SOME RELATIONS BETWEEN VISUAL PERCEPTION AND NON- LINEAR PHOTONIC STRUCTURES

Transcription

1 SOME RELATIONS BETWEEN VISUAL PERCEPTION AND NON- LINEAR PHOTONIC STRUCTURES J.A. Martin-Pereda E.T.S. Ingenieros de Telecomunicación Universidad Politécnica de Madrid SPAIN PHOTOPTICS February, BARCELONA. SPAIN jamp'13 1

2 MAIN OBJECTIVE To present a way to emulate some functions of the mammalian visual system and a model to analyze subjective sensations and visual illusions TOPICS TO BE COVERED 1. Summary of Sensing in Living Bodies 2. Mammalian Visual System: Retina and Visual Cortex 3. Photonic devices with non linear behaviour 4. Retina simulation: motion detection. Ideas from the visual Cortex. 5. Geometrical and Visual Illusions: Analysis of the Müller-Lyer, Zöllner, Wundt and Hering Illusions. 6. Conclusions jamp'13 2

3 SOME PREVIOUS HISTORY TO REMEMBER jamp'13 3

4 Photonics s. XXI LASER: Opt. Coms., Opt. Comp., Imag. Proc.,... Electronics s. XX MAXWELL Ecs: Radio, TV, Radar,... Electricity Magnetism Solid State Optics s. XIX jamp'13 4

5 ? (Neuronics?) Photonics s. XXI LASER: Opt. Coms., Opt. Comp., Imag. Proc.,... Electronics MAXWELL Ecs: Radio, TV, Radar,... Biology s. XX Electricity Magnetism Solid State Optics s. XIX jamp'13 5

6 Possible ways for working Photonics as a tool to understand biology. Biology as a source of ideas for Photonics. Photonics as a source of concepts for Biology and viceversa. jamp'13 6

7 LIVING BODIES AND ARTIFICIAL SYSTEMS jamp'13 7

8 MAIN DIFFERENCE BETWEEN SENSING IN LIVING BODIES AND IN ARTIFICIAL SYSTEMS: LIVING BODIES ARE ABLE TO INTERPRET STIMULI, THAT IS, ENVIRONMENTAL STIMULI AND THE RESPECTIVE RESPONSES OF SENSE ORGANS CORRESPOND TO STATEMENTS BY THE SUBJECT ABOUT HIS SENSATIONS AND PERCEPTIONS. jamp'13 8

9 OUTER WORLD BRAIN ACCIDENTAL ASPECTS OF STIMULUS OBJECT ESSENTIAL FACTS ENVIRONMENT FILTER jamp'13 9

10 Objective sensations Subjective sensations Rel. env. Interaction with senses Training Sensory Impressions CNS Perception Sensory stimuli Excitation in sensory nerves Memory Prev. exp. External Phenomena jamp'13 10

11 EXAMPLE (according to P. MONDRIAN) jamp'13 11

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18 COUNTEREXAMPLE (according to R. MAGRITTE) jamp'13 18

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20 Mammalian Visual System: Retina and Visual Cortex Building blocks Building structures Signals involved Main characteristics jamp'13 20

21 Building blocks: Neurons and Receptors jamp'13 21

22 Different neurons from the mammalian cortex jamp'13 22

23 sensory stimuli impulse initiation Different types of sensory receptor cells in vertebrates jamp'13 23

24 Building structures: Circuits and Networks jamp'13 24

25 The simplest types of microcircuits jamp'13 25

26 Basic circuits, corresponding to different cortex regions, are similar in outline and in several details. Common principles: In each region there is an initial stage of input processing, a second stage of intrinsic operations within the synaptic circuits of the region, and a final stage of output control. jamp'13 26

27 Receptor Cell Receptor Cell Bipolar Cell Horizontal Cell Periglomerular Cell Ganglion Cell Amacrine Cell Granule Cell Mitral Cell (a) RETINA (b) OLFACTORY BULB jamp'13 27

