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An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex
Abstract
1. Using the two-dimensional (2D) spatial and spectral response profiles described in the previous two reports, we test Daugman's generalization of Marcelja's hypothesis that simple receptive fields belong to a class of linear spatial filters analogous to those described by Gabor and referred to here as 2D Gabor filters. 2. In the space domain, we found 2D Gabor filters that fit the 2D spatial response profile of each simple cell in the least-squared error sense (with a simplex algorithm), and we show that the residual error is devoid of spatial structure and statistically indistinguishable from random error. 3. Although a rigorous statistical approach was not possible with our spectral data, we also found a Gabor function that fit the 2D spectral response profile of each simple cell and observed that the residual errors are everywhere small and unstructured. 4. As an assay of spatial linearity in two dimensions, on which the applicability of Gabor theory is dependent, we compare the filter parameters estimated from the independent 2D spatial and spectral measurements described above. Estimates of most parameters from the two domains are highly correlated, indicating that assumptions about spatial linearity are valid. 5. Finally, we show that the functional form of the 2D Gabor filter provides a concise mathematical expression, which incorporates the important spatial characteristics of simple receptive fields demonstrated in the previous two reports. Prominent here are 1) Ca…
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“There is some evidence that certain cells in the mammalian visual cortex (responsible for the perception of texture) can be approximated by such filters [40]”
From A Survey of Underwater Acoustic Data Classification Methods Using Deep Learning for Shoreline Surveillance (2022) · cites this paper as [40]
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MethodEXPERT SYSTEMS WITH APPLICATIONS
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Image representation using 2D Gabor wavelets
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“The careful mapping of the receptive fields of the simple cells by Jones and Palmer [17] confirmed the validity of this model.”
MethodSlow Feature Analysis: Unsupervised Learning of Invariances
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“Consider five monocular simple cells for the left and right eyes with receptive fields, as indicated in Figure 4. The simple cells are modeled by spatial Gabor wavelets ( Jones & Palmer, 1987 ), whose responses Q x.t/ to a visual stimulus smoothly moving across the receptive field are given by a combination of nonnega…”
MethodIdentifying natural images from human brain activity
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MethodHighly selective receptive fields in mouse visual cortex
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Specificity of monosynaptic connections from thalamus to visual cortex
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A Biologically Inspired System for Action Recognition
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Neural Mechanisms of Orientation Selectivity in the Visual Cortex
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“Given the measured aspect ratio of the simple cell subfields (Jones & Palmer 1987a,b) and the cross-correlation studies that suggest that the subfields arise from geniculate input (Tanaka 1983, Reid & Alonso 1995), it seemed likely that the relay cell input to a simple cell would by itself show…”
BackgroundMultiresolution spectrotemporal analysis of complex sounds
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“The aspect ratio of the feedforward LGN input, as well as the number of receptive field subregions, are major factors that affect bandwidth (Hubel and Wiesel, 1962; Jones and Palmer, 1987; Ferster, 1988).”
BackgroundMethodA Deep Learning Ensemble Approach for Diabetic Retinopathy Detection
Qummar, S., Khan, F. G., Shah, S., Khan, A., Shamshirband, S., Rehman, Z. U., Khan, I. A., & Jadoon, W. (2019) · IEEE Access · doi:10.1109/access.2019.2947484 · Cited by 661
“The hand-on engineering methods extract features using traditional approaches such as HoG [11], SIFT [12], LBP [13], Gabor filters [14] and etc which fails to encode the variations in scale, rotation, and illumination.”
MethodShadlen, M. N., & Movshon, J. A. (1999) · Neuron · doi:10.1016/s0896-6273(00)80822-3 · Cited by 606
Gabor-based kernel pca with fractional power polynomial models for face recognition
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Natural image statistics and efficient coding
Olshausen, B. A., & Field, D. (1996) · Network Computation in Neural Systems · doi:10.1088/0954-898x/7/2/014 · Cited by 555
“the spatial frequency response is generally bandpass with bandwidths in the range of 1‐2 octaves [6, 12, 13 , 16].”
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Wagemans, J. P., Feldman, J., Gepshtein, S., Kimchi, R., Pomerantz, J. R., van der Helm, P. A., & van Leeuwen, C. (2012) · Psychological Bulletin · doi:10.1037/a0029334 · Cited by 595
“The similarity of visual receptive fields and Gabor filters is well established (Jones & Palmer, 1987).”
