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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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Effects of surrounding frame on visual search for vertical or tilted bars
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BackgroundIris Encoding and Recognition using Gabor Wavelets
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Perceptual Grouping in a Neural Model: Reproducing Human Texture Perception
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Learning to integrate parts for whole through correlated neural variability
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Disentangled convolution for optimizing receptive field
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“Marcelja (1980) as well as Jones and Palmer (1987b; 1987a) proposed to model simple cells by Gabor functions, motivated by their property of minimizing the uncertainty relation; see also (Porat and Zeevi 1988) for a more general proposal of using the Gabor filter model for visual operations.”
MethodA large-scale neurocomputational model of spatial cognition integrating memory with vision
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Contour Detection by CORF Operator
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Encoding Voxels with Deep Learning
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“For example, the integration of spectral and spatial context was an effective method for HSI classification, and more researchers intended to extract spatial information with different filters, such as guided filter (GDF) [30], bilateral filter (BF) [31], Gabor filter (GF) [32] and etc.”
MethodActive learning of cortical connectivity from two-photon imaging data
Bertrán, M., Martínez, N., Wang, Y., Dunson, D. B., Sapiro, G., & Ringach, D. L. (2018) · PLoS ONE · doi:10.1371/journal.pone.0196527 · Cited by 6
“For example, in studying visual cortex we can select a specific visual stimulus [5–8], or we can stimulate individual neurons directly via two-photon optogenetics [9,10].”
MethodNeural Signatures of Learning Novel Object–Scene Associations
Smith, C. M., & Federmeier, K. D. (2020) · Journal of Cognitive Neuroscience · doi:10.1162/jocn_a_01530 · Cited by 8
“…of any particular waveform feature, we examined low-level visual feature similarity, providing a conservative test of visual form reactivation and taking advantage of the fact that the modeling of such low-level features is well established (Pinto, Cox, & DiCarlo, 2008; Jones & Palmer, 1987).”
BackgroundBeshkov, K., & Tiesinga, P. H. E. (2021) · Biological Cybernetics · doi:10.1007/s00422-021-00906-5 · Cited by 6
“8 Gabor Filters In order to estimate the potential confounds introduced by presenting only a limited sample of stimuli we wanted to see what topology is generated by a simple gabor filter model presented with static gratings Jones and Palmer (1987). The Gabor filter is defined by the equation:”
BackgroundMethodStructured random receptive fields enable informative sensory encodings
Pandey, B., Pachitariu, M., Brunton, B. W., & Harris, K. D. (2022) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010484 · Cited by 6
Efficient Neural Models for Visual Attention
Chevallier, S., Cuperlier, N., & Gaussier, P. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-15910-7_29 · Cited by 6
“In bio-inspired attentional systems, the detection of visual is usually achieved with difference of Gaussians (DOG) filters to reproduce the spatial transformation of retinal ganglion cells [8] and Gabor wavelets to detect orientations, as observed in the simple cells of the primary visual cortex [ 11 ].”
MethodUrsino, M., Cara, G.-E. L., & Ritrovato, M. (2006) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2006.05.002 · Cited by 6
“(13)–(14) have been assigned in acceptable accord with physiological data [2,18,27,29–34] (see Table 1).”
BackgroundRotation-invariant local radius index: A compact texture similarity feature for classification
Zhai, Y., & Neuhoff, D. L. (2014) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.2014.7026155 · Cited by 6
Neurons in cat V1 show significant clustering by degree of tuning
Ziskind, A. J., Emondi, A. A., Kurgansky, А. V., Rebrik, S. P., & Miller, K. D. (2015) · Journal of Neurophysiology · doi:10.1152/jn.00646.2014 · Cited by 6
“, Kaschube et al. 2002), and F1/DC, which is known to cluster by layers [e.g., Martinez et al. (2005) showed that simple cells predominate in cat layer 4, and Ringach et al.”
