Retina Tues. Jan. 23, 2018 1 Layers of the Retina (rods and - PowerPoint PPT Presentation

COMP 546 Lecture 4 Retina Tues. Jan. 23, 2018 1

Layers of the Retina (rods and cones) light signals To the brain 2

Photoreceptor (rod and cone) density This is the left eye. Why? Cone density is very high in the center of the field of view. This area of the retina is called the fovea . 3

Responses of cells in the Retina continuous discrete (“spikes”) 4

ASIDE: neural coding using spikes (retinal ganglion cells) I mentioned this in lecture 0. 5

Response of neuron (measured by experimenter) 0 Membrane depolarized potential (mV) -70 average hyperpolarized time 6

Signalling between cells at synapse (not measured by experimenter) Release rate of neurotransmitters depends on the membrane potential. Neurotransmitters can be either excitatory (depolarizing) or inhibitory (hyperpolarizing). post-synaptic cell pre-synaptic cell 7

Q: How do nerve cells signal over long distances ? input synapses output synapses Axon can be quite long (cm, or up to 1 m). 8

A: Spikes (“Action Potentials”) http://www.youtube.com/watch?v=ifD1YG07fB8 9

• shape • speed • frequency (“firing rate”) • information (see book) https://mitpress.mit.edu/books/spikes 10

Receptive Field of a Retinal Cell y x 11

Receptive field sizes increase with eccentricity 12

Receptive field diameter of retinal ganglion cells NOTE: Log scale 1 6 arcmin = 10 degree 1 2 arcmin = 30 degree 13

Retinal ganglion cells encode image sums and differences : • spectral (wavelength l ) , “chromatic” • spatial (x,y) • temporal (t) • spectral-spatio-temporal ( l, x, y, t) 14

Spectral sums and differences “L + M” red + green = yellow “L - M” red – green “(L + M) - S” yellow – blue 15

Spectral sums and differences L + M S L – M M (L + M) - S L Photoreceptors (cones) Retinal ganglion cells 16

Neural Mechanism “Color Opponency ” (Hering, 19 th century) (modern theory) white L + M red L – M blue yellow green (L + M) - S black Orange is reddish-yellow. Purple is blueish-red. Cyan is greenish-blue. Colors cannot appear reddish-green, blueish-yellow, blackish-white. 17

ASIDE: Classical Color Wheel Art class ROYGBV theory of primary, secondary, and complementary colors is based on mixing pigments, not mixing lights. 18

Polar coordinates for color angle = “hue” radius = “saturation” 19

(for HSV) 'color‘ name purity intensity 20

RGB and HSL (similar to HSV) 21

Retinal ganglion cells encode image differences : • spectral (wavelength l ) , “chromatic” • spatial (x,y) • temporal (t) • spectral-spatio-temporal ( l, x, y, t) 22

Spatial differences: “center - surround receptive fields” - + + - + - - + + - + - - + OFF center, ON center, ON surround OFF surround + and - indicate where the cell is excited or inhibited ( de polarized or polarized) by bright image spot in its receptive field. 23

e.g. Retinal ganglion cells (first experiments on cats done in 1953) - - - - - - + + + - - - - - - - - - Shine light in center Shine light only Shine light only and surround. in surround. in center. (OFF surround) (ON center) time time time 24

Proposed Mechanism (Rodieck, 1965) + - - + + + - - - - + + + - + - + 25

Gaussian model 𝑓 − 𝑦 2 1 G( 𝑦 ) = 2𝜏 2 2𝜌 𝜏 26

Difference of Gaussians (DOG) model − 𝑦 2 − 𝑦 2 1 1 𝐸𝑃𝐻 𝑦, 𝜏 1 , 𝜏 2 = 2𝜏 12 2𝜏 22 𝑓 − 𝑓 2𝜌𝜏 1 2𝜌𝜏 2 + = - 27