BackgroundThe Temporal Correlation Hypothesis of Visual Feature Integration
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Why is Real-World Visual Object Recognition Hard?
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“The responses of these cells to visual stimuli are welldescribed by a spatial linear filter, resembling a Gabor wavelet [29– 31], with a nonlinear output function (threshold and saturation) and some local normalization (roughly analogous to ‘‘contrast gain control’’).”
BackgroundPrecisely correlated firing in cells of the lateral geniculate nucleus
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Independent component analysis of gabor features for face recognition
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“Psychophysicalfindings indicate,however, that “perceptualtaskssuchassimilarity judgmenttend to be performedon a low-dimensionalrepresentationof the sensorydata.”
BackgroundA review on Gabor wavelets for face recognition
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“Note the assumption here that the orientation of the wave vector is the same as that of the major axis of the elliptical Gaussian, which is fully supported by the models of the receptive fields found in simple cells of cat and macaque striate cortices [22, 52 ].”
BackgroundContour detection based on nonclassical receptive field inhibition
Grigorescu, C., Petkov, N., & Westenberg, M. A. (2003) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.814250 · Cited by 445
“particular, a family of two-dimensional Gabor functions was proposed as a model of the linear filtering properties of simple cells [33], [34].”
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Gabor Feature Based Sparse Representation for Face Recognition with Gabor Occlusion Dictionary
Yang, M., & Lei Zhang, A. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-15567-3_33 · Cited by 441
“The Gabor filter was first introduced by David Gabor in 1946 [13], and was later shown as models of simple cell receptive fields [14].”
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Scheibert, J., Leurent, S., Prevost, A. M., & Debrégeas, G. (2009) · Science · doi:10.1126/science.1166467 · Cited by 421
How Close Are We to Understanding V1?
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Spatial Structure and Symmetry of Simple-Cell Receptive Fields in Macaque Primary Visual Cortex
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“In contrast to previous findings (DeAngelis et al. 1993a; Field and Tolhurst 1986; Hamilton et al. 1989; Jones and Palmer 1987a), the macaque data are significantly bimodal [P 0.02, Hartigan’s dip test, (Hartigan and Hartigan 1985)], with cells clustering near 0 (even symmetry) and /2 (odd…”
BackgroundMethodResultInfluentialFusing local patterns of Gabor magnitude and phase for face recognition
Xie, S., Shan, S., Chen, X., & Chen, J. (2010) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2041397 · Cited by 395
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A Cortical Based Model of Perceptual Completion in the Roto-Translation Space
Citti, G., & Sarti, A. (2006) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-005-3630-2 · Cited by 347
“Receptive fields of simple cells are modeled usually as convolution kernels of even and odd filters such as Gabor filters [12, 33 , 42, 52].”
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Deep Hierarchies in the Primate Visual Cortex: What Can We Learn for Computer Vision?
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Deep convolutional models improve predictions of macaque V1 responses to natural images
Cadena, S. A., Denfield, G. H., Walker, E. Y., Gatys, L. A., Tolias, A. S., Bethge, M., & Ecker, A. S. (2019) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1006897 · Cited by 363
“6 Our current standard model of V1 is based on linear-nonlinear models (LN) [4, 5] and 7 energy models [6] to explain simple and complex cells, respectively.”
MethodRoskies, A. L. (1999) · Neuron · doi:10.1016/s0896-6273(00)80817-x · Cited by 347
Solutions to the Binding Problem
Treisman, A. (1999) · Neuron · doi:10.1016/s0896-6273(00)80826-0 · Cited by 324
Facial expression recognition using radial encoding of local Gabor features and classifier synthesis
Gu, W., Xiang, C., Venkatesh, Y. V., Huang, D., & Lin, H. T. (2011) · Pattern Recognition · doi:10.1016/j.patcog.2011.05.006 · Cited by 312
“In order to model the spatial orientation properties of simple cells in the primary cortex, a set of two-dimensional Gabor filters have been proposed [22].”
MethodEncoding of binocular disparity by simple cells in the cat's visual cortex
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BackgroundMethodNew perspectives on the mechanisms for orientation selectivity
Sompolinsky, H., & Shapley, R. M. (1997) · Current Opinion in Neurobiology · doi:10.1016/s0959-4388(97)80031-1 · Cited by 297
Visual Spatial Characterization of Macaque V1 Neurons
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“Simple cells respond best to oriented bars at a specific position in the visual field, and are well modeled by a linear Gabor filter (Jones & Palmer, 1987).”
