Two-dimensional spatial linear filters are constrained by general uncertainty relations that limit their attainable information resolution for orientation, spatial frequency, and two-dimensional (2D) spatial position. The theoretical lower limit for the joint entropy, or uncertainty, of these variables is achieved by an optimal 2D filter family whose spatial weighting functions are generated by exponentiated bivariate second-order polynomials with complex coefficients, the elliptic generalization of the one-dimensional elementary functions proposed in Gabor’s famous theory of communication [ J. Inst. Electr. Eng.93, 429 ( 1946)]. The set includes filters with various orientation bandwidths, spatial-frequency bandwidths, and spatial dimensions, favoring the extraction of various kinds of information from an image. Each such filter occupies an irreducible quantal volume (corresponding to an independent datum) in a four-dimensional information hyperspace whose axes are interpretable as 2D visual space, orientation, and spatial frequency, and thus such a filter set could subserve an optimally efficient sampling of these variables. Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial–2D-spectral information resolution. The variety of their receptive-field dimensions and orientation and spatial-frequency bandwidths, and the correlations among these, reveal several underlying constraints, particularly in width/length aspect ratio and principal axis organization, suggesting a polar division of labor in occupying the quantal volumes of information hyperspace. Such an ensemble of 2D neural receptive fields in visual cortex could locally embed coarse polar mappings of the orientation–frequency plane piecewise within the global retinotopic mapping of visual space, thus efficiently representing 2D spatial visual information by localized 2D spectral signatures.

Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters.

We perceive the visual world as a unitary whole, yet one of the guiding principles of nearly a half century of neurophysiological research since the early recordings by Hartline (1938) has been that the visual system consists of neurons that are driven by stimulation within small discrete portions of the total visual field. These classical receptive fields (CRFs) have been mapped with the excitatory responses evoked by a flashed or moving stimulus, usually a spot or bar of light. Most of the visual neurons, in turn, are organized in a series of maps of the visual field, at least 10 of which exist in the visual cortex in primates as well as additional topographic representations in the lateral geniculate body, pulvinar and optic tectum (Allman 1977, Newsome & Allman 1980, Allman & Kaas 1984). It has been widely assumed that perceptual functions that require the integration of inputs over large portions of the visual field must be either collective properties of arrays of neurons representing the visual field, or features of those neurons at the highest processing levels in the visual system, such as the cells in inferotemporal or posterior parietal cortex that typically possess very large receptive fields and do not appear to be organized in visuotopic maps. These assumptions have been based on the results of the many studies in which receptive fields were mapped with conventional stimuli, presented one at a time, against a featureless background. However, unlike the neurophysiologist's tangent screen, the natural visual scene is rich in features, and there is a growing body of evidence that in many visual neurons stimuli presented outside the CRF strongly and selectively influence neural responses to stimuli presented within the CRF. These results suggest obvious mechanisms for local-global comparisons within visuotopically organized structures. Such broad and specific surround mechanisms could participate in many functions that require the integration of inputs over wide regions of the visual space such as the perceptual constancies, the segregation of figure from ground, and depth perception through motion parallax. In the first section of this paper, we trace the historical development of the evidence of response selectivity for visual stimuli presented beyond the CRF; in the second, examine the anatomical pathways that sub serve these far-reaching surround mechanisms; and in the third, explore the possible relationships between these mechanisms and perception.

Stimulus Specific Responses from Beyond the Classical Receptive Field: Neurophysiological Mechanisms for Local-Global Comparisons in Visual Neurons

1. We recorded responses from neurons in area V1 of the alert macaque monkey to textured patterns modeled after stimuli used in psychophysical experiments of pop-out. Neuronal responses to a single...

Neuronal responses to static texture patterns in area V1 of the alert macaque monkey

Biological image motion processing: A review

NEURONS in the primary visual cortex (VI) respond in well defined ways to stimuli within their classical receptive field, but these responses can be modified by stimuli overlying the surrounding area1–7 For example patch-suppressed cells respond to gratings of a specific orientation within their classical receptive field, but the response diminishes if the grating is expanded to cover the surrounding area1–7 We report here more complex effects in many such cells When stimulated at their optimal orientation, introducing a surrounding field at a significantly different (for example, orthogonal) orientation enhanced their output by both a disinhibi-tory mechanism and an active facilitatory mechanism producing'supra-optimal' responses Importantly, some cells responded well if the orientations of centre and surround stimuli were swapped The output reflected the discontinuity because neither stimulus component alone was effective Under these stimulus conditions simultaneously recorded cells with orthogonally oriented receptive fields showed correlated firing consistent with neuronal binding to the configuration We propose a mechanism integrating orientation-dependent information over adjacent areas of visual space to represent focal orientation discontinuities such as junctions or corners

K. Albus

Papers

Effects of interacting visual patterns on single cell responses in cat's striate cortex

The detection of movement direction and effects of contrast reversal in the cat's striate cortex.

Orientation selectivity of single cells in striate cortex of cat: The shape of orientation tuning curves

Static and dynamic properties of receptive fields of some simple cells in cat's striate cortex.

Inhibitory sidebands of complex receptive fields in the cat's striate cortex