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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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“The standard deviation of the gaussian in the vertical direction was chosen to be 2σ, consistent with the aspect ratio of two observed in cats’ visual cortex ( Jones & Palmer, 1987 ).”
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MethodGabor attributes tracking for face verification
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View Independent Face Detection Based on Combination of Local and Global Kernels
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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 [ 21 ].”
BackgroundFlexibly-bounded Rationality and Marginalization of Irrationality Theories for Decision MakingPreprint
Marwala, T. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1306.2025 · Cited by 13
Khaligh‐Razavi, S. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1407.2776 · Cited by 12
“Indeed it has been shown that 2D Gabor filters can provide a good fit to the receptive field weight functions found in simple cells of cat's striate cortex (Jones and Palmer, 1987).”
BackgroundInception in visual cortex: in vivo-silico loops reveal most exciting imagesPreprint
Walker, E. Y., Sinz, F. H., Froudarakis, E., Fahey, P. G., Muhammad, T., Ecker, A. S., Cobos, E., Reimer, J., Pitkow, X., & Tolias, A. S. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/506956 · Cited by 9
“In primary visual cortex (V1) the most effective stimuli — obtained by assuming a linear model — resemble Gabor patterns (4).”
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“The visual feature for shape is the output of Gabor filters [14].”
BackgroundLiang, J., & Zuo, G. (2022) · Scientific Programming · doi:10.1155/2022/1838468 · Cited by 8
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“The Gabor wavelets are mostly used in five different scales v 2 {0, . . . ,4 } and eight different orientations l 2 {0, . . . ,7 } (Jones and Palmer 1987).”
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“This feature is consistent with in vivo measurements of simple-cell like RFs [14, 15] (Fig.”
BackgroundResultComputing local edge probability in natural scenes from a population of oriented simple cells
Ramachandra, C. A., & Mel, B. W. (2013) · Journal of Vision · doi:10.1167/13.14.19 · Cited by 8
Active Object Recognition with a Space-Variant Retina
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Analysis and interpretation of quadratic models of receptive fields
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Effects of contrast and contrast adaptation on static receptive field features in macaque area V1
Durand, J., Girard, P., Barone, P., Bullier, J., & Nowak, L. G. (2012) · Journal of Neurophysiology · doi:10.1152/jn.00936.2011 · Cited by 8
“…and Palmer 1987b; Niell and Stryker 2008; Sharpee et al. 2008; Usrey et al. 2003), while the optimal spatial frequency can be predicted from the number and width of the subregions (DeAngelis et al. 1993b; Field and Tolhurst 1986; Jones and Palmer 1987b; Movshon et al. 1978a; Smyth et al. 2003).”
BackgroundMethodInfluentialGabor based face recognition with dynamic time warping
Sistla, V., & Prasad, V. K. (2013) · International Conference on Contemporary Computing · doi:10.1109/ic3.2013.6612218 · Cited by 8
“Hence, Gabor wavelets [3,4,5,6] are used to extract such local features from the training data.”
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“Jones and Palmer [ 5 ] modelled the shape of the RFs by 2D Gabor filters.”
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Guo, J., Shi, C., Azzopardi, G., & Petkov, N. (2017) · IBM Journal of Research and Development · doi:10.1147/jrd.2017.2679458 · Cited by 9
“cells in area V1 of the visual cortex [36].”
BackgroundFeature Engineering and Selection
Sarkar, D., Bali, R., & Sharma, T. (2017) · Apress eBooks · doi:10.1007/978-1-4842-3207-1_4 · Cited by 8
Driver Behavior Recognition in Driver Intention Inference Systems
Xing, Y., Lv, C., & Cao, D. (2020) · Elsevier eBooks · doi:10.1016/b978-0-12-819113-2.00005-1 · Cited by 8
The Portilla-Simoncelli Texture Model: towards Understanding the Early Visual Cortex
Vacher, J., & Briand, T. (2021) · Image Processing On Line · doi:10.5201/ipol.2021.324 · Cited by 10
“In a way, this corresponds to statistics between sub-bands obtained by convolution with generic “textons” such as scaled and oriented Gabor functions, which are known to correctly model neuron receptive fields [26].”