BackgroundRandomly oriented edge arrangements dominate naturalistic arrangements in binocular rivalry
Hunt, J. J., Mattingley, J. B., & Goodhill, G. J. (2012) · Vision Research · doi:10.1016/j.visres.2012.05.007 · Cited by 6
“Gabors were used as the basic building block because they are both a good description of V1 simple cell receptive fields (Jones et al., 1987) and the independent components of natural images are Gabor-like (Bell & Sejnowski, 1997; Van Hateren & Van der Schaaf, 1998).”
A spatial-constrained multi-target regression model for human brain activity prediction
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“Based on the aspect ratio in the simple sensory field of a cat's visual cortex, which ranges from 0.23 to 0.92 [57], we set γ = 0.5 .”
BackgroundInfluentialAn Encoding Framework With Brain Inner State for Natural Image Identification
Wu, H., Zhu, Z., Wang, J., Zheng, N., & Chen, B. (2020) · IEEE Transactions on Cognitive and Developmental Systems · doi:10.1109/tcds.2020.2987352 · Cited by 6
“1) Gabor wavelet pyramid model: The Gabor wavelet pyramid (GWP) model has long been considered as a standard model of how early visual cortex represents local shape [27], [28], [29].”
BackgroundA Differential Model of the Complex Cell
Hansard, M. E., & Horaud, R. (2011) · Cited by 6
Brain-Inspired Algorithms for Processing of Visual Data
Strisciuglio, N., & Petkov, N. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-82427-3_8 · Cited by 6
Pattern Recognition with Localized Gabor Wavelet Grids
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Feature-Specific Denoising of Neural Activity for Natural Image Identification
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Human face recognition by adaptive processing of tree structures representation
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Spatial and temporal jitter distort estimated functional properties of visual sensory neurons
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“In particular, the spikeconditioned mean is often interpreted as the stimulus “feature” to which a cell responds (Jones and Palmer 1987; Meister et al. 1994; Poon and Yu 2000; Reid and Alonso 1995; Schwartz et al. 2006; Simoncelli et al. 2004).”
BackgroundInfluentialRetinotopy and spatial phase in topographic maps
Mayer, N. M., Herrmann, J. M., & Geisel, T. (2000) · Neurocomputing · doi:10.1016/s0925-2312(00)00198-3 · Cited by 6
Robust local feature extraction algorithm with visual cortex for object recognition
Lee, J., Roh, K. A., Wägner, D., & Ko, H. (2011) · Electronics Letters · doi:10.1049/el.2011.1832 · Cited by 6
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“…sensitivity profiles of many simple cells in cat and monkey visual cortex can be described quite well as Gabor functions (Field & Tolhurst 1986; Jones & Palmer 1987; Hawken & Parker 1987; Ringach 2002), and the Gabor equation (Equation 1) is very versatile, allowing the easy construction of…”
BackgroundReceptive Field Map Development by Anti-Hebbian Learning
Andrade-Navarro, M. A., & Morán, F. (1997) · Neural Networks · doi:10.1016/s0893-6080(97)00003-8 · Cited by 6
Interpreting the neural code with Formal Concept Analysis
Endres, D., & Földiák, P. (2008) · Cited by 6
An efficient multimodal face recognition method robust to pose variation
Cheraghian, A., Karim Faez, A., Dastmalchi, H., & Oskuie, F. B. (2011) · IEEE Symposium on Computers & Informatics (ISCI) · doi:10.1109/isci.2011.5958954 · Cited by 6
“A Gabor wavelet is complex sinusoids which are modulated by a 2D Gaussian function and represents the properties of spatial localization, orientation selectivity, spatial frequency selectivity, and quadrature phase relationships [ 15 ].”
MethodVisual Odometry Based on Gabor Filters and Sparse Bundle Adjustment
Kwolek, B. (2007) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/robot.2007.364025 · Cited by 6
Biologically inspired Cartesian and non-Cartesian filters for attentional sequences
Bozma, H. I., Çakıroğlu, G., & Soyer, Ç. (2003) · Pattern Recognition Letters · doi:10.1016/s0167-8655(02)00333-1 · Cited by 6
Building Gabor Filters From Retinal Responses
Partzsch, J., Mayr, C., & Schüffny, R. (2007) · doi:10.5281/zenodo.1074626 · Cited by 6
Parallel Pathways of Primate Vision
Silveira, L. C. L., & de Mello, H. D. (1998) · Springer eBooks · doi:10.1007/978-1-4615-5333-5_10 · Cited by 6
Evolutionary reconfigurable architecture for robust face recognition
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View independent face recognition based on kernel principal component analysis of local parts
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“It is known that Gabor filters are well fitted to the receptive field profiles of the simple cells of cat’s visual cortex [19].”
