Part IV · Chapter 10 · Lectures 8 & 9

LGN, V1 & receptive fields

The two pathways through the thalamus, the four properties of primary visual cortex, and how receptive fields are built step by step — from a single photoreceptor to an orientation-tuned simple cell — with the Hermann grid and tilt adaptation explained by the mechanism.

1. The lateral geniculate nucleus (LGN)

The LGN is the thalamus's visual relay. It has 6 layers, receives input from both eyes in different layers, and sends out different kinds of information along two pathways:

	Magnocellular (M)	Parvocellular (P)
LGN layers	1–2	3–6
Carries	Motion & coarse detail; less colour	Colour & fine detail
Speed	Fast	Slow
Input	More rods, more peripheral, low resolution	More cones, more central, high resolution
Hook	M = Motion, Massive (big, coarse)	P = Precise, Pigment (colour)

Recall the Monroe/Einstein hybrid (Ch. 9): the coarse, blurry Monroe is magno-style information; the fine Einstein detail is parvo-style. From the LGN, information goes to layer 4 of primary visual cortex (V1) — the input layer from Chapter 3.

2. Four properties of V1

1 · Retinotopic V1 keeps a map of visual space: neighbouring points in the world → neighbouring neurons. Evidence: an anaesthetized monkey viewed a flickering bull's-eye; injected radioactive glucose was taken up by active neurons; the flattened V1, laid on film, showed the bull's-eye pattern.

2 · Corticomagnification The fovea (central field, dense cones) is represented disproportionately: a tiny patch of the central field gets a large patch of cortex.

3 · Eye-specific Ocular dominance columns: stripes of cells processing input from one eye. Evidence: a patient who lost one eye before death donated their brain; cytochrome-oxidase stain showed dark stripes where recently active (one-eye) regions were.

4 · Orientation-specific Orientation columns: orientation-tuned cells arranged so preferred orientation changes in an orderly way across the cortex. Also blobs: colour-sensitive cells. Human fMRI shows both eye and orientation maps.

Corticomagnification — the same rings, before and after V1's map

What to notice: in the visual field (left) the rings are at 1°, 2°, 4°, 8°, 16°, 32° — each twice the last. In cortex (right) they come out roughly evenly spaced (band widths 0.41 → 0.66 in model units). So the 1–2° ring, which covers 1/256 of the area of the 16–32° ring, still gets over 60% as wide a strip of cortex. That's what "the fovea is disproportionately represented" means. Computed with a standard log-polar model of V1 (w = log(z + 1)), not the lecture's figure.

Clinical link — strabismus and amblyopia (L8 study guide) Strabismus (a wandering eye) sends the brain mismatched images; the brain starts ignoring the weaker eye, which can progress to amblyopia ("lazy eye"). Treatment: patch the strong eye to force the brain to develop and process signals from the weaker eye. It must happen during the critical period of development. Mechanism: ocular dominance columns are plastic early in life — the patched eye's columns shrink and the weak eye's grow (Ch. 2's plasticity at the column scale).

3. Receptive fields, built up step by step

Definition Receptive field — the specific region on the retina where light affects a cell's activity.

The lecture builds them in four steps. Each step pools the previous one:

#	Cell	Receptive field	Sensitive to
1	Photoreceptor	Itself — its own spot on the retina	Light at that spot
2	Retinal ganglion cell	Center–surround (many photoreceptors pooled)	Contrast, position
3	LGN cell	Center–surround	Contrast, position
4	V1 simple cell	Elongated — lines & edges (LGN cells lined up)	Contrast, position, orientation

Center–surround

ON-center, OFF-surround: light in the center excites the cell; light in the surround inhibits it. OFF-center, ON-surround is the reverse. Why build it that way? Uniform light excites the center and inhibits the surround about equally — they cancel. The cell only fires strongly when center and surround differ. It's a contrast detector.

