Chapter 2 · Optional lab
The visual lab
Realistic illustrations of the eye and retina, an interactive model of receptive fields and clickable maps of the visual pathways. No scores or assessments – explore for as long as it helps.
Orientation in V1
Which tilt and position does a V1 cell prefer?
A narrow bright or dark bar is shown against a grey field. Two example cells in the model both prefer a vertical bar at the field's centre. The simple cell needs the right position and contrast polarity; the complex cell tolerates shifts and light–dark swaps within the field. Rotate and move the bar and compare.
The dashed contour marks a chosen level of model sensitivity. Sensitivity declines gradually, without a sharp field boundary.
Relative model response
- Simple-cell model
- 1.00
- Complex-cell model
- 1.00
1.00 = the response to a bright vertical bar at the centre. Not impulses per second and not measured data.
The bar is vertical, near the centre and has the right contrast: both model cells respond strongly.
A static, spatial teaching model. It does not simulate motion, action potentials, adaptation, learning, feedback, attention, all V1 cell types or human measurements.
How this model works
The visual field is a grid of 49 × 49 points. The bar is a signed contrast relative to mean grey: positive for bright, negative for dark, with soft edges. The image above draws exactly the values the model computes with.
The field has two weight patterns, both vertical stripes inside an elongated bell-shaped region: an even pattern with a strong central stripe and an odd pattern shifted by a quarter period. Each has zero mean, so uniform grey gives no response. The simple cell is the even pattern's summed response, with negative sums set to zero.
The complex cell combines both patterns as √(even² + odd²), an energy amplitude. The idea comes from energy models (Adelson & Bergen 1985) but is simplified here to a static spatial version; we use the square root of the energy rather than the raw squared energy. The two patterns are mathematical parts of the model, not a claim about exactly two biological cells.
All responses are divided by one fixed number – the even response for a bright vertical bar at the centre – so changes stay visible instead of being hidden by rescaling each stimulus.
Sources
- Hubel, D. H. & Wiesel, T. N. (1962). Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. Journal of Physiology, 160, 106–154. DOI: 10.1113/jphysiol.1962.sp006837.
Single cells in cat visual cortex: the description of simple and complex receptive fields. Not a universal human circuit.
- Hubel, D. H. & Wiesel, T. N. (1968). Receptive fields and functional architecture of monkey striate cortex. Journal of Physiology, 195, 215–243. DOI: 10.1113/jphysiol.1968.sp008455.
Monkey physiology: orientation selectivity and columnar organisation. The authors note that a strict hierarchy may be an oversimplification.
- Hubel, D. H. & Wiesel, T. N. (1974). Uniformity of monkey striate cortex: A parallel relationship between field size, scatter, and magnification factor. Journal of Comparative Neurology, 158, 295–305. DOI: 10.1002/cne.901580305.
Monkey: relationship between field size, scatter and cortical magnification. Used for the concept; no exact fractions.
- Hubel, D. H. & Wiesel, T. N. (1974). Sequence regularity and geometry of orientation columns in the monkey striate cortex. Journal of Comparative Neurology, 158(3), 267–293. DOI: 10.1002/cne.901580304.
Macaque: how orientation preference changes across the cortical surface. A classical organisational description, not a regular grid or a map measured for this book.
- Dumoulin, S. O. & Wandell, B. A. (2008). Population receptive field estimates in human visual cortex. NeuroImage, 39, 647–660. DOI: 10.1016/j.neuroimage.2007.09.034.
Human fMRI: retinotopic maps and population fields that grow with eccentricity. A voxel is not an individual neuron.
- Adelson, E. H. & Bergen, J. R. (1985). Spatiotemporal energy models for the perception of motion. Journal of the Optical Society of America A, 2(2), 284–299.
Computational model, not a physiological measurement. The lab's static spatial amplitude is a simplified adaptation of the model family, not their motion model.
- Hupé, J. M. et al. (1998). Cortical feedback improves discrimination between figure and background by V1, V2 and V3 neurons. Nature, 394, 784–787. DOI: 10.1038/29537.
Macaque: inactivating area V5 changed figure–background responses in V1–V3, an example of feedback's contribution.
- Chawla, D., Rees, G., & Friston, K. J. (1999). The physiological basis of attentional modulation in extrastriate visual areas. Nature Neuroscience, 2, 671–676.
Human fMRI: attention to colour and motion. The task figure contains no measured activity values.
- Horton, J. C. & Hoyt, W. F. (1991). The representation of the visual field in human striate cortex. A revision of the classic Holmes map. Archives of Ophthalmology, 109, 816–824. DOI: 10.1001/archopht.1991.01080060080030.
Human map revised using visual-field defects and MRI-defined lesions. Supports retinotopy and central magnification, not universal V1 percentages.
- Duncan, R. O. & Boynton, G. M. (2003). Cortical magnification within human primary visual cortex correlates with acuity thresholds. Neuron, 38, 659–671. DOI: 10.1016/S0896-6273(03)00265-4.
Same human observers: linear V1 magnification with fMRI and psychophysical acuity. A relationship, not evidence that V1 alone determines acuity; the measure is mm/degree.
- Benson, N. C., Yoon, J. M. D., Forenzo, D., Engel, S. A., Kay, K. N. & Winawer, J. (2022). Variability of the Surface Area of the V1, V2, and V3 Maps in a Large Sample of Human Observers. Journal of Neuroscience, 42, 8629–8646. DOI: 10.1523/JNEUROSCI.0690-21.2022.
181 human observers: variability in V1–V3 map areas and relative central magnification. A limited retinotopically mapped region, not whole-V1 surface area; no universal exact shares inferred.
- Pack, C. C., Livingstone, M. S., Duffy, K. R. & Born, R. T. (2003). End-stopping and the aperture problem: two-dimensional motion signals in macaque V1. Neuron, 39(4), 671–680. DOI: 10.1016/S0896-6273(03)00439-2.
Macaque V1: end-stopping and contour endpoints in motion processing. The static comparison does not simulate these experiments.
- Yazdanbakhsh, A. & Livingstone, M. S. (2006). End stopping in V1 is sensitive to contrast. Nature Neuroscience, 9(5), 697–702. DOI: 10.1038/nn1693.
Macaque V1 complex cells: length sensitivity depends on relative end-zone contrast. End-stopping also occurs in simple cells.
- Dougherty, K., Cox, M. A., Westerberg, J. A. & Maier, A. (2019). Binocular modulation of monocular V1 neurons. Current Biology, 29(3), 381–391.e4. DOI: 10.1016/j.cub.2018.12.004.
Macaque laminar recordings: even input-layer neurons driven by one eye can be binocularly modulated. No figures from the study are used here.
- Cumming, B. G. & Parker, A. J. (2000). Local disparity not perceived depth is signaled by binocular neurons in cortical area V1 of the macaque. Journal of Neuroscience, 20(12), 4758–4767. DOI: 10.1523/JNEUROSCI.20-12-04758.2000.
Macaque V1 single-unit recordings with locally ambiguous gratings; distinguishes local disparity from perceived depth, not human neuronal recordings.
Illustrations and models for learning; not measurements.