Spike Correlation Measures that Eliminate Stimulus Effects in Response to White Noise
Nykamp, D. Q. (2003) · Journal of Computational Neuroscience · doi:10.1023/a:1021958802403 · Cited by 6
“…and somatosensory systems (Reid and Alonso, 1995; Marmarelis and Marmarelis, 1978; DeBoer and Kuyper, 1968; deCharms et al., 1998; Jenison et al., 2001; Jones and Palmer, 1987; DeAngelis et al., 1993a, 1993b; Reid et al., 1997; Ringach et al., 1997; DiCarlo et al., 1998; DiCarlo and Johnson, 1999).”
BackgroundMethodAn architecture for feature detection utilizing dynamic synapses
Heittmann, A., & Ramacher, U. (2004) · IEEE International Midwest Symposium on Circuits and Systems (MWSCAS) · doi:10.1109/mwscas.2004.1354171 · Cited by 6
“In [ 4 ][5] the assumption was made, that the response of a simple cell is due to a behavior similar to linear filters.”
BackgroundAngular Induction as a Function of the Length and Position of Segments and Gaps
Greene, E. G., & Levinson, D. M. (1994) · Perception · doi:10.1068/p230785 · Cited by 6
A multi-chip implementation of cortical orientation hypercolumns
Choi, T. Y. W., Shi, B. E., & Boahen, K. A. (2004) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2004.1328671 · Cited by 6
“The linear filter for an orientation selective neuron is commonly modelled using a spatial Gabor filter [ 3 ], whose impulse response is a 2-D sinusoid modulated by a Gaussian.”
MethodAn orientation selective 2D AER transceiver
Choi, T. Y. W., Shi, B. E., & Boahen, K. A. (2003) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2003.1206324 · Cited by 6
Correlation-based feature detection using pulsed neural networks
Heittmann, A., & Ramacher, U. (2004) · Machine learning for signal processing ... · doi:10.1109/nnsp.2003.1318047 · Cited by 6
Yoshida, T., & Ohki, K. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/300863 · Cited by 5
Towards a simplified model of primary visual cortexPreprint
Du, F., Núñez-Ochoa, M. A., Pachitariu, M., & Stringer, C. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.06.30.601394 · Cited by 6
“Simple models of V1 responses include simple/complex cell models [3], linear-nonlinear models [4, 5], Gabor functions [6], and orientation tuning curves [7, 8].”
MethodEarly visual signatures and benefits of intra-saccadic motion streaks
Schweitzer, R., Seel, T., Raisch, J., & Rolfs, M. (2025) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1013544 · Cited by 5
“…to 1440 Hz to match the projection system’s temporal resolution) from the concurrent placement of the stimulus center. as well as even and odd phases ( 𝜙 ; levels: 0 and 90 deg), as Gabor filters have been shown to be very suitable models for early-visual receptive fields (RFs; [96–98]).”
Research of multi-focus image fusion algorithm based on Gabor filter bank
Xue-jun, L., & Wang, M. (2014) · doi:10.1109/icosp.2014.7015092 · Cited by 5
Ryu, J., & Lee, S. (2024) · Communications Biology · doi:10.1038/s42003-024-05846-x · Cited by 5
Foveated Image and Video Processing and Search
Floren, A., & Bovik, A. C. (2014) · Academic press library in signal processing · doi:10.1016/b978-0-12-396501-1.00014-5 · Cited by 5
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Spoerer, C. J., Eguchi, A., & Stringer, S. M. (2016) · Vision Research · doi:10.1016/j.visres.2015.12.008 · Cited by 5
“Pre-processing of the visual input by Gabor filters Before images are presented to layer 1 of VisNet, they are preprocessed by a set of Gabor filters that correspond to the known response profiles of V1 simple cells (Jones & Palmer, 1987; Cumming & Parker, 1999).”
