1 Computational Modelling of Visual Illusions Astrid Zeman, B.Eng (Software Hons I) Dip. Eng. Prac Department of Cognitive Science ARC Centre of Excellence in Cognition and its Disorders Faculty of Human Sciences Macquarie University, Sydney, Australia This thesis is presented for the degree of Doctor of Philosophy (PhD) February, 2015 2 Table of Contents Computational Modelling of Visual Illusions ......................................................................... 1 Thesis Abstract .......................................................................................................................... 5 Statement of Candidate ............................................................................................................ 6 Acknowledgments ..................................................................................................................... 7 1 Introduction ......................................................................................................................... 9 1.1 General overview ........................................................................................................ 10 1.2 Defining illusions ........................................................................................................ 14 1.2.1 A general definition ............................................................................................... 14 1.2.2 Illusions as source reconstructions ........................................................................ 16 1.3 Categorising illusions ................................................................................................. 19 1.4 Aims, strengths and limitations of models .................................................................. 22 1.4.1 Limitations of Models ........................................................................................... 22 1.4.2 From theories to models and back ......................................................................... 25 1.5 Marr’s different levels of description .......................................................................... 26 1.6 Biological analogies ................................................................................................... 28 1.6.1 Historical influences from biology ........................................................................ 28 1.6.2 Biologically inspired systems ................................................................................ 31 1.7 Computational models of vision .................................................................................. 32 1.7.1 Deterministic versus probabilistic ......................................................................... 32 1.8 Pre-cortical models ..................................................................................................... 34 1.8.1 Historical context .................................................................................................. 34 1.8.2 Current models applied to illusions ....................................................................... 36 1.8.3 Our model selection: Exponential filter family model .......................................... 38 1.9 Ventral stream models ................................................................................................ 40 1.9.1 General properties ................................................................................................. 40 1.9.2 Hierarchical models in historical context .............................................................. 42 1.9.3 Our model selection: feed-forward model HMAX ............................................... 43 1.9.4 Feedback models ................................................................................................... 45 1.10 Existing computational models of visual illusions .................................................... 46 3 1.10.1 How to model illusions ........................................................................................ 46 1.11 Scope of this thesis .................................................................................................... 48 1.12 Thesis layout ............................................................................................................. 49 1.13 References ................................................................................................................. 49 2 Study 1 ............................................................................................................................... 60 Abstract ................................................................................................................................ 61 2.1 Introduction ................................................................................................................. 61 2.2 Methods ....................................................................................................................... 65 2.2.1 HMAX Layer Descriptions ................................................................................... 66 2.2.2 Task Description .................................................................................................... 68 2.2.3 Experimental Setup ............................................................................................... 68 2.3 Results ......................................................................................................................... 70 2.3.1 Experiment I: Control ............................................................................................ 70 2.3.2 Experiment II: Illusion Effect ................................................................................ 71 2.3.3 Experiment III: Illusion Strength Affected by Angle ............................................ 73 2.4 Discussion ................................................................................................................... 76 2.5 References ................................................................................................................... 84 2.6 Appendix: Determining whether low spatial frequency information may be influencing the SVM ................................................................................................................................ 87 2.6.1 Stage I: Extracting the highest weights entering the SVM layer .......................... 87 2.6.2 Stage II: Identify the spatial scale of the top contributing features in C2. ............ 89 3 Study 2 ............................................................................................................................... 92 3.1 Abstract ....................................................................................................................... 93 3.2 Introduction ................................................................................................................. 94 3.3 Materials and Methods ............................................................................................... 99 3.3.1 Computational model: HMAX .............................................................................. 99 3.3.2 Stimuli: Training and test sets (Control and Müller-Lyer) .................................. 100 3.3.3 Procedure: Learning, parameterization, illusion classification ........................... 103 3.4 Results ....................................................................................................................... 104 3.4.1 Experiment I: Classification of ML images after each level of HMAX ............. 104 3.4.2 Experiment II: HMAX classification of ML images with reduced variance ...... 110 4 3.5 Discussion ................................................................................................................. 112 3.6 References ................................................................................................................. 117 4 Study 3 ............................................................................................................................. 121 Abstract .............................................................................................................................. 122 4.1 Introduction ............................................................................................................... 123 4.2 Material & Methods .................................................................................................. 129 4.2.1 Stimuli ................................................................................................................. 129 4.2.2 Model ................................................................................................................... 132 4.3 Results ....................................................................................................................... 138 4.4 Discussion ................................................................................................................. 144 4.5 References ................................................................................................................. 154 5 Discussion & Conclusion ................................................................................................ 158 5.1 Chapter overview ...................................................................................................... 159 5.2 Summary and integration of studies .......................................................................... 159 5.2.1. Each of the studies in summary .........................................................................