A ON-Center OFF-Center DeAngelis, Ohzawa, Freeman 1995
Nobel Prize 1981: Physiology and Medicine D.H. Hubel and T.N. Wiesel T.N. Wiesel D.H. Hubel
V1/V2: (spikes) Display? Amplifiers and Filters
V1 - simple cell Simple Cell Complex Cell MT t (ms) x (deg) ( DeAngelis et al. 1995 )
Hubel & Wiesel Model Simple Cells Complex Cells
LGN output is nonlinear Troyer and Miller, 1998
LGN output is nonlinear, but simple cell is linearized Troyer and Miller, 1998 Push-Pull Amplifier, 2007, 5, p.152
Simple Cells are Linearized by Push-Pull Organization T.W. Troyer et al. 1998 G Retina ON OFF B Photoreceptors OFF ON LGN V1 Simple
Spatial Frequency High Medium Low
Ringach DL et al. 1997
V Blob
Orientation and Spatial Frequency Tunings [spikes/sec] 60 40 80 20 40 0 0 0 45 90 135 180 0.04 0.12 0.34 1.00 [deg] [cycles/deg]
(Fourier Transform) Any arbitrary image is a sum of many sine waves of different spatial frequencies and orientations.
(Fourier Transform) 1/ f - f 0 f frequency 1/ f 0 θ f Gabor Function 0 f θ
(Fourier Transform) Einstein reconstructed from about 30 sine wave components. Einstein reconstructed from several hundred sine wave components.
V1 Collected in Ohzawa lab 2004-2009 ON region OFF region Visual angle: 10 degs
V1 ON OFF 10
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.
Reverse Correlation Reverse Correlation Jones & Palmer 1987 Ohzawa et al. 1990, 1996 DeAngelis et al. 1993
Reverse Correlation Spike-Triggered Average (STA) of stimuli Jones & Palmer 1987 Ohzawa et al. 1990, 1996 DeAngelis et al. 1993
ON OFF 10 http://ohzawa-lab.bpe.es.osaka-u.ac.jp/resources/movies/rf/manygaborsatoneplace.mov Animation
... 2 orientation ; spatial frequency phase amplitude
G(x, y) = e Gabor, D (1946). Theory of communication. J. IEE 93:429 459. y Gabor Wavelet x 2 +y 2 2σ 2 cos(2πfx + φ) x Dennis Gabor Nobel Prize 1971 in Physics
Kay/Gallant et al. 2008, Nature
Gabor Wavelet Pyramid Representation (log) FOV: field of view
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
V1 - complex cell Simple Cell Simple Cell Complex Cell MT Complex cell ( DeAngelis, Ohzawa, Freeman. 1995 )
Simple and Compex Cell Models Simple Cell Complex Cell
V1 (V1).......Wavelet V1.. ( )..
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
DCT DCT (Discrete Cosine Transform) Basis Functions v\u
What about the time domain?
Reverse Correlation Spike-Triggered Average (STA) of stimuli Jones & Palmer 1987 Ohzawa et al. 1990 DeAngelis et al. 1993
400 25 Time [msec] 0 Space [deg] 6 Temporal Frequency [Hz] -1.2 0 1.2 Spatial Frequency [c/deg]
250 25 Time [msec] Space [deg] 7 Temporal Frequency [Hz] 0 1.04 Spatial Frequency [c/deg]
Direction-Selective V1 (Fx-Ft) Blob) (Fx-Fy-Ft) Blob) Complex Cell
V1 (Fx-Fy-Ft) Blob)
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.
Elementary V1 Signal A Movie Atom
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.
x(t) input h(t): impulse response y(t) output y(t) = x(t) * h(t) -- convolution input image Receptive Field neural response
FIR (Finite Impulse Response) Filter For One RF location Recent input Delay Line Past input Input D D D D D D Weights + Output
FIR OK Past -2-3 -3-2 2-2 -3 2 3 Time Delay Line Now -2-3 -3-2 -2-3 -3-2 2 2 2-2 2 3 3 2 2 3 3 3 2 3 2 + Weighted Sum over Space-Time X 1 X 2 X 3 X 4 X 5 X 6 Space
VNS: Visual Neuron Simulator
Simple and Compex Cell Models Simple Cell Complex Cell
V1 90 direction-selective simple cells 2 Adelson, Bergen 1985
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