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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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“(Jones and Palmer 1987a).”
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“Our biologically inspired model of the processing in primary visual cortex (V1) uses the magnitude responses of Gabor filters at 8 orientations and 4 frequencies (Jones & Palmer, 1987).”
MethodClarke, A., Herzog, M. H., & Francis, G. (2014) · Frontiers in Psychology · doi:10.3389/fpsyg.2014.01193 · Cited by 25
“Examples include Altmann et al. (2003) reporting evidence for feedback processing in an fMRI study of perceptual organization; Enns and Di Lollo (2000) arguing that some forms of visual masking require re-entrant signals that represent objects; Juan and Walsh (2003) using TMS to argue that the…”
BackgroundEmergent self-organizing feature map for recognizing road sign images
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MethodA Multimodal Approach for Face Modeling and Recognition
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“Gabor filters have similar shapes as the receptive fields of simple cells in the visual cortex of vertebrate animals [137, 77, 46] and can be statistically derived from the images of natural scenes, at least qualitatively [123] [20].”
BackgroundDynamics of Tuning in the Fourier Domain
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“After this initial surgery the animal is transferred to a stereotaxic frame.”
BackgroundContrast-dependent surround suppression models for contour detection
Tang, Q., Sang, N., & Liu, H. (2016) · Pattern Recognition · doi:10.1016/j.patcog.2016.05.009 · Cited by 23
A central mechanism enhances pain perception of noxious thermal stimulus changes
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“VAS > 0 trials 16 [3,8,0,5] 16 [2,3,1,10] 16 [1,5,3,7] 23 [0,6,4,13] 53 [3,17,13,20]”
Fleischer, J., & Krichmar, J. L. (2007) · Journal of Integrative Neuroscience · doi:10.1142/s0219635207001568 · Cited by 22
“The concept is due to [29] and was first tested rigorously by [21].”
BackgroundPredicting bias in perceived position using attention field models
Klein, B. P., Paffen, C. L. E., Pas, S. F. T., & Dumoulin, S. O. (2016) · Journal of Vision · doi:10.1167/16.7.15 · Cited by 23
“…& Wandell, 2008; Harvey & Dumoulin, 2011; Hubel & Wiesel, 1962; Van Essen, Newsome, & Maunsell, 1984) and tuning to lower spatial frequencies (Jones & Palmer, 1987), we expect that attention induces a larger positional bias for stimuli presented at higher eccentricities as well as stimuli…”
BackgroundMethodInfluentialKawakami, S., & Okamoto, H. (1996) · Vision Research · doi:10.1016/0042-6989(95)00086-f · Cited by 23
Sabatini, S. P. (1996) · Biological Cybernetics · doi:10.1007/bf00652220 · Cited by 23
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“…1: The example for learning complex cell behavior based on simple cell outputs follows the view that simple cells can be modeled by Gabor wavelets ( Jones & Palmer , 1987), while a complex cell combines the responses of several simple cells of same orientation and location but different phase, e.g.…”
BackgroundNowak, L. G., Sanchez-Vives, M. V., & McCormick, D. A. (2005) · Journal of Neuroscience · doi:10.1523/jneurosci.3897-04.2005 · Cited by 24
“The Gabor has been shown to be an optimal expression to formalize the RF features of simple cells (Field and Tolhurst, 1986; Jones and Palmer, 1987b): y A exp( (x xc) 2/2 2) cos((2 Fopt (x xc)) ), where, in addition to the parameters A, xc, and corresponding to the Gaussian envelope, Fopt is the…”
BackgroundMethodImage Representation with Gabor Wavelets and Its Applications
Navarro, R., Tabernero, A., & Cristóbal, G. (1996) · Advances in imaging and electron physics · doi:10.1016/s1076-5670(08)70093-4 · Cited by 23
Reconstruction from graphs labeled with responses of Gabor filters
Pötzsch, M., Maurer, T., Wiskott, L., & von der Malsburg, C. (1996) · Lecture notes in computer science · doi:10.1007/3-540-61510-5_142 · Cited by 23
“Eq. (1) and t he image can be reconstructed directly by I n = ~ J~r However, in the sense of the findings in [ 7 ], this approach cannot serve as a model for the cell responses in sensory cortex.”
ResultA computational feature binding model of human texture perception
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“Kreiter and Singer (1996) showed that cells in the middle temporal (MT) area, associated with motion processing, show selective synchronization if stimulated by a single bar stimulus and no synchronization if stimulated by two coherently moving but separate bars. For reviews discussing neurophysiological evidence of t…”
BackgroundInfluentialResearch of Ateb-Gabor Filter in Biometric Protection Systems
Nazarkevych, M., Бурячок, В. Л., Lotoshynska, N., & Dmytryk, S. (2018) · IEEE International Conference on Computer Sciences and Information Technologies (CSIT) · doi:10.1109/stc-csit.2018.8526607 · Cited by 22
Predictive coding accounts for V1 response properties recorded using reverse correlation
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“Consistent with the majority of the neurophysiological experiments (Jones and Palmer 1987b,a; DeAngelis et al. 1993) the reconstructed RFs were Gabor-like (Table 1, rows 1 and 2).”
