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A complex cell in primary visual cortex typically responds to a suitably oriented bar, edge or grating over a finite receptive-field region, with less dependence on precise spatial phase and contrast polarity than a simple cell. Its response need not reveal separated linear ON and OFF subregions. Many cells have additional motion or binocular selectivity, so phase tolerance alone is not a complete account of every complex cell. Moving the feature beyond its receptive field still reduces the response.

In a pooling model of a complex cell, several simple cells with similar preferred orientation but different positions or phases feed the output. For linear subunit responses $a_m=⟨k_m,I⟩$, a possible model is $r=f({\sum }_m{w}_m[a_m-{\theta }_m{]}_{+})$, with $w_m\ge 0$. Include opposite-polarity filters if both light and dark features are to drive the cell. Rectification stops cancellation between subunits, and pooling spreads position and phase sensitivity across their coverage.

In a quadrature energy model of a complex cell, use two oriented filters of matching frequency but quadrature phase, and setFor a matched grating, choose the pair so $a_e=A\cos \phi$, $a_o=A\sin \phi$; then $E=A^2$, independent of grating phase while retaining orientation and frequency tuning. Finite approximate filter pairs give only approximate invariance for general images. The quadrature construction underlies the primary Adelson–Bergen energy-model work; temporal filters can extend it to motion sensitivity.

The pooling model emphasizes a circuit of rectified subunits and can flexibly cover translated positions. The energy model gives an explicit algebraic phase-invariance mechanism with quadratic contrast dependence before its output nonlinearity. They are not mutually exclusive biological alternatives: suitable subunit pooling can approximate an energy computation. Their spatial tolerance, contrast response and direction selectivity depend on the chosen filters and nonlinearities, and both require comparison with measured receptive fields.

A visual neuron's receptive field specifies the region of visual space and stimulus features whose changes affect its response, with the surrounding and temporal context held appropriately controlled. A linear receptive-field approximation is a signed spatial weighting kernel. A simple cell in primary visual cortex commonly has elongated alternating ON and OFF subregions and orientation selectivity. Brightening an ON region increases its drive; darkening an OFF region does likewise, while opposite contrasts oppose that drive in the linear approximation.

The original sketch below uses a Gaussian-windowed cosine to depict an elongated ON strip with OFF flanks. A bar aligned with these regions can produce strong net drive, whereas an orthogonal bar produces more cancellation. This is an illustrative signed filter, not a claim that every simple cell has exactly this analytical shape.

Different unsupervised learning models address different developmental aspects. Oja's rule can select a dominant direction of correlated input and provides normalization that a bare Hebbian update lacks. By itself, one linear principal component need not be localized, nor does it create a cortical map. Additional spatial constraints and competition are needed to explain a collection of spatially organized selective cells.

Competitive Hebbian learning among correlated ON and OFF inputs can separate those input types into adjacent subregions and generate orientation selectivity. Competition among inputs from the two eyes can similarly contribute to eye-specific preference and ocular dominance columns; spatial interactions between cortical units are needed for an organized map rather than merely one cell choosing one input pool. These models connect developmental organization to input correlations and normalization constraints. The ON/OFF competition model gives a concrete orientation-development example.

A different approach is sparse coding: learn features that reconstruct natural images while limiting simultaneous activity. This can yield localized, oriented, band-pass filters resembling simple-cell receptive fields, because it uses structure in natural-image statistics beyond the covariance alone. The original sparse-code model demonstrates this functional account. It does not by itself establish an exact developmental mechanism.

Correlated input, competition and normalization can produce selectivity; the objective and network constraints determine which aspect of cortical organization is explained. Anatomical constraints, spontaneous activity and experience must still be tested experimentally. A final receptive-field resemblance is weaker evidence than accurate predictions about its development and responses to altered input statistics.

The primary visual cortex, often abbreviated V1, is an early cortical stage of visual processing. Its neurons have receptive fields: changing a stimulus in a particular part of the visible scene can change their spike trains. Orientation selectivity adds a further distinction: at the same location, a properly aligned bar can evoke a strong response while a rotated bar evokes little. Simple cells make the dependence on local position and visual contrast especially clear. See the original experiments under orientation selectivity and simple cell.

In their 1962 study, David Hubel and Torsten Wiesel recorded from forty cats under thiopental anesthesia, maintained light anesthesia while monitoring cortical electrical activity, and used succinylcholine to stabilize the eyes. White-light patterns were projected onto a screen $1.5\mathrm{m}$ away. Extracellular single-unit recording with tungsten electrodes sampled individual units; receptive fields were mapped separately for each eye. This connected controlled stimulus geometry to individual spike trains. ^[ref]

These acute, anesthetized-cat recordings do not directly measure human perception or responses during awake behavior. The useful idea is a local description of structure: a population can distinguish where a feature lies, which way it is aligned, and which side is brighter. The signed spatial filter model of a simple cell turns that idea into a computable example. One neuron's preferred stimulus does not establish recognition of an entire object. Likewise, orientation selectivity in one neuron and an orderly map of preferences across primary visual cortex are different findings: rodents can have strong orientation selectivity without the orderly arrangement typical of some other species. ^[ref] The existing correlation-based development of visual cortical maps and orientation-map self-organization sections describe hypotheses about how organization develops.

Cortical systems processing visual information, including primary visual cortex and extrastriate regions. Delay-period information in these systems can be consistent with sensory recruitment without proving that a single local region independently maintains the memory.