Survey of neural network technology for automatic target recognition
Roth, M. W. (1990) · IEEE Transactions on Neural Networks · doi:10.1109/72.80203 · Cited by 267
Discriminative Blur Detection Features
Shi, J., Xu, L., & Jia, J. (2014) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2014.379 · Cited by 266
“We also study how spatial filters such as Gabor [10] and Laplacian, can be used in this detection problem.”
MethodTexture Feature Analysis for Computer-Aided Diagnosis on Pulmonary Nodules
Han, F., Wang, H., Zhang, G., Han, H., Song, B., Li, L. C., Moore, W. H., Lu, H., Zhao, H., & Liang, Z. (2014) · Journal of Imaging Informatics in Medicine · doi:10.1007/s10278-014-9718-8 · Cited by 266
Characterizing the sparseness of neural codes
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Fully Automatic Facial Feature Point Detection Using Gabor Feature Based Boosted Classifiers
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“Gabor wavelets seem to be a good approximation to the sensitivity profiles of neurons found in visual cortex of higher vertebrates [ 16 ].”
BackgroundHalf-squaring in responses of cat striate cells
Heeger, D. J. (1992) · Visual Neuroscience · doi:10.1017/s095252380001124x · Cited by 262
Depth is encoded in the visual cortex by a specialized receptive field structure
DeAngelis, G. C., Ohzawa, I., & Freeman, R. D. (1991) · Nature · doi:10.1038/352156a0 · Cited by 252
Robust classification of hand postures against complex backgrounds
Triesch, J., & von der Malsburg, C. (2002) · International Conference on Automatic Face and Gesture Recognition · doi:10.1109/afgr.1996.557260 · Cited by 249
Local diversity and fine-scale organization of receptive fields in mouse visual cortex
Bonin, V., Histed, M. H., Yurgenson, S., & Reid, R. C. (2011) · The Journal of Neuroscience · doi:10.1523/jneurosci.2974-11.2011 · Cited by 247
“Random stimuli are useful to quantify receptive fields (Jones and Palmer, 1987a; Reid and Shapley, 1992; Reid and Alonso, 1995; Reid et al., 1997; Ringach et al., 1997; DeAngelis et al., 1999).”
BackgroundMethodInfluentialBen Hamed, S., Duhamel, J.-R., Bremmer, F., & Graf, W. (2001) · Experimental Brain Research · doi:10.1007/s002210100785 · Cited by 242
Three-dimensional solid texture analysis in biomedical imaging: Review and opportunities
Depeursinge, A., Foncubierta–Rodríguez, A., Ville, D. V. D., & Müller, H. (2013) · Medical Image Analysis · doi:10.1016/j.media.2013.10.005 · Cited by 241
“2-D Gabor filters are modeling neurophysiological measurements of the two-dimensional anisotropic receptive field profiles describing single neurons in the mammalian visual cortex (Jones and Palmer, 1987).”
BackgroundAge estimation from face images: Human vs. machine performance
Han, H., Otto, C., & Jain, A. K. (2013) · International Conference on Biometrics · doi:10.1109/icb.2013.6613022 · Cited by 245
Training deep neural density estimators to identify mechanistic models of neural dynamics
Gonçalves, P. J., Lueckmann, J.-M., Deistler, M., Nonnenmacher, M., Öcal, K., Bassetto, G., Chintaluri, C., Podlaski, W. F., Haddad, S. A., Vogels, T. P., et al. (2020) · eLife · doi:10.7554/elife.56261 · Cited by 287
Camouflage and visual perception
Trościanko, T., Benton, C. P., Lovell, P. G., Tolhurst, D. J., & Pizlo, Z. (2008) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2008.0218 · Cited by 236
“Moreover, edge detectors do not only detect features such as edges or line segments; they will respond to any feature that has any similarity to an edge, provided that the feature is intense enough (Maffei & Fiorentini 1973; Movshon et al. 1978; Jones & Palmer 1987; Smyth et al. 2003).”
