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1 A ON-Center OFF-Center DeAngelis, Ohzawa, Freeman 1995

2 Nobel Prize 1981: Physiology and Medicine D.H. Hubel and T.N. Wiesel T.N. Wiesel D.H. Hubel

3 V1/V2: (spikes) Display? Amplifiers and Filters

4 V1 - simple cell Simple Cell Complex Cell MT t (ms) x (deg) ( DeAngelis et al )

5 Hubel & Wiesel Model Simple Cells Complex Cells

6 LGN output is nonlinear Troyer and Miller, 1998

7 LGN output is nonlinear, but simple cell is linearized Troyer and Miller, 1998 Push-Pull Amplifier, 2007, 5, p.152

8 Simple Cells are Linearized by Push-Pull Organization T.W. Troyer et al G Retina ON OFF B Photoreceptors OFF ON LGN V1 Simple

9 Spatial Frequency High Medium Low

10 Ringach DL et al. 1997

11 V Blob

12 Orientation and Spatial Frequency Tunings [spikes/sec] [deg] [cycles/deg]

13 (Fourier Transform) Any arbitrary image is a sum of many sine waves of different spatial frequencies and orientations.

14 (Fourier Transform) 1/ f - f 0 f frequency 1/ f 0 θ f Gabor Function 0 f θ

15 (Fourier Transform) Einstein reconstructed from about 30 sine wave components. Einstein reconstructed from several hundred sine wave components.

16 V1 Collected in Ohzawa lab ON region OFF region Visual angle: 10 degs

17 V1 ON OFF 10

18 Decomposing images into activities of a set of neurons with Gabor-like RF. Each area of the visual field has such a set of visual neurons.

19 Reverse Correlation Reverse Correlation Jones & Palmer 1987 Ohzawa et al. 1990, 1996 DeAngelis et al. 1993

20 Reverse Correlation Spike-Triggered Average (STA) of stimuli Jones & Palmer 1987 Ohzawa et al. 1990, 1996 DeAngelis et al. 1993

21 ON OFF 10 Animation

22 ... 2 orientation ; spatial frequency phase amplitude

23 G(x, y) = e Gabor, D (1946). Theory of communication. J. IEE 93: y Gabor Wavelet x 2 +y 2 2σ 2 cos(2πfx + φ) x Dennis Gabor Nobel Prize 1971 in Physics

24 Kay/Gallant et al. 2008, Nature

25 Gabor Wavelet Pyramid Representation (log) FOV: field of view

26

27 Simple and Complex Cells of V1 Represent Local Fourier Components A pair of simple cells represents both the amplitude and phase θ of a Fourier component. Firing rate of sine-phase simple cell Rodd Complex cell response represents the absolute value of a complex Fourier component: Rcx = (Rodd 2 + Reven 2 ) 0.5 θ Firing rate of cosine-phase simple cell Reven

28 V1 - complex cell Simple Cell Simple Cell Complex Cell MT Complex cell ( DeAngelis, Ohzawa, Freeman )

29 Simple and Compex Cell Models Simple Cell Complex Cell

30 V1 (V1) Wavelet V1.. ( )..

31 8px JPEG "Receptive Fields" for JPEG 8px 8px 8px Minimum Coding Unit (MCU) JPEG encoding process divides an image into 8x8 pixel blocks. JPEG 8x8

32 DCT DCT (Discrete Cosine Transform) Basis Functions v\u

33 What about the time domain?

34 Reverse Correlation Spike-Triggered Average (STA) of stimuli Jones & Palmer 1987 Ohzawa et al DeAngelis et al. 1993

35 Time [msec] 0 Space [deg] 6 Temporal Frequency [Hz] Spatial Frequency [c/deg]

36 Time [msec] Space [deg] 7 Temporal Frequency [Hz] Spatial Frequency [c/deg]

37 Direction-Selective V1 (Fx-Ft) Blob) (Fx-Fy-Ft) Blob) Complex Cell

38 V1 (Fx-Fy-Ft) Blob)

39 Space-Time (XYT) Frequency Receptive Field of V1 Neuron Space-Time Frequency Space-Time I made up these words yesterday :>> Elementary V1 Signal A Movie Atom It is a "blob" in the spatial frequency-time frequency (Fx-Fy-Ft) space.

40 Elementary V1 Signal A Movie Atom

41 Can it be done by a simple stupid computation that a single neuron can handle? Yes. just with: Additions and subtractions, via various synaptic connection strengths, and with different time delays.

42 x(t) input h(t): impulse response y(t) output y(t) = x(t) * h(t) -- convolution input image Receptive Field neural response

43 FIR (Finite Impulse Response) Filter For One RF location Recent input Delay Line Past input Input D D D D D D Weights + Output

44 FIR OK Past Time Delay Line Now Weighted Sum over Space-Time X 1 X 2 X 3 X 4 X 5 X 6 Space

45 VNS: Visual Neuron Simulator

46

47

48 Simple and Compex Cell Models Simple Cell Complex Cell

49 V1 90 direction-selective simple cells 2 Adelson, Bergen 1985

50 Simple: Complex: x 2 +y 2 S(x, y) = e 2σ 2 cos(2πfx + φ) C(x, y) = e x 2 +y 2 σ 2 cos 2 (2πfx + φ) + e x 2 +y 2 σ 2 sin 2 (2πfx + φ) = e x 2 +y 2 σ 2 XT Quadrature pair; 90

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