The RF-cinematogram. A cross-correlation technique for mapping several visual receptive fields at once.

Decision letter: Visual and motor signatures of locomotion dynamically shape a population code for feature detection in Drosophila

The functional properties of neural sensory cells or small neural ensembles are often characterized by analyzing response-conditioned stimulus ensembles. Many widely used analytical methods, like receptive fields (RF), Wiener kernels or spatio-temporal receptive fields (STRF), rely on simple statistics of those ensembles. They also tend to rely on simple noise models for the residuals of the conditional ensembles. However, in many cases the response-conditioned stimulus set has more complex structure. If not taken explicitly into account, it can bias the estimates of many simple statistics, and lead to erroneous conclusions about the functionality of a neural sensory system. In this article, we consider sensory noise in the visual system generated by small stimulus shifts in two dimensions (2 spatial or 1-space 1-time jitter). We model this noise as the action of a set of translations onto the stimulus that leave the response invariant. The analysis demonstrates that the spike-triggered average is a biased estimator of the model mean, and provides a de-biasing method. We apply this approach to observations from the stimulus/response characteristics of cells in the cat visual cortex and provide improved estimates of the structure of visual receptive fields. In several cases the new estimates differ substantially from the classic receptive fields, to a degree that may require re-evaluation of the functional description of the associated cells.

We quantitatively studied the excitatory receptive fields of 297 neurons recorded from the forelimb infragranular somatosensory cortex of the rat while touch stimuli were applied to discrete locations on the forelimbs. Receptive fields were highly heterogeneous, but they were regulated, on average, by an underlying spatio-temporal structure. We found the following. (i) Neurons responded with decreasing magnitude and increasing latency when the stimulus was moved from the primary location to secondary locations and to far ispilateral locations of their excitatory receptive fields, displaying smooth transitions from the primary location to secondary locations. (ii) Receptive field patterns revealed functional connectivity between the digits and ventral palm, which did not depend on whether the digits were stimulated dorsally or ventrally. (iii) The structure of the receptive fields (i.e. the neural responses to stimulation of secondary locations compared to the neural responses to stimulation of the primary location), reflected cortical (rather than body) distances. (iv) There was a functional separation between the forepaw and the rest of the forelimb. Namely: if the primary location was in the digits or palm, secondary locations were biased toward the digits and palm; if the primary location was in rest of the forelimb, secondary locations appeared equally distributed over forelimb, digits and palm. (v) More than 40% of neurons extended their receptive field to the ipsilateral forelimb, without any evident spatial organization. Overall, the stimuli evoked approximately 3 times more spikes from secondary responses than from primary responses. These results suggest that a rich repertoire of spatio-temporal responses is available for encoding tactile information. This highly distributed receptive field structure provides the electrophysiological architecture for studying organization and plasticity of cortical somatosensory processing.

A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space–time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative agreement are obtained for (i) spatial on-center/off-surround and off-center/on-surround receptive fields in the fovea and the LGN, (ii) simple cells with spatial directional preference in V1, (iii) spatio-chromatic double-opponent neurons in V1, (iv) space–time separable spatio-temporal receptive fields in the LGN and V1, and (v) non-separable space–time tilted receptive fields in V1, all within the same unified theory. In addition, the paper presents a more general framework for relating and interpreting these receptive fields conceptually and possibly predicting new receptive field profiles as well as for pre-wiring covariance under scaling, affine, and Galilean transformations into the representations of visual stimuli. This paper describes the basic structure of the necessity results concerning receptive field profiles regarding the mathematical foundation of the theory and outlines how the proposed theory could be used in further studies and modelling of biological vision. It is also shown how receptive field responses can be interpreted physically, as the superposition of relative variations of surface structure and illumination variations, given a logarithmic brightness scale, and how receptive field measurements will be invariant under multiplicative illumination variations and exposure control mechanisms.

The macaque putamen contains neurons that respond to somatosensory stimuli such as light touch, joint movement, or deep muscle pressure. Their receptive fields are arranged to form a map of the body. In the face and arm region of this somatotopic map we found neurons that responded to visual stimuli. Some neurons were bimodal, responding to both visual and somatosensory stimuli, while others were purely visual, or purely somatosensory. The bimodal neurons usually responded to light cutaneous stimulation, rather than to joint movement or deep muscle pressure. They responded to visual stimuli near their tactile receptive field and were not selective for the shape or the color of the stimuli. For cells with tactile receptive fields on the face, the visual receptive field subtended a solid angle extending from the tactile receptive field to about 10 cm. For cells with tactile receptive fields on the arm, the visual receptive field often extended further from the animal. These bimodal properties provide a map of the visual space that immediately surrounds the monkey. The map is organized somatotopically, that is, by body part, rather than retinotopically as in most visual areas. It could function to guide movements in the animal's immediate vicinity. Cortical areas 6, 7b, and VIP contain bimodal cells with very similar properties to those in the putamen. We suggest that the bimodal cells in area 6, 7b, VIP, and the putamen form part of an interconnected system that represents extra personal space in a somatotopic fashion.