28 CONVERGENCE AND DIVERGENCE Once the superficial sensing units have received the external signal, a first processing step is carried out in a few cell layers. Usually, the number of sensing cells, in the first stratum, is much larger than the corresponding to neurons at successive layers. jamp'13 28

29 Approaching to the mammalian retina: a model jamp'13 29

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31 The neural chain: (a) input part of the visual system, (b) convergence and divergence jamp'13 31

32 t R.L. R 1 H R 2 B 1 A B 2 O.L. I.L. Dowling s model of the mammalian retina G 1 G 2 G 3 G.L. jamp'13 32

33 Tools for modeling the mammalian retinal: non linear photonic devices jamp'13 33

34 1 nj 1 pj 20 ps Semiconductor Electronic Devices LCLV 1 fj PTS FP NbO 3 Li Hybrid FP 20 fj GaAs MQW, FP SEED GaAs neuron 100 photons (λ 0 = 1 μm) 1 aj 1 fs 1 ps 1 ns 1 μs 1 ms 1 s based on P.W. Smith. Bell Syst. Tech. Jour jamp'13 34

35 Input Beam p-algaas V - + Multiquantum well (GaAs-AlGaAs) n-algaas SEED I out ( W) ON Output Beam Output Beam OFF B A Input Beam I in ( W) jamp'13 35

36 Basic configurations of FP laser diode amplifiers (a) transmission and (b) reflection. I bias Optical input Optical output Optical output (a) I bias Optical input Optical output Optical output (b) jamp'13 36

37 Fabry-Perot Laser Diode Amplifiers They exhibit Optical Bistability (OB) under external signal injection. Dispersive Optical Bistability. Presence of Optical Gain. Low Input Power Requirements. Different operating Wavelengths. Easy to obtain. jamp'13 37

38 Bistability in FPLDAs P out (a.u.) Reflection Transmission 0.97 I th 0.97 I th 0.94 I th 0.91 I th 0.94 I th 0.91 I th P in (a.u.) P in (a.u.) Transmission: Anticlockwise bistable loops. Reflection: Anticlockwise, X- and clockwise bistable loops. jamp'13 38

39 Individual Responses Reflection Transmission Laser1 Laser Parameter Laser2 350 Cavity Length (µm) Left/Right Facet Reflectivity Confinement Factor Linear Material Gain Coeff. (cm 2 ) Linewidth Enhancement Factor Fixed Internal Loss (1/m) Bias/Threshold current π Initial frequency jamp'13 detuning π 39

40 Laser 1 Laser 2 I bias1 I bias2 Optical input Optical output I ref (a) Laser 1 Laser 2 Optical input I bias1 I bias2 Optical output (b) I ref Possible configurations for feedback in laser structures, (a) with transmitting signal, and (b) with reflecting signal from the first laser. jamp'13 40

41 Laser 1 Laser 2 I 1 + I 2 g I bias1 I bias2 O 1 I ref1ected jamp'13 41

42 h I 1 I 2 g Q Basic unit to configurate the main architecture: Optical Programmable Logic Cell (OPLC) P O 2 O 1 jamp'13 42

43 Block Diagram a Q-device Logic Table for the OLG. h 0 h 1 h 2 O 1 AND OR ON Block Diagram of P-Device. g 0 g 1 g 2 g 3 g 4 O 2 OR NAND NOR AND OR jamp'13 43

44 Block Diagram a Q-device Logic Table for the OLG. h 0 h 1 h 2 O 1 AND OR ON Transfer characteristic P out (P in ) Fabry-Perot Laser Diode DFB Laser Diode jamp'13 44

45 Block Diagram of P-Device. Logic table for OLG. g 0 g 1 g 2 g 3 g 4 O 2 OR NAND NOR AND OR FP-LD configuration jamp'13 45

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47 Schematic of the model simulated by VPI_ComponentMaker th software tool for Q-device I 1 I 2 I 1 +I 2 +h O 2 h jamp'13 47