BackgroundVirtual spatial overlap modulation microscopy for resolution improvement
Kuo, W.-C., Shih, Y., Hsu, H., Cheng, Y.-H., Liao, Y., & Sun, C. (2013) · Optics Express · doi:10.1364/oe.21.030007 · Cited by 8
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Wundrich, I. J., von der Malsburg, C., & Würtz, R. P. (2002) · Lecture notes in computer science · doi:10.1007/3-540-36181-2_12 · Cited by 8
“They seem to be implemented in the first stages of processing in the visual cortex of higher vertebrates, as the receptive fields of the so-called simple cells can be described to some accuracy as Gabor functions [1, 7].”
BackgroundA Network Model of Motion Processing in Area MT of Primates
Wang, R. (1997) · Journal of Computational Neuroscience · doi:10.1023/a:1008868232355 · Cited by 10
“A widely accepted model for the V1 cells is the spatiotemporal energy model (Adelson and Bergen, 1985; Grzywacz and Yuille, 1990), which has found biological supports ( Jones and Palmer, 1987a, 1987b; McLean et al., 1989) and can account for some of the V1 response selectivities.”
BackgroundBiology-Inspired Early Vision System for a Spike Processing Neurocomputer
Thiem, J., Wolff, C., & Hartmann, G. (2000) · Lecture notes in computer science · doi:10.1007/3-540-45482-9_39 · Cited by 8
“The RFs of cat's simple cells are investigated in great detail [10].”
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Boehme, H.-J., Braumann, U., Corradini, A., & Groß, H. (1999) · Lecture notes in computer science · doi:10.1007/3-540-46616-9_11 · Cited by 8
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Receptive field organization of disparity‐sensitive cells in Macaque medial superior temporal cortex
González, F., Perez, R., Justo, M. S., & Bermúdez, M. A. (2001) · European Journal of Neuroscience · doi:10.1046/j.0953-816x.2001.01626.x · Cited by 8
“To study the responsiveness to disparity within the cellular receptive ®eld we constructed spatio-temporo-disparity receptive ®eld maps (RF-maps) by using a reverse cross-correlation technique (DeBoer & Kuyper, 1968; Jones & Palmer, 1987; Krause et al., 1987).”
MethodA similarity-based approach to perceptual feature validation
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“…rise to a large number of feature extraction algorithms, including biologically-inspired .lters which mimic the response of cells in visual cortex [Jones and Palmer 1987], algorithms purely derived from statistical optimization procedures [Schmid and Mohr 1997], as well as measures which…”
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Multi-modal (2-D and 3-D) face modeling and recognition using Attributed Relational Graph
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“Gabor filters have similar shapes as the receptive fields of simple cells in the visual cortex of vertebrate animals [13, 14 , 15] and can be statistically derived from the images of natural scenes, at least qualitatively [16] [17].”
BackgroundCutini, S., Ferdinando, A. D., Basso, D., Bisiacchi, P. S., & Zorzi, M. (2008) · Cognitive Neuropsychology · doi:10.1080/02643290701606408 · Cited by 8
“These components comprise: (a) a visual module, in which the input pattern is processed by Gabor filters (Jones & Palmer, 1987) to simulate the processes responsible for visuo-spatial analysis and perceptual grouping; (b) a competitive selection module that simulates the internal dynamics for the…”
BackgroundMethodEarly Cognitive Vision as a Frontend for Cognitive Systems
Krüger, N., Pugeault, N., Başeski, E., Kalkan, S., Kraft, D., Jessen, J. B., Pilz, F., Kjær‐Nielsen, A., Popović, M., Asfour, T., et al. (2010) · University of Southern Denmark Research Portal (University of Southern Denmark) · Cited by 8
A connectionist approach to processing dimensional interaction
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“However, the similarity of Gabor filters to simple cells in the primary visual cortex (Marcelja 1980, Jones and Palmer 1987) may be an indication that the same cause underlies human subject data.”