Hooshangnejad, H., Gharibzadeh, S., & Towhidkhah, F. (2016) · Advances in Science and Technology – Research Journal · doi:10.12913/22998624/62771 · Cited by 5
Akamatsu, Y., Harakawa, R., Ogawa, T., & Haseyama, M. (2019) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2019.8682402 · Cited by 5
Sub-Optimality of the Early Visual System Explained Through Biologically Plausible Plasticity
Chauhan, T., Masquelier, T., & Cottereau, B. R. (2021) · Frontiers in Neuroscience · doi:10.3389/fnins.2021.727448 · Cited by 5
“…support complex computational operations implied by such optimisation may emerge, how these structures adapt, even in adulthood (Hübener & Bonhoeffer, 2014; Wandell & Smirnakis, 2010), and why some neurones possess receptive fields (RFs) which are sub-optimal (Jones & Palmer, 1987; Ringach, 2002).”
BackgroundResultUnsupervised Learning for the Segmentation of Small Crystalline Particles at the Atomic Level
Bárcena‐González, G., Hernández‐Robles, A., Mayoral, Á., Martínez, L., Huttel, Y., Galindo, P. L., & Ponce, A. (2023) · Crystal Research and Technology · doi:10.1002/crat.202200211 · Cited by 5
Nguyen, P., Sooriyaarachchi, J., Huang, Q., & Baker, C. L. (2024) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1012127 · Cited by 5
“These functions fit most receptive fields well [52,53], provide parameters of interest directly in the fitted function, and also have a rich theoretical underpinning [53].”
BackgroundMethodInfluentialFu, J., Pierzchlewicz, P. A., Willeke, K. F., Bashiri, M., Muhammad, T., Diamantaki, M., Froudarakis, E., Restivo, K., Ponder, K., Denfield, G. H., et al. (2024) · Cell Reports · doi:10.1016/j.celrep.2024.114639 · Cited by 5
Pengenalan Ekspresi Wajah berbasis Filter Gabor dan Backpropagation Neural Network
Raharjo, P. M. (2012) · Jurnal EECCIS (Electrics Electronics Communications Controls Informatics Systems) · doi:10.21776/jeeccis.v4i1.96 · Cited by 5
Efficient object detection based on selective attention
Yu, H., Chang, Y., Lü, P., Xu, Z., Fu, C., & Wang, Y. (2013) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2013.09.002 · Cited by 5
Bayesian segmentation of AM-FM texture images
Yap, T. B., Havlicek, J., & DeBrunner, V. (2001) · Asilomar Conference on Signals, Systems and Computers (ACSSC) · doi:10.1109/acssc.2001.987673 · Cited by 5
“AM-FM models [4,5, 10, 11, 15, 161 provide a powerful means of characterizing texture in terms of nonstationary joint amplitude and frequency modulations and are also parsimonious with certain plausible models of early processing in biological vision systems [7,9, 13 ,22].”
MethodFace Recognition Using DT-CWT Feature-Based 2DPCA
Sun, Z., Yang, W., Sun, C., & Shen, J. (2010) · Chinese Conference on Pattern Recognition · doi:10.1109/ccpr.2010.5659291 · Cited by 5
“To evaluate the performance of the proposed approach, we compare it with the following methods: LDA [1], inverse FDA [9], 2DPCA [10], 2DFDA [11] and 2DIFDA [ 14 ] in two face image databases, namely, the ORL database and FERET database.”