2D Gaussian and 2D DOG 𝐻 𝑦, 𝑧, 𝜏 ≡ 𝐻 𝑦, 𝜏 𝐻 𝑧, 𝜏 𝑓 − 𝑦 2 𝑓 − 𝑧 2 1 1 2𝜏 2 2𝜏 2 ∗ = 2𝜌𝜏 2𝜌𝜏 2𝜌𝜏 2 𝑓 − 𝑦 2 +𝑧 2 1 2𝜏 2 = 𝐸𝑃𝐻 𝑦, 𝑧, 𝜏 1 , 𝜏 2 = 𝐻 𝑦, 𝑧, 𝜏 1 - 𝐻 𝑦, 𝑧, 𝜏 2 28

Response of a cell (DOG) - - + DOG cell centered at (𝑦 0 , 𝑧 0 ) - - - Response depends on: 𝑀 = 𝐽 𝑦, 𝑧 𝐸𝑃𝐻 𝑦 − 𝑦 0 , 𝑧 − 𝑧 0 , 𝜏 1 , 𝜏 2 𝑒𝑦 𝑒𝑧 Here I am ignoring temporal properties for simplicity. 29

Linear response model 𝑀 = 𝐸𝑃𝐻 𝑦 − 𝑦 0 , 𝑧 − 𝑧 0 , 𝜏 1 , 𝜏 2 𝐽 𝑦, 𝑧 𝑒𝑦 𝑒𝑧 Alternatively we can write it as a sum: 𝑀 = 𝐸𝑃𝐻 𝑦 − 𝑦 0 , 𝑧 − 𝑧 0 , 𝜏 1 , 𝜏 2 𝐽 𝑦, 𝑧 𝑦,𝑧 30

“Static Non - linearity” Spike firing rate (spikes per second) ~200 10 𝑀 Spike train 𝑢 31

Half-wave rectification model Spike “firing rate” Max firing rate: in practice there is a cutoff 𝑀 𝑀 = max( 0, 𝐽 𝑦, 𝑧 ) 𝐸𝑃𝐻 𝑦 − 𝑦 0 , 𝑧 − 𝑧 0 , 𝜏 1 , 𝜏 2 𝑦,𝑧 32

Responses of a population of DOGs - - - - - - - - + + + + - - - - - - - - - - - - - - - - - - - - + + + + - - - - - - - - - - - - - - - - - - - - + + + + - - - - - - - - - - - - … and many overlapping ones which I am not showing because it would be too messy 33

“Cross correlation” image - - + - - - DOG 34

Responses of a population of DOGs Cross correlation operator 𝑀 𝑦 0 , 𝑧 0 ≡ 𝐸𝑃𝐻 𝑦 , 𝑧 , 𝜏 1 , 𝜏 2 ⨂ 𝐽 𝑦, 𝑧 ≡ 𝐸𝑃𝐻 𝑦, 𝑧 𝐽 𝑦 0 + 𝑦, 𝑧 0 + 𝑧 𝑦,𝑧 change of variables ≡ 𝐸𝑃𝐻 𝑣 − 𝑦 0 , 𝑤 − 𝑧 𝐽 𝑣, 𝑤 0 𝑣,𝑤 35

Cross correlation 𝑔 𝑦, 𝑧 ⨂ 𝐽 𝑦, 𝑧 ≡ 𝑔 𝑣 − 𝑦, 𝑤 − 𝑧 𝐽 𝑣, 𝑤 𝑣,𝑤 Convolution (to be discussed later) ≡ 𝑔 𝑦 − 𝑣, 𝑧 − 𝑤 𝐽 𝑣, 𝑤 𝑔 𝑦, 𝑧 ∗ 𝐽 𝑦, 𝑧 𝑣,𝑤 36

Technical detail (boundary effects) - - Not well defined + responses - - - - - + - - - image (photoreceptors) - - - + - - - - + - - - Well defined response 37