Generic neighborhood operators
Koenderink, J. J., & van Doorn, A. J. (1992) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.141551 · Cited by 231
Attention Based Detection and Recognition of Hand Postures Against Complex Backgrounds
Pisharady, P. K., Vadakkepat, P., & Loh, A. P. (2012) · International Journal of Computer Vision · doi:10.1007/s11263-012-0560-5 · Cited by 228
“The cortical simple cell receptive fields are modeled (Jones and Palmer 1987) using a Gabor filter (Gabor wavelet) (1), (2). s.t. x 0 = x cos θ + y sin θ and y 0 = − x sin θ + y cos θ. (2) where, γ the spatial aspect ratio of the Gaussian function, σ the standard deviation of the Gaussian function, λ…”
MethodRobust Methods for Real-Time Diabetic Foot Ulcer Detection and Localization on Mobile Devices
Goyal, M., Reeves, N. D., Rajbhandari, S. M., & Yap, M. H. (2018) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2018.2868656 · Cited by 227
“filter [32], Histogram of Oriented Gradients (HOG) [33], shape based descriptors such as hough transform [34] and color descriptors such as Normalized RGB, HSV, and L*u*v features”
BackgroundPredictive coding as a model of response properties in cortical area V1
Spratling, M. W. (2010) · The Journal of Neuroscience · doi:10.1523/jneurosci.4911-09.2010 · Cited by 206
“The RF of a simple cell in primary visual cortex can be accurately modeled by a two-dimensional Gabor function (Daugman, 1980, 1988; Marcelja, 1980; Jones and Palmer, 1987; Lee, 1996).”
MethodPrince, S. J. D., Pointon, A. D., Cumming, B. G., & Parker, A. J. (2002) · Journal of Neurophysiology · doi:10.1152/jn.00465.2000 · Cited by 219
“A suitable function is the Gabor function, which has been extensively evaluated as a suitable function for describing both monocular RF profiles of simple cells (Daugman 1985; Jones and Palmer 1987; Marcelja 1980) in cortical area V1.”
A Synaptic Explanation of Suppression in Visual Cortex
Carandini, M., Heeger, D. J., & Senn, W. (2002) · Journal of Neuroscience · doi:10.1523/jneurosci.22-22-10053.2002 · Cited by 219
“The spatial receptive field of our V1 neuron is given by a Gabor function (Hawken and Parker, 1987; Jones and Palmer, 1987),”
MethodNonlinear operator for oriented texture
Kruizinga, P., & Petkov, N. (1999) · IEEE Transactions on Image Processing · doi:10.1109/83.791965 · Cited by 214
“It has been found to vary in a limited range of [43].”
BackgroundAutomatic Identification of the Pectoral Muscle in Mammograms
Ferrari, R. J., Rangayyan, R. M., Desautels, J. E. L., Borges, R. A., & Frere, A. F. (2004) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2003.823062 · Cited by 213
“5 octaves, and their angular bandwidth is expected to be smaller than 30 [13], [14].”
BackgroundA model for the estimate of local image velocity by cells in the visual cortex
Grzywacz, N. M., & Yuille, A. (1990) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.1990.0012 · Cited by 213
The “silent” surround of V1 receptive fields: theory and experiments
Seriès, P., Lorenceau, J., & Frégnac, Y. (2003) · Journal of Physiology-Paris · doi:10.1016/j.jphysparis.2004.01.023 · Cited by 214
“2A), a first Gaussian (Lc), represents the excitatory contribution of the CRF center and can be assumed to correspond to the envelope of a Gabor function representing the CRF’s spatial structure [73], while the second Gaussian (Ls), centered at the same position, describes the suppressive contribution of the surround.”
BackgroundMechanisms of Neuronal Computation in Mammalian Visual Cortex
Priebe, N. J., & Ferster, D. (2012) · Neuron · doi:10.1016/j.neuron.2012.06.011 · Cited by 209
“When assayed from spike rate, however, there is a strong mismatch between predicted and measured width of tuning (Gardner et al., 1999; Jones and Palmer, 1987).”
BackgroundCenter-surround patterns emerge as optimal predictors for human saccade targets
Kienzle, W., Franz, M., Schölkopf, B., & Wichmann, F. A. (2009) · Journal of Vision · doi:10.1167/9.5.7 · Cited by 197
“This analysis is more generally known as system identification and is commonly used for identifying biological systems (Victor, 2005), e.g., neuronal receptive fields (Jones & Palmer, 1987) (“reverse correlation”).”
MethodThe Psychophysical Evidence for a Binding Problem in Human Vision
Wolfe, J. M., & Cave, K. R. (1999) · Neuron · doi:10.1016/s0896-6273(00)80818-1 · Cited by 197
Are Cortical Models Really Bound by the “Binding Problem”?