48 Schematic of the model simulated by VPI_ComponentMaker th software tool for P-device I 1 I 1 +I 2 +g O 1 I 2 g jamp'13 48

49 INSTABILITIES: τ e OB CONFIGURATION τ i jamp'13 49

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51 Characteristics of the output signals, according to the delay times. t p τ e τ i τ i /τ e Period τ e = external delay time τ e = internal delay time jamp'13 51

52 Output signal with a period of 280. Output signal with a period of 140. Output signal with a period of 70 jamp'13 52

53 APPLICATION TO THE MAMMALIAN RETINA jamp'13 53

54 Information about the intensity of each one of the scene details are transferred from the third retina layer to following levels after a conversion from intensity level to frequency. Lower intensities correspond with lower frequencies. R 1 H R 2 B 1 t A B 2 G 1 G 2 G 3 R.L. O.L. I.L. G.L. jamp'13 54

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58 FIRST STEPS TOWARDS THE DETECTION OF SOME GENERAL PROPERTIES OF IMAGES jamp'13 58

59 Control signal Input signals XOR Output signals Control signal 59 jamp'13 59

60 (a) Symmmetry: A logic "0" is always obtained at the 6th layer (b) Asymmetry: A logic "1" is always obtained at the 6th layer jamp'13 60

61 Other Asymmetries A logic "1" is obtained at the center of an even row jamp'13 61

62 Approaching to the visual cortex: signals processing and sensing jamp'13 62

63 Motor control of mouth and lips Broca s area Motor cortex Primary gustatory cortex Primary auditory cortex Wernicke s area Visual cortex Brodmann s cytoarchitectural map of the human cerebral cortex jamp'13 63

64 (1) Information is always transferred in a parallel way. As a consequence, the number of physical paths is very high. jamp'13 64

65 (2) Each small piece of information goes to a particular area in the cortex where is analyzed with respect to other inputs and memories. jamp'13 65

66 Response (frequency of action potentials) S 0 S (Stimulus intensity at receptor) Behavior of the living beings sensors depolarization Receptor potential Stimulus intensity Action potentials threshold time time time jamp'13 66

67 THE CASE OF THE VISUAL CORTEX jamp'13 67

68 Highly schematic view of the projections from the retina to various visual areas of the cerebral cortex jamp'13 68

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70 PROJECTIONS FROM THE RETINA TO THE OCULAR DOMINANCE COLUMNS jamp'13 70

71 Cortical blobs or pegs I C I C ca. 500 µm I II III IV a IV b IV c-alpha IV c-beta IV a V VI Cortical orientation columns Information about different line orientations is transferred to selected areas at the visual cortex. These areas become excited by this information and living beings get a stimulus concerning that orientation in the visual scene. jamp'13 71

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73 Each particular orientation, or each particular shape, goes to a precise area in the V1 area of the visual cortex. There is a certain type of mapping from the scene to the cortex: distributed measurements are transferred through a multiplexed system jamp'13 73

74 Visual cortex, at area V1, gets a virtual image of the real image appearing in the scene as seen by the living beings. jamp'13 74

75 Maps of the Visual Field onto Area V1 When a pattern of flickering lights is shown in the visual field of a macaque, a map of striate cortex is revealed by 2-DG uptake jamp'13 75

76 Information about different visual information is transferred to selected areas at the visual cortex. These areas become excited by this information and living beings get a stimulus concerning that information in the visual scene jamp'13 76

77 Responses to faces in inferotemporal cortex (a) The location of area IT in the inferior temporal lobe (b) Responses of a face cell. The histograms show the response of a neuron (spikes/sec) in monkey inferotemporal cortex to different views of a monkey's head. The horizontal bar under each histogram indicates when the stimulus was present. jamp'13 77

78 Although different types of information processing appear in the retina and visual cortex this processing is the result of interchange of information among neurons in the same level. No feedback processes appears in the neural network. jamp'13 78

79 Any biological information processing is performed by non linear effects. jamp'13 79

80 The number of levels needed to go from receptor neurons in the retina to V1 layer in the cortex is lower than 15. jamp'13 80