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Zhou, W., Yu, L., Qiu, W., Luo, T., Wang, Z., & Wu, M. (2016) · Signal Processing · doi:10.1016/j.sigpro.2016.06.005 · Cited by 22
Towards a Theory of Computation in the Visual Cortex
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“A good linear filter model that can be well fitted to simple cells is the Gabor filter [55, 11, 12, 43].”
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Franceschiello, B., Sarti, A., & Citti, G. (2017) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-017-0740-6 · Cited by 20
“Daugman [6], Jones and Palmer [18] showed that Gabor filters were a good approximation for receptive profiles of simple cells in the primary visual cortices V1 and V2.”
BackgroundEdge detection based on Hodgkin–Huxley neuron model simulation
Yedjour, H., Meftah, B., Lézoray, O., & Benyettou, A. (2017) · Cognitive Processing · doi:10.1007/s10339-017-0803-z · Cited by 22
“This function was used to describe the behavior of simple cells in the V1 area of the human visual cortex (Jones and Palmer 1987).”
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Taylor, M. M., Sedigh-Sarvestani, M., Vigeland, L. E., Palmer, L. A., & Contreras, D. (2017) · Journal of Neuroscience · doi:10.1523/jneurosci.2099-17.2017 · Cited by 22
Self-citationA comparison of texture quantification techniques based on the Fourier and S transforms
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Gepshtein, S., Tyukin, I., & Kubovy, M. (2007) · Journal of Vision · doi:10.1167/7.8.8 · Cited by 22
“To display the isosensitivity contours in the space–time distance plot, we use Equations 5–8 of Kelly (1979), with which he fit the spatiotemporal thresholds for the detection of drifting sinusoidal gratings.”
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“We therefore use a Gabor filter-based approach, proposed in [22] for the power spectrum dimensionality reduction, that approximates, as shown in [15] , and [29] , the behavior of the primary visual cortex cells receptive fields.”
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“Since the diversity of receptive field shapes was suggested as a means for comparison of models to experimental data [14,34], different modeling approaches have been shown to result in broad distributions of Gabor shapes.”
ResultJohnson, K. O., Hsiao, S. S., & Blake, D. T. (1996) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-9016-8_19 · Cited by 21
Conditions of Similarity between Hermite and Gabor Filters as Models of the Human Visual System
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“which is more used in image processing (essentially for texture), is that of Gabor [8] [14] [2] [20]; the second, which is more adapted to a local analysis (generally to process edges), is that of the Gaussian derivative [25].”
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Ritter, H. J., Obermayer, K., Schulten, K., & Rubner, J. (1991) · Physics of neural networks · doi:10.1007/978-3-642-97171-6_8 · Cited by 21
Two-dimensional receptive-field organization in striate cortical neurons of the cat
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Spatial structure of chromatically opponent receptive fields in the human visual system
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“, difference of Gaussian (DOG), Gabor filters) [38,39].”
BackgroundDo Simple Cells in Primary Visual Cortex Form a Tight Frame?
Salinas, E., & Abbott, L. F. (2000) · Neural Computation · doi:10.1162/089976600300015817 · Cited by 20
“The filter functions f j for simple cells are often fit using plane waves multiplied by Gaussian envelopes, known as Gabor functions (Daugman, 1985; Jones and Palmer, 1987; Webster and De Valois, 1985), f j (x) = 1 2 2 j exp ? jx ? a j j 2 2 2 j ! cos(k j x ? j ) : (2.2) These filters are…”
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BackgroundYoshihara, S., Fukiage, T., & Nishida, S. (2023) · Frontiers in Psychology · doi:10.3389/fpsyg.2023.1047694 · Cited by 20
“The Gabor functions are known to be good approximations of the spatial properties of V1 simple cell receptive fields (Jones and Palmer, 1987).”
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Rau, F., Clemens, J., Naumov, V., Hennig, R. M., & Schreiber, S. (2015) · Journal of Comparative Physiology A · doi:10.1007/s00359-015-1036-1 · Cited by 20
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Image Understanding Using Sparse Representations
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Towards cost reduction of breast cancer diagnosis using mammography texture analysis
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“Tuning Gabor filters to specific frequencies and directions can lead them to detect both local orientation and frequency information from an image (Jones & Palmer, 1987; Weldon, Higgins, & Dunn, 1996).”