Visual response properties were examined in the superficial layers of the superior colliculus (SC) of anesthetized, paralyzed cats before and after i.v. administration of d-amphetamine. Receptive fields (RFs) of single SC units were plotted using small spots of light presented to the contralateral eye. Within the first hour following d-amphetamine injections, RF size gradually increased, reaching a maximum 86 min post-injection. On average, the area of the RF increased by 5.6 times and RF expansion was observed in all single units examined in the superficial layers. Over the subsequent 4-8 h following the injection, RF area gradually decreased and returned to control dimensions. Most RFs displayed asymmetrical patterns of expansion, showing relatively more horizontal than vertical growth. As RF expansion developed, responses to stimuli flashed "on" and "off" at various locations both inside and outside the borders of the control RF became progressively more vigorous. In contrast, no significant changes were noted in direction-selective responses at any time after d-amphetamine injections. Using an array of light bar stimuli of different lengths, the strength of surround suppression was found to be significantly diminished by d-amphetamine. The reduction in surround suppression was especially clear for bar lengths which exceeded the diameter of the control RF. No RF expansion was observed in the superficial layers of the SC when d-amphetamine was injected intravitreally. Furthermore, d-amphetamine had no discernable effect on the RF sizes of cells in the visual cortex. These results suggest that the RF changes in the SC were not of either retinal or cortical origin. We conclude that the mean retinal area which can potentially influence the activity of RFs in the superficial layers of the SC may be on average over 5 times greater than the RF area determined using conventional methods and criteria. These findings raise the interesting possibility that the relatively small size and sharp borders characteristic of RFs in the superficial layers arise from local inhibitory networks which delimit a broader field of excitatory activity supplied by retinal and cortical afferent terminals. Thus, in order to generate the RF changes observed here, either these local inhibitory circuits are amphetamine sensitive, or more likely, these inhibitory networks are dynamically modulated by an, as yet unidentified, amphetamine-sensitive input affecting visual RFs in the superficial layers.

Contribution of linear spatiotemporal receptive field structure to velocity selectivity of simple cells in area 17 of cat

Extracellular microelectrode recordings were carried out on 150 neurons in the anterior ectosylvian sulcal region of halothane-anesthetized, immobilized, artificially ventilated cats. Fifty-nine neurons were visual, 60 were auditory and 31 were bimodal visual-auditory. As the extent of the receptive fields has never been exactly determined, we introduced a quasi-objective, computer-based, statistical method in order to estimate the receptive field sizes in the anterior half of the perimeter. The visual, auditory and bimodal cells had very large receptive fields, often with portions extending well into the ipsilateral hemifield. The mean extents of the visual and auditory receptive fields in the horizontal plane were 75.75 degrees (N=59, SD: +/- 28.620, range: 15-135 degrees), and 132.5 degrees (N=60, SD: +/- 46.72 degrees, range: 15-165 degrees) respectively. These data suggest that a single visual neuron can carry information from the whole visual field of the right eye and a single auditory unit can carry information of azimuths throughout the whole area of the horizontal plane studied. The mean extent of the bimodal receptive fields in the horizontal plane was 82.1 degrees (N=31, SD: +/- 24.24 degrees, range: 30-135 degrees). In 21 of the 31 bimodal cells we observed a facilitatory interaction between visual and auditory stimuli. The mean extent of the facilitatory interactions in these cells was 75.75 degrees (N=21, SD: +/- 24.56 degrees, range: 45-135 degrees).

