Coding the Presence of
Visual Objects in a
Recurrent Neural Network of
Visual Cortex
Dissertation
zur Erlangung des Doktorgrades
der Naturwissenschaften
(Dr. rer. nat.)
dem Fachbereich Physik
der Philipps-Universität Marburg
vorgelegt von
Timm Zwickel
Marburg/Lahn, Juni 2006Vom Fachbereich Physik der Philipps-Universität Marburg als
Dissertation angenommen am 12.07.2006
Erstgutachter: Prof. Dr. Reinhard Eckhorn
Zweitgutachter: Prof. Dr. Heiko Neumann
Tag der mündlichen Prüfung: 13.07.2006To JuliaTruth is I thought it mattered,
I though that musiced,
But does it bollocks,
Not compared to our people matter.
ChumbawambaContents
Zusammenfassung (Abstract in German) 1
Abstract 3
1 Introduction 5
1.1 Object Coding in Visual Cortex . . . . . . . . . . . . . . 5
1.1.1 Dorsal and Ventral Pathways and Feedback . . 5
1.1.2 Border-Ownership . . . . . . . . . . . . . . . . . 6
1.1.3 Feedback Models . . . . . . . . . . . . . . . . . . 7
1.1.4 Gestalt Rules . . . . . . . . . . . . . . . . . . . . 8
1.2 Chapter Overview . . . . . . . . . . . . . . . . . . . . . 9
2 Methods 11
2.1 Conceptual Modelling of Functional Mechanisms . . . 11
2.2 Model Neuron De nition . . . . . . . . . . . . . . . . . 12
2.3 Neuron Dynamics . . . . . . . . . . . . . . . . . 13
2.3.1 Excitatory-Neuron-Inhibitory-Neuron Unit . . . 14
2.3.2 Divisive Inhibition . . . . . . . . . . . . . . . . . 15
2.3.3 Lateral Linking . . . . . . . . . . . . . . . . . . . 17
2.4 Feedback Effect Quanti cation . . . . . . . . . . . . . . 18
3 Model Architecture 19
3.1 Model Architecture . . . . . . . . . . . . . . . . . . . . . 19
3.2 Stimulus Input . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Area-1: Orientation Detection . . . . . . . . . . . . . . . 20
3.4 Area 2: Curvature Detectors . . . . . . . . . . . . . . . . 25
3.5 Area-3: Convex Object Detection . . . . . . . . . . . . . 29
3.6 Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Results of the Main Border-Ownership Model 33
4.1 Overview Over Stimuli . . . . . . . . . . . . . . . . . . . 33
4.2 Response of the Network Areas to an Example Stimulus 344.3 Stimuli Eliciting Opposite BO Preference in One Neuron 38
4.4 of Varying Position, Size and Form . . . . . . . 38
4.5 Feedback Effect Quanti cation . . . . . . . . . . . . . . 40
4.6 Multiple-Object Stimulus . . . . . . . . . . . . . . . . . . 40
4.6.1 Separate Objects . . . . . . . . . . . . . 44
4.6.2 Stimulus Objects Sharing an Edge . . . . . . . . 44
4.6.3 Overlapping Stimulus Objects . . . . . . . . . . 50
4.7 Incomplete Objects and Non-Objects . . . . . . . . . . . 52
4.8 BO in Neurons Not Receiving Direct Feedback . . . . . 54
4.9 Figure-Ground Segregation . . . . . . . . . . . . . . . . 58
5 Model with Delays 61
5.1 Lateral Conduction Delays . . . . . . . . . . . . . . . . . 61
5.2 Delays in the Model . . . . . . . . . . . . . . . . . . . . . 62
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6 Closed Feedback Loop 65
6.1 to Area-1a . . . . . . . . . . . . . . . . . . . . 65
6.2 Modi cations to the Model . . . . . . . . . . . . . . . . 65
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.4 Discussion of Closed Feedback Loop . . . . . . . . . . . 68
7 Learning Feedback 69
7.1 Why Learn What? . . . . . . . . . . . . . . . . . . . . . . 69
7.2 Learning Rule . . . . . . . . . . . . . . . . . . . . . . . . 71
7.3 Feedback: Simple Model . . . . . . . . . . . . 72
7.4 Learning Complex Model . . . . . . . . . . . 74
8 Discussion 81
8.1 Comparison of Our Model to Properties of BO Neurons 81
8.1.1 Reproducing Effects Measured in BO Experi-
ments . . . . . . . . . . . . . . . . . . . . . . . . . 81
8.1.2 Coding BO by Feedback . . . . . . . . . . . . . . 83
8.1.3 BO by Only . . . . . . . . . . . 83
8.1.4 BO Coding in Concave Objects . . . . . . . . . . 84
8.1.5 Limitations of the Model . . . . . . . . . . . . . . 85
8.2 Comparison Between Model and Physiology . . . . . . 86
8.2.1 Input - Filtering - Processing . . . . . . . . . . . 86
8.2.2 Gestalt Rules and Intra- and Inter-Areal Con-
nectivity . . . . . . . . . . . . . . . . . . . . . . . 87
8.2.3 Correspondence of Network Areas and Visual
System Areas . . . . . . . . . . . . . . . . . . . . 878.2.4 Alternative Localisation of Feed-Forward Path
of Model in Ventral Pathway . . . . . . . . . . . 88
8.2.5 BO Feedback: Selective to Orientation . . . . . . 89
8.2.6 Predictions for Future Experiments . . . . . . . 90
8.2.7 Extension of Architecture: Indirect BO Feed-
back via Area-2 . . . . . . . . . . . . . . . . . . . 90
8.3 Comparison with Other Border-Ownership Models . . 91
8.3.1 Review of BO Models . . . . . . . . . . . . 91
8.3.2 Border-Ownership and Delays . . . . . . . . . . 92
8.4 Feedback and Figure-Ground-Segregation . . . . . . . . 94
8.4.1 Closed Loop . . . . . . . . . . . . . . . . . . . . . 94
8.4.2 Feedback Improves Figure-Ground-Segregation 94
8.4.3 Model of Dorsal and Ventral Pathway . . . . . . 95
8.4.4 Our Model and Bistable Stimuli . . . . . . . . . 96
9 Conclusions 99
Bibliography 100
Statement of Originality 108
Acknowledgements 110