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Biologically Inspired Intelligent Systems

Biologically Inspired Intelligent Systems. Lecture 4 Dr. Roger S. Gaborski. Human Visual System – sensory input. The cornea and lens together focus images on the retina. The retina is part of the central nervous system. http://faculty.washington.edu/chudler. Retina. Five types of neurons:

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Biologically Inspired Intelligent Systems

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  1. Biologically Inspired Intelligent Systems Lecture 4 Dr. Roger S. Gaborski Roger S. Gaborski

  2. Human Visual System – sensory input The cornea and lens together focus images on the retina. The retina is part of the central nervous system http://faculty.washington.edu/chudler Roger S. Gaborski

  3. Retina • Five types of neurons: • Photoreceptors • Bipolar cells • Ganglion cells • Horizontal cells • Amacrine • Information Flow: photoreceptor bipolar cell ganglion cell (outputs spike train) • Only the ganglion cells spike in the retina Roger S. Gaborski

  4. Photoreceptors:Rods and Cones • Two types of photoreceptors –rods and cones • Rods have very low spatial resolution, but extremely sensitive to light – allows us to see at night in starlight conditions • Cones have high spatial resolution, but relatively insensitive to light – responsible for our color vision Roger S. Gaborski

  5. Radio Frequency Spectrum • 531 559 • Cone Peak Responses Roger S. Gaborski

  6. Cone Responses Rods respond to a wide range of wavelengths Roger S. Gaborski

  7. Retina Diagram Roger S. Gaborski

  8. Fovea A few remarks about rod and cone spatial distribution Roger S. Gaborski www.undergrad.ahs.uwaterloo.ca/~tbolton/

  9. Roger S. Gaborski www.undergrad.ahs.uwaterloo.ca/ ~tbolton/

  10. Information Flow • Each photoreceptor (rod or cone) does not feed directly to the visual cortex • A number of photoreceptors are connected to a ganglion cell whose axon forms part of the optical nerve • The collection of photoreceptors connected to a particular ganglion cell forms that cell’s receptive field • A photoreceptor may be connected to more than one ganglion cell Roger S. Gaborski

  11. Receptive Fields www.yorku.ca/ eye Roger S. Gaborski

  12. Two Types of Retinal Ganglion Cell Receptive Fields On Center Off Surround (Maximum response: white spot on a black background Off Center On Surround (Maximum response: black spot on a white background Roger S. Gaborski

  13. Response of On Center to a Spot of Light • In darkness the ganglion cell fires at a ‘spontaneous’ rate • When RF is stimulated with a small diameter light spot the cell increases its firing rate – this continues to increase until the light reaches the edge of the on center region • When the spot is increased further and light strikes the inhibitory surround, the firing rate begins to decrease • It continues to decrease until the whole surround is covered with light Roger S. Gaborski

  14. Simple Center Surround Receptive Field MODEL: output Ganglion Cell : Rod or Cone Positive Weight Negative Weight Ganglion Cell Roger S. Gaborski

  15. Receptive Fields Different sizes, center on or off and overlap • - One photo-receptive cell (rod or cone) may be a member • of several receptive fields • Receptive fields are modeled by Difference of Gaussians • The output of the ganglion cells form the optic nerve Roger S. Gaborski

  16. SUMMARIZE: Retina - Receptive Field Model • Light travels through layers of the retina cells and strikes the cones and rods in the receptive layer • Spatially local collections of rods or cones form receptive fields • The receptive field of a neuron can be defined as the area on the retina from which the activity of a neuron can be influenced by the light on the retina area Roger S. Gaborski

  17. Models – Receptive FieldsImplementation W1 W2 w3 Analog inputs and outputs f Positive weights – excitatory Negative weights - inhibitory Roger S. Gaborski

  18. Linear-Nonlinear Model (LN) • Early visual processing • Response of neuron: • Dot product of image and linear filter • Output of linear filter is passed to a non-linear function • Output of non-linear filter is neuron firing rate Roger S. Gaborski

  19. Neuron Firing Rate Filter Output Basic Neuron Models Output Spikes Fires strongest when Image matches linear filter Linear Filter Non-linear Function Roger S. Gaborski

