1. Development of Horizontal Connections :

2. An Individual Cell : (20, 25)

3. Lateral Connections

4. Role of Lateral Connections

- Scatter Plot : hwhh

- Tuning Plots

• Improvement : Inhibition Excitation LGN

• Deterioration : Inhibition

- Locations : Inh Exc LGN

- Contextual Effects

5. Result Discussions

Simulation Results

Movie

B

C

D

Effect of Receptive Field Overlap on Lateral Connections

Reference Cell

Target Cell

Target Cell

Target Cell

o37.21=Φi

Cell (30,17)

Cell (9,41),Edist=31.9, wij =0.471

o24.21=Φ j

Cell (18,36), Edist=22.5, wij=0.132

o7.20=Φ j

Cell (45,19), Edist=15.1,wij=0.124

o3.109=Φ j

Scatter Plots : Tuning Half Widths

(a) (b)

(c)

(a) : LGN Contribution only

(b) : LGN + Lateral Contributions

Role of Lateral Connections


- Improvement due to Inhibition



- Improvement due to Excitation



- Improvement due to LGN



- Deterioration due to Inhibition



- Locations : Improvement due to Inhibition

Spike < 150 Spike >150



- Locations : Improvement due to Excitation



- Locations : Improvement due to LGN


• Lesion Experiment

50x50

RF : 13x13

LGN : 42x42

RF-VS : 79x79

VS : 195x195


• Lesion Experiment Result


• Determination of RF by Reverse Correlation Technique

(Jones and Pakmer, 1978a)

(a) (b)

RF of a cortical cell shown (a) as a set a set of LGN weights(b) as obtained through reverse correlation technique


• Contextual Effects Experiment Results

(b)

(a)

Cell : (31,13)Location : Boundary between

two zones

Cell : (40,25)Location : Pinwheel

Development of Lateral Connections : Result Discussions

• Characteristics of the Developed Horizontal Connections are Similar to the Experimental Findings

• Improvement in Tuning of Cortical Cells are due toVarious Mechanisms rather than one single mechanism

• Various Mechanisms Correspond to Various Locations in the Orientation Map

• Context Dependent Modulation of Cortical Cell Responseis dependent upon the Location of the cell in the Orientation Map

Axon Growth Model

• The Model

- Axon Growth

- Cell Connectivity to the Axonal Branches

- Modeling the Optimization Process

• Results

• Force Directed Partitioning

• Bhaumik B., and Mandal A.S. (2004) A computational model for the development of lateral connections among cells inthe visual cortex : A simulation study, International Conference on Molecular Biology, IIT Kanpur.

Modeling the Axon Growth

• The Model – Axon Growth

Location of the Growth Cone at Time t :

( ) ( ) ( )11 LAtAtA Δ+−=

where

( )

( )⎩⎨⎧ >

=

−∗=Δ

otherwisekif

kU

MMUaAiadistdisti

:00:1

_


• The Model – Cell Connectivity to the Axonal Branches

Number of Cells Connected at Time t :

( ) ( ) NtNtN Δ+−= 1

where

( ) ( ) ( ) ( )( )( )

∑∑= =

−−∗∗−∗=ΔrN

i

tM

jpdistdistijiji i

MMUdhdlUpUN1 1

max

( ) ( )⎩⎨⎧ Φ=Φ

=otherwise

pifpU i

i :0:1


• The Model – Cell Connectivity to the Axonal Branches

( )⎩⎨⎧

=otherwise

dfordh ij

ij :0

min:1

otherwiseM

lMl

lMl

l

dist

pdist

pdist

i

i

:exp

:

maxmax

maxmax

max⎪⎩

⎪⎨

⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−∗

≤

= −

−


• The Model – Optimization Process (Jaydeva & Bhaumik, 1994)

( ) ( )∑ ∑∑= = =

+ +=M

i

N

i

M

jijijii dhdxxdistE

1 1 11,,2

where( ) ( )

( ) ( )( )( )( )∑

=

++

−

−=

==

M

lij

ijij

jiijiiii

td

tddh

xpdistdxxxxdist

1

22

22

211

/exp

/exp

,,2,,,,2

β

β

Dynamic Equation( )( )

( )( )

( ) ( )

( ) ( ) ( ) ( )( )∑

∑

=

=

−

−

+

+

−−+

−∗+

−+

−=

∂∂

−=

N

kkikikjij

ki

ijkjki

N

k

ii

ii

ii

ii

ijij

dhdht

px

dxp

dh

xxdistxx

xxdistxx

xEx

12

1

1

1

1

1'

11

,,2,,2

β

(a) (b) (c)

Modeling the axon Growth

• Results : Neural Optimization : Features Incorporated

1. Curves of Various Shapes

2. Importance of Merging Partitions

3. Number of Curve Points Added

4. Direction of Curve Opening

5. Algorithm Used for Partition

• Mandal A.S. and Bhaumik B. (2003), Techniques for improving the neural optimization method, Progress in VLSI Design & Test, Bangalore, 270-277.