BackgroundRajaei, K., Khaligh‐Razavi, S., Ghodrati, M., Ebrahimpour, R., & Abadi, M. E. S. A. (2012) · PLoS ONE · doi:10.1371/journal.pone.0038478 · Cited by 20
“The Gabor function has many free parameters, which agrees well with physiological data recorded from simple cell receptive fields in cat striate cortex [43].”
BackgroundAbdel‐Nasser, M., Melendez, J., Moreno, A., & Puig, D. (2016) · International Journal of Optics · doi:10.1155/2016/1370259 · Cited by 23
“Tuning GF to specific frequencies and directions can lead them to detect both local orientation and frequency information from an image [27].”
BackgroundFacial Expression Recognition Using Fusion Features Based on Center-Symmetric Local Octonary Pattern
Hu, M. Q., Zheng, Y., Yang, C., Wang, X., He, L., & Ren, F. (2019) · IEEE Access · doi:10.1109/access.2019.2899024 · Cited by 20
“(b) detecting and cropping the region of interest and normalize the image size (JAFFE:64 × 96, CK: 96× 96); (c) processing image with Gaussian filter [33] to eliminate the effect of noise and improve the recognition accuracy.”
BackgroundSurround suppression by high spatial frequency stimuli in the cat primary visual cortex
Osaki, H., Naito, T., Sadakane, O., Okamoto, M., & Sato, H. (2011) · European Journal of Neuroscience · doi:10.1111/j.1460-9568.2010.07572.x · Cited by 20
Sequential Architecture for Efficient Car Detection
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Lightness computation by the human visual system
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When Holistic Processing Is Not Enough: Local Features Save the Day
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Quadrature-phase simple-cell pairs are appropriately described in complex analytic form
Daugman, J. G. (1993) · Journal of the Optical Society of America A · doi:10.1364/josaa.10.000375 · Cited by 20
Normative theory of visual receptive fields
Lindeberg, T. (2017) · KTH Publication Database DiVA (KTH Royal Institute of Technology) · Cited by 17
Investigation the Ateb-Gabor Filter in Biometric Security Systems
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“It follows that a sufficiently well localized in the t and k-space function of the Gabor cannot be a basis of the wavelet transform, since the basis based on it does not have the properties of self-similarity [9].”
BackgroundBera, K., Katz, I. A., & Madabhushi, A. (2020) · JCO Clinical Cancer Informatics · doi:10.1200/cci.20.00110 · Cited by 20
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“However, as the Gabor filter features are more discriminative than the ones mentioned before, as shown in (Jones and Palmer 1987), we are employing them here without segmentation. i).”
BackgroundMarrazzo, G., Martino, F. D., Lage‐Castellanos, A., Vaessen, M. J., & de Gelder, B. (2023) · NeuroImage · doi:10.1016/j.neuroimage.2023.120240 · Cited by 20
A simple cell model with dominating opponent inhibition for robust image processing
Hansen, T., & Heiko Neumann, B. (2004) · Neural Networks · doi:10.1016/j.neunet.2004.04.002 · Cited by 19
“Aspect ratios of 5 and larger have been reported (Gardner, Anzai, Ohzawa, & Freeman, 1999; Jones & Palmer, 1987a,b), while others have found considerably smaller aspect ratios with a mean of 1.7 (Pei, Vidyasagar, Volgushev, & Creutzfeldt, 1994).”
BackgroundInfluential3D Face recognition using Corresponding Point Direction Measure and depth local features
Wang, X., Ruan, Q., & Ming, Y. (2010) · International Conference on Signal Processing · doi:10.1109/icosp.2010.5656654 · Cited by 19
“The Gabor wavelets ,v μ ψ can be defined as follows [14]:”
BackgroundRepresentation Learning in Sensory Cortex: A Theory
Anselmi, F., & Poggio, T. (2022) · IEEE Access · doi:10.1109/access.2022.3208603 · Cited by 20
“This is the only computational justification we know 2 of the Gabor shape of simple cells in V1 which seems to be remarkably universal: it holds in primates (Ringach 2002), cats (Jones et al. 1987) and mice (Striker and Neill 2008) (see also Figure 3 for results of simulations).”
BackgroundToward a Biologically Plausible Model of LGN-V1 Pathways Based on Efficient Coding
Lian, Y., Grayden, D. B., Kameneva, T., Hamish Meffin, A., & Burkitt, A. N. (2019) · Frontiers in Neural Circuits · doi:10.3389/fncir.2019.00013 · Cited by 19
A zero-shot learning approach to the development of brain-computer interfaces for image retrieval
McCartney, B., del Rincón, J. M., Devereux, B. J., & Murphy, B. (2019) · PLoS ONE · doi:10.1371/journal.pone.0214342 · Cited by 19
Yang, J., Bian, Z., Zhao, Y. S., Lu, W. B., & Gao, X. (2021) · IEEE Transactions on Broadcasting · doi:10.1109/tbc.2021.3064266 · Cited by 19
Object feature validation using visual and haptic similarity ratings
Cooke, T., Kannengiesser, S., Wallraven, C., & Bülthoff, H. (2006) · ACM Transactions on Applied Perception · doi:10.1145/1166087.1166093 · Cited by 19
“…in this .eld has given rise to a large number of feature-extraction algorithms, including biologically inspired .lters (Gabor jets), which mimic the response of cells in visual cortex [Jones and Palmer 1987] and algorithms derived from statistical optimization procedures [Ankerst et al. 1999].”