BackgroundMethodInfluentialProperties of the magnitude terms of orthogonal scaling functions
Tay, P. C., Havlicek, J., Acton, S. T., & Hossack, J. A. (2010) · Digital Signal Processing · doi:10.1016/j.dsp.2009.12.013 · Cited by 5
Comparing performance of humans and pigeons in rule-based visual categorization tasks
Berg, M. E., Ward, M. D., Dai, Z., Arantes, J., & Grace, R. C. (2013) · Learning and Motivation · doi:10.1016/j.lmot.2013.11.001 · Cited by 5
Ursino, M., Magosso, E., & Cuppini, C. (2008) · Vision Research · doi:10.1016/j.visres.2008.04.002 · Cited by 5
Depth and Intensity Gabor Features Based 3D Face Recognition Using Symbolic LDA and AdaBoost
Hiremath, P. S., & Hiremath, M. (2013) · International Journal of Image Graphics and Signal Processing · doi:10.5815/ijigsp.2014.01.05 · Cited by 5
“This is why the face recognition is performed by combin ing depth and intensity informat ion [23].”
Signal-Tuned Gabor Functions as Models for Stimulus-Dependent Cortical Receptive Fields
Torreão, J. R. A., Victer, S. M. C., & Amaral, M. S. (2014) · Neural Computation · doi:10.1162/neco_a_00581 · Cited by 5
“For any given stimulus, this receptive field has the effect of a quasi-linear filter, generally modeled as a Gabor function (Marcelja, 1980; Jones & Palmer, 1987; Sun & Bonds, 1994), whose output, subsequently submitted to a half-wave rectification, yields the full simple cell response.”
MethodFace Recognition Based on Digital Curvelet Transform
Lee, Y.-C., & Chen, C. (2008) · International Conference on Intelligent Systems Design and Applications (ISDA) · doi:10.1109/isda.2008.281 · Cited by 5
“The Gabor wavelet representation captures the local structure corresponding to spatial frequency, spatial localization, and orientation selectivity [3] [5].”
BackgroundModeling oxytocin induced neurorobotic trust and intent recognition in human-robot interaction
Anumandla, S. R., Bray, L. C. J., Thibeault, C. M., Hoang, R. V., Dascalu, S. M., Harris, F. C., & Goodman, P. H. (2011) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2011.6033647 · Cited by 5
“The Gabor filter is considered one of the better representations of mammalian visual receptive field profiles [ 29 ].”
BackgroundMulti-band Gradient Component Pattern (MGCP): A New Statistical Feature for Face Recognition
Guo, Y., Chen, J., Zhao, G., Pietikäinen, M., & Xu, Z. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-02230-2_24 · Cited by 5
“In most cases, Gabor wavelets at five different scales v : {} 4 0 and eight orientations u : {} 7 0 are used [18, 19 ,20].”
MethodThe role of non-CRF inhibition in contour detection
Grigorescu, C., Petkov, N., & Westenberg, M. A. (2003) · University of Groningen research database (University of Groningen / Centre for Information Technology) · Cited by 5
Mlynek, J., Buckhout, T. J., Wiskott, L., Peter König, B., & Herz, A. V. M. (2005) · Cited by 5
The effect of eccentricity and spatiotemporal energy on motion silencing
Choi, L. K., Bovik, A. C., & Cormack, L. K. (2016) · Journal of Vision · doi:10.1167/16.5.19 · Cited by 5
Detection and tracking of dim objects in infrared (IR) images using Support Vector Machine
Alsulami, F. N., Ahmadi, K., & Salari, E. (2016) · IEEE International Conference on Electro Information Technology · doi:10.1109/eit.2016.7535265 · Cited by 5
Age of acquisition in facial identification: A connectionist approach
Cottrell, G. W., & Lake, B. M. (2005) · eScholarship (California Digital Library) · Cited by 5
Look Ma! No Network!: PCA of Gabor Filters Models the Development of Face Discrimination
Cottrell, G. W., & Zhang, L. (2006) · eScholarship (California Digital Library) · Cited by 5
Contour detection model based on neuron behaviour in primary visual cortex
Lin, C., Xu, G., & Cao, Y. (2018) · IET Computer Vision · doi:10.1049/iet-cvi.2017.0661 · Cited by 5
Features Extraction for Pollen Recognition Using Gabor Filters
Nikolov, D. N., & Tsankova, D. D. (2018) · Food Science and Applied Biotechnology · doi:10.30721/fsab2018.v1.i2.11 · Cited by 5
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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