81 A possible way to implement a similar philosophy is with WDM techniques: a large number of information channels may go through the same physical path. jamp'13 81

82 Photonic processing subsystem based on visual cortex architecture jamp'13 82

83 Processing of data Extension of lines in each direction Distance between lines in each direction Main direction in object Analysis of orientations in each area Image details: orientations appearing in the subject Image division in small areas IMAGE TO BE ANALYZED jamp'13 83

84 FEATURE INTEGRATION FRAMEWORK Integrated Map Attention window Color Size Orientation Stimulus jamp'13 84

85 DISTRIBUTION SYSTEM (1) HS DS VS INFORMATION CORRESPONDING TO DIRECTION CHARACTERISTICS jamp'13 85

86 Example: transferring information from a 2 - D image jamp'13 86

87 DATA OBTAINED FROM LETTER F (JUST 2 DIRECTIONS) jamp'13 87

88 DATA OBTAINED FROM LETTER H (JUST 3 DIRECTIONS) jamp'13 88

89 Distribution system... Signal conversion i/p... Wavelength conversion λ 1 λ 2 λ 3... Mux λ n λ 1, λ 2,..., λ n Demux λ 1 λ 2 λ 3... λ n Signal conversion p/c Wavelength conversion Redistribution system GENERAL STRUCTURE OF THE SYSTEM jamp'13 89

90 Sampling (4 directions) Redistribution (4 directions) Threshold (1.5 p.e.) 90

91 SOME CONCLUSIONS Once the signal is perceived, similar circuits are in charge of the information processing, without taking into account the type of sensed signal. Information is always analyzed, just by hardware tools, as a function of the resulting frequency and no of its absolute value. Transferring of information is by parallel paths. Signals travel along long paths without change in their properties. Each type of information is processed at specific places in the cortex jamp'13 91

92 SOME POINTS TO BE CONSIDERED IN THE NEXT FUTURE: At a high level, in the human brain, many cells cooperate in a purposeful manner to produce perception, thinking, speech, writing and many other phenomena. In all these cases, new qualities emerge at a macroscopic level, qualities that are absent at the microscopic level of the individual jamp'13 92

93 ON SUBJECTIVE IMPRESSIONS OR HOW TO PUT NUMBERS TO VISUAL ILLUSIONS jamp'13 93

94 Müller-Lyer Illusion Effect of angles on the length sensation jamp'13 94

95 Hering s Illusion Zöllner Illusion jamp'13 95

96 Extended Parallelism Illusion from the Zöllner effect jamp'13 96

97 Analysis of the Müller-Lyer Illusion jamp'13 97

98 MÜLLER-LYER ILLUSION A B Λ n 1 = n 1 σ σ B n B n λ λ 2 n n Λ: subjective length n: total number of excited columns σ Bn : total number of bits obtained from the nth column λ n : distance of column n to the centre of image in column units jamp'13 98

99 Λ n 1 = n 1 σ σ B n B n λ λ 2 n n 45º 45º 45º 45º A B A B Col. num Bits Tot. Bits 8 8 Tot. Col. 4 6 Length 4 4 Λ 2 x 13/7 = x 23/9 = 5.1 ( )/( ) jamp'13 99

100 ANALYSIS OF THE ZÖLLNER ILLUSION jamp'13 100

101 ANALYSIS OF PARALLELISM Main factor: symmetry with respect to the parallel line located at the middle between the two parallel lines. Main influences: location and angles - weight - of the intersecting lines. jamp'13 101

102 EXPERIMENTAL MEASUREMENT OF THE MÜLLER-LYER ILLUSION (Black and blue curves correspond to two different conditions of the experiment)(from R. Gregory. Eye and Brain. 1990) jamp'13 102

103 MAIN RULES: 1. Take the principal symmetry axis 2. Divide each region in sensory zones 3. Analyze each zone with respect to the principal axis 4. Construct the sensory matrix with elements from each zone 5. Apply the main symmetry operation to overlap different motives 6. Normalize 7. Reduce to a 1 x 1 matrix jamp'13 103