MethodThe group theoretic approach to image representation
Gertner, I., & Tolimieri, R. (1990) · Journal of Visual Communication and Image Representation · doi:10.1016/1047-3203(90)90017-p · Cited by 19
MULTIMODAL BIOMETRICS BY FACE AND HAND IMAGES TAKEN BY A CELL PHONE CAMERA
Rokita, J., Krzyżak, A., & Suen, C. Y. (2008) · International Journal of Pattern Recognition and Artificial Intelligence · doi:10.1142/s0218001408006302 · Cited by 19
“The most popular kernel functions include(5): • linear kernel K(xi, xj) = xi xj , (10) • polynomial kernel K(xi, xj) = (γxi xj + r) , γ ≥ 0, (11) • radial basis function (RBF) kernel K(xi, xj) = exp(−γ‖xi − xj‖(2)), γ ≥ 0, (12) • sigmoid kernel K(xi, xj) = tanh(xi xj + r).”
Holistic Processing Develops Because it is Good
Zhang, L., & Cottrell, G. W. (2005) · eScholarship (California Digital Library) · Cited by 19
Bipartite invariance in mouse primary visual cortexPreprint
Ding, Z., Tran, D. T., Ponder, K., Cobos, E., Ding, Z., Fahey, P. G., Wang, E. Y., Muhammad, T., Fu, J., Cadena, S. A., et al. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.03.15.532836 · Cited by 27
“2a, simulated simple), aligning with linear-nonlinear (LN) model predictions (Buss-gang, 1952; Jones and Palmer, 1987a; Heeger, 1992).”
Direction-selective motion discrimination by traveling waves in visual cortex
Heitmann, S., & Ermentrout, B. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1008164 · Cited by 18
“Inhibitory-surround coupling also has conceptual links to the difference of Gaussians in the motion-energy model [16] and is crucial for the formation of standing wave patterns in neural field models [21–25].”
BackgroundInfluentialLooking down: a model for visual route following in flying insects
Stankiewicz, J., & Webb, B. H. (2021) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/ac1307 · Cited by 22
“The CWSSIM approach is biologically relevant in that orientated bandpass filters are known to receive input from the invertebrate vision system [56, 82] and mammalian vision systems [5, 25, 26].”
BackgroundFACE RECOGNITION USING GABOR-BASED IMPROVED SUPERVISED LOCALITY PRESERVING PROJECTIONS
Jin, Y., & Ruan, Q. Q. (2009) · Cited by 18
A Neural Model of Distance-Dependent Percept of Object Size Constancy
Qian, J., & Yazdanbakhsh, A. (2015) · PLoS ONE · doi:10.1371/journal.pone.0129377 · Cited by 18
The Embedded Neuron, the Enactive Field?
Chirimuuta, M., & Gold, I. (2009) · Oxford University Press eBooks · doi:10.1093/oxfordhb/9780195304787.003.0010 · Cited by 18
An application of formal concept analysis to semantic neural decoding
Endres, D., Földiák, P., & Priss, U. E. (2009) · Annals of Mathematics and Artificial Intelligence · doi:10.1007/s10472-010-9196-8 · Cited by 18
“This technique is feasible even for high-level visual codes, where linear decoding methods [20, 21] fail, and it provides qualitative information about the structure of the code which goes beyond stimulus label decoding [1–4].”
Graph matching based hand posture recognition using neuro-biologically inspired features
Kumar, P., Vadakkepat, P., & Loh, A. P. (2010) · International Conference on Control, Automation, Robotics and Vision (ICARCV) · doi:10.1109/icarcv.2010.5707352 · Cited by 18
ML4IoT: A Framework to Orchestrate Machine Learning Workflows on Internet of Things Data
Alves, J. M., Honório, L. D. M., & Capretz, M. A. M. (2019) · IEEE Access · doi:10.1109/access.2019.2948160 · Cited by 18
“In addition, a Gabor filter [30] was used to reduce noise and unwanted entries in the SIoT data.”
MethodA robust contour detection operator with combined push-pull inhibition and surround suppression
Melotti, D., Heimbach, K., Rodríguez-Sánchez, A., Strisciuglio, N., & Azzopardi, G. (2020) · Information Sciences · doi:10.1016/j.ins.2020.03.026 · Cited by 18
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
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