An ON-center ganglion cell — move the spot of light

Spot x Spot size OFF-center cell

What to notice: a small spot filling the center gives the biggest response. Grow the spot until it covers the surround too, and the response falls back — more light, less firing. Slide a small spot into the ring and the cell is pushed below its baseline. Firing depends on contrast, not on the amount of light.

Which stimulus excites an ON-center, OFF-surround ganglion cell most?

Why: Center excited, surround not inhibiting = max. Uniform light is the tempting answer — "more light, more firing" — but the surround cancels it. The ring is the best stimulus for an OFF-center cell.

The Hermann grid (exit-ticket question, answered)

Why grey dots appear at the intersections

The answer Both cells' centers sit on white. But at an intersection, white extends in four directions, so more light falls on the OFF-surround than in a corridor, where white runs in only two directions. More surround light → more inhibition → the intersection cell fires less → you perceive that spot as darker: a grey dot. going deeper Look straight at an intersection and the dot vanishes — foveal receptive fields are much smaller than the white bars, so the effect disappears.

Simple cells: lines up the center–surrounds

A V1 simple cell combines LGN inputs whose centers lie along a line. The result is an elongated receptive field: an excitatory strip flanked by inhibitory strips. It responds best to a bar of light at one position, contrast and orientation. Discovered in cat V1 by Hubel & Wiesel (Nobel Prize 1981).

Orientation tuning — rotate the bar

Bar orientation (°) Bar offset

What to notice: the response (right) is a peaked tuning curve — maximal when the bar lines up with the excitatory strip (vertical, 0°), near zero when perpendicular. Slide the bar sideways onto the inhibitory flank and the response drops even when the orientation is perfect: simple cells care about position too. Response is computed as the overlap of the bar with the receptive field.

Tilt adaptation: fatigue a channel, bias the percept

Stare at lines tilted one way for a while, then look at vertical lines: they seem tilted the other way. Mechanism: many simple cells, each tuned to a different orientation, vote on what you see. Prolonged exposure fatigues the cells tuned near the adapting tilt. When a vertical line arrives, the tired cells on one side vote less, so the population's "average" lands on the other side.

Population of orientation-tuned cells — adapt, then test with vertical

Adapting tilt (°) Adaptation strength

What to notice: each bar is one cell's response to a vertical test line. With strength at 0 the pattern is symmetric and the decoded orientation is 0°. Add adaptation and the cells near the adapting tilt are suppressed; the decoded percept moves away from the adapting tilt. Adapt at exactly 0° and there's no bias at all — only a weaker response. Population-vector decoding, toy tuning widths.

Population coding The lecture's final point: no single cell "sees" the line. A group of cells tuned to the line's orientation is excited, others are inhibited, and the pattern across the population generates the perception. Tilt adaptation is evidence for exactly that — you can bias the percept by fatiguing part of the population.

4. Edge detection at Marr's three levels — now with the implementation filled in

Level	Answer
Computational	Recognize objects, detect motion, spatial navigation
Algorithmic	Sobel operator — find where intensity changes sharply (Ch. 4)
Implementation	Receptive fields (different cells respond to different places) · contrast sensitivity (center–surround) · orientation sensitivity (simple cells). Edge detection is supported by V1.

5. Check yourself

A cell responds strongly to a 45° bar at one location and hardly at all to a 135° bar there. It's most likely a…

Why: Orientation selectivity first appears in V1 simple cells. Ganglion and LGN cells have circular center–surround fields — they don't care about orientation.

Information about fast motion and coarse shape travels through…

Why: Magno = motion, coarse, fast. Parvo = colour, fine, slow. Blobs are V1's colour cells.

After staring at lines tilted 15° clockwise, a vertical line looks…

Why: The clockwise-tuned cells are fatigued, so the population is biased away from the adapting tilt. The first option is the most common wrong answer.

A child's wandering eye is untreated past the critical period. The likely outcome and its V1 basis?

Why: Strabismus → amblyopia if untreated. Patching the strong eye only works while the columns are still plastic (the critical period).