In our previous study of the cytoarchitectonic field 7 of cat cortex we had described neurons with extremely elongated receptive fields (RFs). The long axes of these RFs were oriented radially, towards the centre of the retina. These neurons represented only the lower contralateral part of visual field. They were surrounded from all sides by neurons with clearly different RF properties. We proposed that neurons with a similar radial organization and with RFs in the upper visual field also exist in the cortex but are localized in the area that was distant from the representation of the corresponding lower visual field. We expected to find these neurons in front of the representation of the upper visual field in areas V1, V2 and V3 (fields 17, 18 and 19), behind the central representation in area 21a. This cortical region was studied in five behaving cats. In all animals, neurons with radial RFs in the upper visual field were found in the expected location. As in the lower visual field, their RFs always spared the central visual field. Other RF properties of these neurons were also very similar to those found previously in the lower visual field. It became obvious that neurons with radial RFs are included into the fourth extrastriate crescent with complete contralateral representation. However, in the fourth crescent, RF properties in the central visual field differed significantly from those on the periphery. As a result, neurons with similar radial RFs in the upper and lower visual fields were located in the distant cortical regions, and were separated by the representation of the central visual field presented by the non-radial neurons of the cytoarchitectonic area 21a.

Neurons in the visual system vary widely in the spatiotemporal properties of their receptive fields (RFs), and understanding these variations is key to elucidating how visual information is processed. We present a new approach for mapping RFs based on the filtered back projection (FBP), an algorithm used for tomographic reconstructions. To estimate RFs, a series of bars were flashed across the retina at pseudo-random positions and at a minimum of five orientations. We apply this method to retinal neurons and show that it can accurately recover the spatial RF and impulse response of ganglion cells recorded on a multi-electrode array. We also demonstrate its utility for in vivo imaging by mapping the RFs of an array of bipolar cell synapses expressing a genetically encoded Ca2+ indicator. We find that FBP offers several advantages over the commonly used spike-triggered average (STA): (i) ON and OFF components of a RF can be separated; (ii) the impulse response can be reconstructed at sample rates of 125 Hz, rather than the refresh rate of a monitor; (iii) FBP reveals the response properties of neurons that are not evident using STA, including those that display orientation selectivity, or fire at low mean spike rates; and (iv) the FBP method is fast, allowing the RFs of all the bipolar cell synaptic terminals in a field of view to be reconstructed in under 4 min. Use of the FBP will benefit investigations of the visual system that employ electrophysiology or optical reporters to measure activity across populations of neurons.

1. The receptive fields of collicular neurons in the cat, recorded in a single microelectrode penetration, were not centered on a point in visual space, but nested eccentrically with the smaller fields displaced toward the area centralis. The eccentric nesting was not eliminated by correcting the fields for the tangent screen distortion or by making penetrations normal to the collicular surface in coronal and parasagittal planes. These findings do not support the idea that collicular cells form topographically organized columns oriented normal to the collicular surface. 2. When the receptive fields were plotted in the visual coordinate system of the collicular map, the nesting became much more concentric, suggesting that the eccentric nesting of the receptive fields in visual space was largely a product of the retinotectal coordinate transformation. 3. The profile of a collicular receptive field, plotted in the collicular visual coordinate system is called the receptive-field image. Receptive-field images tended to have oval shapes with the long axis oriented mediolaterally. Clusters of receptive-field images, plotted for single penetrations, appeared similar wherever they occurred in the collicular map, suggesting that a common pattern of neural convergence determines the geometry of the receptive-field images in all parts of the colliculus. 4. The neural substrate of the receptive-field images was examined by tracing the theoretical patterns of neural activity which a point stimulus would produce in the retinotectal system. This analysis suggested that the shape and dimensions of the receptive-field images, and consequently the receptive fields, might be accounted for in large part by the geometry of collicular dendritic fields, the dimensions of the visual receptive fields of afferent fibers, and the retinotectal coordinate transformation. 5. Because it adjusts for the retinotectal distortion of visual space, the receptive-field image may be used to outline the distribution of collicular cells excited by a point stimulus. This makes it possible to show that a point stimulus activates large-field cells in the superficial gray layer over an area of about 2.5 by 1.5 mm in the central parts of the colliculus. It is suggested that such cells may organize the directional signals required by the oculomotor system for visual orienting behavior.

We mapped the receptive fields of 49 cells from primary visual cortex and 19 cells from medial superior temporal cortex in two awake monkeys. The receptive field structures we obtained lasted a mean time of 32.7 ms in primary visual cortex and 38.4 ms in medial superior temporal cortex, showing no statistical difference. This result suggests that both areas have the same time requirements for processing visual information. In primary visual cortex, 100% of cells had conformed the receptive field structure at 65 ms pre-spike, whereas in medial superior temporal cortex it occurred at 150 ms. In both areas, cells with shorter response latencies had receptive field structures with longer durations. This may indicate that cells tend to synchronize their output to other areas.