  20. Simplified Example - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Roger S. Gaborski

  21. Simplified Example – case 1 Point by point multiply and sum results - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Linear Filter Image Maximum Response because - * - = + and + * + = + (large positive number) .* = Roger S. Gaborski

  22. Simplified Example – case 2 Point by point multiply and sum results ++++++++++++++++++ ++++++++++++++++++ ++++++++++++++++++ +++++ - - - - - +++++ +++++ - - - - - +++++ +++++ - - - - - +++++ +++++ - - - - - +++++ +++++ - - - - - +++++ ++++++++++++++++++ ++++++++++++++++++ ++++++++++++++++++ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Linear Filter Image Minimum Response because - * + = - and + * - = - (large negative number) * = Roger S. Gaborski

  23. Filter Responses Maximum Neuron Response (large positive number) Minimum Neuron Response (large negative number) Linear Filter Image key: black = -1, white = +1 Roger S. Gaborski

  24. Basic Neuron Models Squaring function Neuron Firing Rate Output Spikes Filter Output 0 Fires strongest when Image matches linear filter (no output for negative filter output) Linear Filter Non-linear Function Roger S. Gaborski

  25. Basic Neuron Models Squaring function Neuron Firing Rate Output Spikes Filter Output Fires strongest when Image matches linear filter Linear Filter Non-linear Function Roger S. Gaborski

  26. Nonlinear function: y=x2 x: Filter output value y: neuron firing rate Roger S. Gaborski

  27. Matlab Examples • Create a Difference of Gaussians (DoG) Receptive Field • One Dimensional Gaussian Function: F = a*exp( -(x-b)2 /2*c2) Where: a is the maximum value, b is the position of the center c is the standard deviation Roger S. Gaborski

  28. Let b = 0 • F = a*exp( -x2/2*c2) Roger S. Gaborski

  29. One dimensional RF • F = a*exp( -x2/2*c2) • x1 = linspace(-63, 64, 128); • imageSize = 128; • sigmaex = .095*ReceptiveFieldSize; • sigmainh = .19*ReceptiveFieldSize; Roger S. Gaborski

  30. Excitatory Gaussian: • a = 7.5 • Fe = a*exp( -1*( x1 .* x1 )./(2*sigmaex*sigmaex)); • Inhibitory Gaussian: • b = 1.95 • Fi = b*exp( -1*( x1 .* x1 )./(2*sigmainh*sigmainh)); Roger S. Gaborski

  31. Difference of Gaussians Dog128 =.0013*(Fe - Fi); Roger S. Gaborski

  32. Difference of Gaussians (DoG) Receptive Field Model First Gaussian Second Gaussian Roger S. Gaborski

  33. Roger S. Gaborski

  34. Roger S. Gaborski

  35. We Need a Two Dimension DoG Receptive Field Roger S. Gaborski

  36. Positive and Negative Response Roger S. Gaborski

  37. Increase Inhibitory Contribution Roger S. Gaborski

  38. Two Dimensional RF For a one dimensional 128 element RF we used x1: x1 = linspace(-63, 64, 128); A two dimensional 128 x 128 will require both x and y indices. The 2 dimensional index matrix can be generated using the Matlab function meshgrid A two dimensional Gaussian function is needed to generate the Two dimensional DoG receptive field. Roger S. Gaborski

  39. Suggested Parameters These are only suggested parameters. Parameters can be modified to obtain a more realistic DoG receptive field Roger S. Gaborski

  40. Homework #4: Nine Teams, Three Members Each Teams: Receptive Fields Matlab Models 1and 2 128x128, 8x8 3 and 4 128x128 and 16x16 5 and 6 128x128 and 32x32 7, 8 and 9 128x128 and 64x64 Tuesday’s Presentation A representative from each team will present the teams results, including Matlab code and 3 dimensional figures of receptive fields Roger S. Gaborski

  41. Positive Response Negative Response Roger S. Gaborski

  42. Response of RF • The G32 receptive field will have the greatest response to circular objects that are the same size as the circular positive response region of the RF. Roger S. Gaborski

  43. Receptive Field Response Roger S. Gaborski

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