Riesenhuber, M., & Poggio, T. (1999) · Neuron · doi:10.1016/s0896-6273(00)80824-7 · Cited by 194
Encoding of Binocular Disparity by Complex Cells in the Cat's Visual Cortex
Ohzawa, I., DeAngelis, G. C., & Freeman, R. D. (1997) · Journal of Neurophysiology · doi:10.1152/jn.1997.77.6.2879 · Cited by 186
“AL , AR, and AB are scaling factors that account for ocular dominance and balance of monocular and binocular(binocular) term is a two-dimensional Gabor function (Daugmann 1985; Gabor 1946; Jones and Palmer 1987a,b; terms.”
BackgroundMethodDeep neural networks in computational neuroscience
Kietzmann, T. C., McClure, P., & Kriegeskorte, N. (2019) · Oxford Research Encyclopedia of Neuroscience · doi:10.1093/acrefore/9780190264086.013.46 · Cited by 186
Koenderink, J. J., & van Doorn, A. J. (1990) · Biological Cybernetics · doi:10.1007/bf00203452 · Cited by 181
“The wavelets are of interest because they most closely resemble the RFS's actually encountered in the mammalian primary visual cortex [18, 7, 8 ].”
BackgroundPetkov, N., & Kruizinga, P. (1997) · Biological Cybernetics · doi:10.1007/s004220050323 · Cited by 180
“It has been found to vary in a limited range of 0.23 γ 0.92 (Jones and Palmer 1987).”
BackgroundInfluentialMcLean, J., & Palmer, L. A. (1989) · Vision Research · doi:10.1016/0042-6989(89)90029-1 · Cited by 179
“METHODS In order to test this hypothesis, we modified our reverse correlation procedure used previously to characterize single receptive fields in two spatial dimensions (Jones & Palmer, 1987a).”
MethodSelf-citationSpatial and temporal receptive fields of geniculate and cortical cells and directional selectivity
Valois, R. L. D., Cottaris, N. P., Mahon, L. E., Elfar, S. D., & Wilson, J. A. (2000) · Vision Research · doi:10.1016/s0042-6989(00)00210-8 · Cited by 179
Localized texture processing in vision: analysis and synthesis in the Gaborian space
Porat, M., & Zeevi, Y. Y. (1989) · IEEE Transactions on Biomedical Engineering · doi:10.1109/10.16457 · Cited by 177
Evidence and a computational explanation of cultural differences in facial expression recognition.
Dailey, M. N., Joyce, C. A., Lyons, M. J., Kamachi, M., Ishi, H., Gyoba, J., & Cottrell, G. W. (2010) · Emotion · doi:10.1037/a0020019 · Cited by 181
“They act as edge detectors and have been shown to accurately model the receptive fields of simple cells in primary visual cortex (Jones & Palmer, 1987).”
BackgroundDevelopment of feature detectors by self-organization
Rubner, J., & Schulten, K. (1990) · Biological Cybernetics · doi:10.1007/bf00198094 · Cited by 169
Logical/linear operators for image curves
Iverson, L., & Zucker, S. W. (1995) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.464562 · Cited by 168
Metadata
- Authors
- Jones, J. P., & Palmer, L. A.
- Affiliations
- University of Pennsylvania (US)
- Venue
- Journal of Neurophysiology
- Publisher
- American Physiological Society
- Published
- 1987-12-01
- Volume
- 58
- Issue
- 6
- Pages
- 1233-1258
- ISSN
- 0022-3077 (ISSN-L)
- 1522-1598
- OpenAlex
- W1914401667
- Cited by
- 1,658
- References
- 22
- Citations by year
- 2026: 15 · 2025: 38 · 2024: 31 · 2023: 36 · 2022: 56 · 2021: 47 · 2020: 75 · 2019: 60 · 2018: 56 · 2017: 64 · 2016: 61 · 2015: 64 · 2014: 81 · 2013: 63 · 2012: 63
- FWCI
- 6.85
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Neurophysiology (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Eye Institute (R01-EY-04638)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Life Sciences › Neuroscience › Cellular and Molecular Neuroscience › Neuroscience and Neuropharmacology Research
- Keywords
- simple cells, spatial linearity
- MeSH terms
- Animals, Cats, Mathematics, Models, Neurological, Visual Cortex, Visual Fields, Visual Perception
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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