In previous work, it was suggested that the sequence regularity property of cortical neurons could be accounted for if the local geometric structure of the cortex were a recapituation of the global complex logarithmic structure of the retinotopic mapping. This model is developed in detail: the excitatory and inhibitory structure of cortical receptive fields may be approximated by a complex logarithmic local geometry, coupled with an intra-cortical lateral inhibition operator which may flow unidirectionally yet still create "rotating" receptive field structure. The direction of intra-cortical lateral inhibition follows the borders of cortical ocular dominance columns, which are the approximate images under the global complex logarithmic mapping, of exponentially spaced, horizontal straight lines in the visual field. Two different topological structures are discussed for the local cortical manifold. The binocular trigger features of cortical neurons follow from the same geometric model, and the ratio of binocular to monocular cortical cells is related to the size and shape of cortical dendritic tree's by an application of integral geometry. Recent results in optical pattern recognition are cited to suggest that the rotation and size invariant properties of the cortical map are essential to any cross-correlational basis for stereopsis. Finally, a meromorphic function is presented which is both locally and globally complex logarithmic in its structure, and therefore represents the model presented in this and previous papers in a concise mathematical form. This function is closely related to the description of a Karman vortex pattern, in fluid mechanics, and leads to the suggestion that the boundary conditions of layer IV of the cortex (i.e. periodic ocular dominance columns) are causally related to the existence of sequence regularity in the cortex. The developmental implications of this statement are that the specification of neural connections in the cortex may follow directly, both locally and globally, from the detailed nature of the cortical boundary conditions (i.e. anatomy), coupled with general physico-mathematical considerations of continuity and differentiability in the neural fiber flow.

1. The response properties of 182 units were studied in the primary visual cortices (155 in area 18 and 27 in area 17) in eight cats reared from birth in a stroboscopically illuminated environment (frequency, 2/s; duration, 200 microseconds). Multihistogram quantitative testing was carried out in 82 units (64 in area 18 and 18 in area 17). Two hundred three neurons recorded and quantitatively tested in areas 17 and 18 of the normal adult cat were used for comparison. 2. Spatial characteristics of receptive fields investigated using hand-held stimuli were found to be abnormal. The correlation between receptive-field width and eccentricity was lost in area 18 and consequently, receptive fields were significantly wider in area 18 subserving central vision. Cells could be classified according to the spatial characteristics of their receptive fields. There was a much smaller proportion of end-stopped cells in strobe-reared animals. Orientation tuning in the deprived animals was normal except for a small number of cells that showed no selectivity for stimulus orientation. 3. Compilation of velocity-response curves made it possible to classify areas 17 and 18 neurons into four categories: velocity low-pass, velocity broad-band, velocity tuned, and velocity high-pass cells. The proportion of velocity high-pass cells was reduced in area 18 subserving peripheral vision, as was the proportion of velocity-tuned cells in area 18 subserving central vision. 4. In the strobe-reared animal velocity sensitivity was somewhat different from that of the normal animal. Neurons in area 18 subserving the peripheral visual field failed to respond to fast velocities. Neurons in area 17 subserving the central visual field in strobe-reared animals responded to slightly higher velocities than in the normal animal. 5. In the deprived animals the number of neurons that were selective to the direction of motion was strongly reduced. The majority of neurons failed to show a selectivity for direction at all velocities. A number of neurons could be directional at some velocities but were unreliable, since they inverted their preferred direction with velocity changes. 6. Binocular convergence onto visual cortical cells was perturbed. In area 18 the majority of neurons were driven by the contralateral eye. In area 17 most neurons could be driven only by either the ipsilateral or contralateral eye. 7. Quantitative testing (of direction selectivity, sensitivity to high velocities, response latency, and strength) and qualitative testing (receptive-field width, end stopping, and ocular dominance) showed that the normal influence of eccentricity on functional properties was strongly reduced by strobe rearing.

Neurons in the primary auditory cortex (AI) of anesthetized cats were studied for their sensitivity to directions of transient sounds in virtual acoustic space under a variety of conditions. An effective transient sound evokes a single spike or short burst of spikes with a precisely timed onset. The aggregate of effective directions forms a spatial receptive field. Typically, spatial receptive fields are large, often occupying a quadrant or more of acoustic space. Within the receptive field onset latency varies systematically with direction thereby providing information about source direction. This receptive field structure is highly robust, remaining relatively stable under conditions of competing sounds. Maximum likelihood analysis suggests that psychophysical spatial acuity can be achieved with a relatively small ensemble of AI neurons with broad receptive fields having response gradients of latency. Using reverse correlation and white-noise analysis receptive fields were mapped in space and time. This analysis revealed that spatial receptive fields of AI neurons need not be static but may exhibit marked temporal dynamics. This suggests a sensitivity for direction and speed of moving sound sources.