104 Symmetry operations in two sets of parallel lines with small crossing lines α C 2 (a) D 2 T (b) C 2 = twofold axis T = translation D 2 = inversion 104

105 σ αk = PROPOSED FORMULAE: { } ω δ S ω δ + α k n i = 1 i i k n j = 1 j j α ω = line weight δ = distance to the central line S = symmetry operation i, j = each one of the lines α, k = each one of the unit intervals sensory matrix: σ α = [σα1, σα2,..., σαk,... ] reference matrix: α = [ α1, α2,..., αk,... ] normalized matrix: π α = [σ α1 / α1, σ α2 / α2,..., σ αk / αk,... ] reduced matrix: π β = [π α1 -π α2,..., π αk -π α(k+1),... ] If Π γ = [ 0,0,... ] If Π γ [ 0,0,... ] parallelism is seen parallelism is not seen { is a similar effect corresponding to the parallel lines} jamp'13 105

106 Subjective parallelism: Π L P 1 C 2 L P 1 σ 1 : (6x1+9x0.5) ; (6x1+7x0.5) ; (6x1+5x0.5) ; (6x1+3x0.5) σ 2 σ T T : (6x1+9x0.5) ; (6x1+7x0.5) ; (6x1+5x0.5) ; (6x1+3x0.5) σ 1 + C 2 σ 2 [ ; ; ; ] [ ] 1 + C 2 2 [ 6+6; 6+6; 6+6; 6+6 ] [ ] π i = ( T / σ T ) i [ ] π l = π i π i-1 : π m = π l π l-1 : π n = π m π m-1 : 0.02 Π jamp'13 106

107 L 1 P 1 2 C 2 L P 1 σ 1 : (6x1+9x0.5); (6x1+7x0.5); (6x1+5x0.5); (6x1+3x0.5) σ 2: (6x1+3x0.5); (6x1+5x0.5); (6x1+7x0.5); (6x1+9x0.5) σ T σ 1 + C 2 σ 2: ; ; ; T 1 + C 2 2 : 6+6 ; 6+6 ; 6+6 ; π i = ( T / σ T ) i : π l = π i π i-1 : π m = π l π l-1 : π n = π m π m-1 : 0.00 Π jamp'13 107

108 Analysis of the Hering and Wundt Illusions jamp'13 108

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111 R i D p T p (affected by the corresponding weight) jamp'13 111

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122 REFERENCES D.H. Hubel and T.N. Wiesel, "The Ferrier Lecture: Functional architecture of macaque monkey visual cortex", Proc. R. Soc. London. B 198, 1-59 (1977). G.M. Shepherd, The Synaptic Organization of the Brain. Oxford Neuro-vision Systems. Principles and Applications. Eds.: Madam M. Gupta and George K. Knopf. IEEE Press. New York A. González-Marcos & J.A. Martín-Pereda, Digital Chaos Synchronization In Optical Networks. In OPTICAL NETWORK DESIGN AND MODELLING II. Eds.: G. de Marchis y R.Sabella. Kluwer Academic Publishers, pp A. González-Marcos & J.A. Martín-Pereda, Analysis of irregular behaviour on an optical computing logic cell. Optics & Laser Technology, 32, (2000) A. González-Marcos and J.A. Martín-Pereda, Method to analyze the influence of hysteresis in optical arithmetic units. Optical Engineering, 40, (2001) A. González-Marcos and J.A. Martín-Pereda, "A New Approach to a Model of the Mammalian Retina with Optically programmable Logic Cells". 1st. International IEEE EMBS Conference on Neural Engineering. Capri (Italia) de marzo, ISBN: jamp'13 122

123 Children of the Brain. Montreal Neurological Institute Look, what thy memory cannot contain Commit to these waste blanks, and thou shall find Those children nursed, delivered from thy brain To take a new acquaintance from thy mind (W. Shakespeare) jamp'13 123