• Simulation Result

• Axon Growth: Movie • Optimization Process : Movie


• Results : Axon Growth


• Results : Axon Growth

• Optimization Process : Movie


• Results : Optimization


• Result : Optimization

Force Directed Partitioning

( )( )

∑=

∗=rn

jj

iji pU

rF

12

1

where

( ) ( )⎩⎨⎧ Φ=Φ

=otherwise

pifpU j

j :0

:1


• Result : Force Directed Axon Growth : Movie


• Result : Force Directed Axon Growth


• Force directed partitioning of a displaced point set.

Force Directed Axon Growth

Axon Growth on Ferret Orientation Map

IC-Design Group, CEERI, Pilani

Principal contributions

• Tuning improvements of cortical cells are due to multiple mechanisms

• Cortical Excitation is also one of the mechanisms .

• Effects of lateral connections on orientation tuning of cortical cells are location dependent.

• Contextual Effects are also location dependent

•Force directed mechanism can be a natural mechanism for the movement of growth-cones.

• An optimization based neural network approach with force directedmechanism is used to model the growth of long-range horizontalconnections.

Future and Present Activities

• Integration of Short-Range and Long-Range Model

• Development of an Event Driven Simulator

• Use of the Model as a Pattern Recognition System

•VLSI Implementation

Some of the Important References• Bhaumik B, Mathur M (2003), A cooperation and competition based simple cell receptive field model and study of feed-forward linear and nonlinear contributions to orientation selectivity. J. Comp. Neurosci. 14:211-217.

• Buzás P, Eysel UT, Kisvárdy ZF (1998), Functional topography of single cortical cells: an intracellular approach combined with optical imaging. Brain Research Protocol, 3: 199-208.

• Callaway EM, Katz LC (1990), Emergence and refinement of clustered horizontal connections in cat striate cortex.J. Neuroscience, 10: 1134–1153.

• Changizi MA (2005), Scaling the brain and its connections. In Evolution of Nervous Systems, (ed.) Kaas JH, Elsevier.

• Jayadeva and Basabi Bhaumik, (1994), A Neural Network for the Steiner Minimal Tree Problem. Biological Cybernetics, 70:485-494.

• Kandler K (2004), Activity-dependent organization of inhibitory circuits: lessons from the auditory system. Current Opinion in Neurobiology, 14:96 – 104.

• Kisvárday ZF, Toth E, Rausch M, and Eysel UT (1997), Orientation-Specific Relationship Between Populations of Excitatory and Inhibitory Lateral Connections in the Visual Cortex of the Cat. Cerebral Cortex, 7(7):605-618

• Knierim JJ, Van Essen DC (1992), Neuronal Responses to Static Texture Patterns in Area V1 of the Alert Macaque Monkey, J. Physiology, 67:961-980.

• Mariño J, Schummers J, Lyon DC, Schwabe L, Beck O, Wiesing P (2005), Invariant computations in local cortical networks with balanced excitation and inhibition. Nature Neuroscience, 8(2):194 – 201.

• Roerig B, and Chen B (2002), Relationship of Local Inhibitory and Excitatory Circuitry to Orientation Preference Maps in Ferret Visual Cortex. Cereb. Cortex, 12:187-198.

• Yousef T, Toth E, Rausch M, Eysel UT, and Kisvarday ZF (2001), Topography of Orientation Center Connections in Primary Visual Cortex of the Cat. Neuro Report, 12(8):1693-1699.

Neuro Vision :Pattern Recognition

Neuro Vision : Pattern Recognition

Rupasi Bangla of Jivananda Das

Neuro Vision : Pattern Recognition

CONTROLLER

Post

Proc

essi

ng

Pre

Proc

essi

ng

INPUT

Neuro Vision : Future Work

VLSI Implementation of a Neuro ChipColour PerceptionDepth PerceptionMotion PerceptionFeature PerceptionTexture PerceptionLearning Memory

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