BackgroundOptimal Gabor Encoding Scheme for Face Recognition Using Genetic Algorithm
Jeon, I. J., Kwon, K., & Rhee, P.-K. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-30133-2_30 · Cited by 8
“Gabor wavelet is usually used at five different frequencies, ν = 0,…, 4, and eight orientations, µ= 0,…, 7 [5],[ 14 ].”
BackgroundParallel computation of 2-D wavelet transforms
Misra, M., & Prasanna, V. K. (2003) · IAPR International Conference on Pattern Recognition (ICPR) · doi:10.1109/icpr.1992.202142 · Cited by 8
“His development of 2-D Gabor Functions was motivated by the observation that such functions would closely match experimentally measured two-dimensional visual neural receptive field profiles [ 5 ].”
BackgroundBayesian and information-theoretic tools for neuroscience
Endres, D. (2006) · St Andrews Research Repository (St Andrews Research Repository) · Cited by 8
Relaxation network for Gabor image decomposition
Pattison, T. R. (1992) · Biological Cybernetics · doi:10.1007/bf00201806 · Cited by 8
“The so-called "simple cells" in the feedforward input layer of feline primary visual cortex have been shown to have spatial receptive field profiles (RFPs) which are statistically indistinguishable from two-dimensional Gabor functions (Gaussian-weighted sinusoids) (Jones and Palmer 1987a).”
BackgroundMethodResultInfluentialColor face recognition using quaternionic gabor filters
Jones, C. F., & Abbott, A. L. (2005) · VTechWorks (Virginia Tech) · Cited by 8
Loxley, P. N. (2017) · Neural Computation · doi:10.1162/neco_a_00997 · Cited by 7
“We know that simple cells in the primary visual cortex have spatially localized receptive fields and are sensitive to visual stimulus features such as orientation, spatial frequency, and location in the receptive field (Hubel & Wiesel, 1959, 1962; Daugman, 1985; Jones & Palmer, 1987).”
BackgroundMethodResultInfluentialRepresentation learning with reward prediction errors
Alexander, W. H., & Gershman, S. J. (2022) · Neurons Behavior Data analysis and Theory · doi:10.51628/001c.37270 · Cited by 7
Selecting Optimal Orientations of Gabor Wavelet Filters for Facial Image Analysis
Zhang, T., & Lu, B. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-13681-8_26 · Cited by 7
“The motivation of using Gabor-based feature is mostly biological, since Gabor-like receptive fields have been found in the visual cortex of primates [14] [15] [16].”
BackgroundTransfer learning using adaptive SVM for image classification
Jain, A., Srivastava, S., & Soman, S. (2013) · International Conference on Image Information Processing (ICIIP) · doi:10.1109/iciip.2013.6707659 · Cited by 7
Generalizing a closed-form correlation model of oriented bandpass natural images
Sinno, Z., & Bovik, A. C. (2015) · IEEE Global Conference on Signal and Information Processing · doi:10.1109/globalsip.2015.7418220 · Cited by 7
“Spatial processing in primary visual cortex is often modeled in image analysis algorithms by a Gabor filter bank [8], [9], which decomposes and decorrelates the received signal over multiple scales and orientations, followed by nonlinear adaptive gain control (ACG) [10].”
MethodTraining a V1 Like Layer Using Gabor Filters in Convolutional Neural Networks
Bai, J., Zeng, Y., Zhao, Y., & Zhao, F. (2019) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2019.8852439 · Cited by 8
“The modeling of V1 cortex using Gabor filters is also proposed by neuroscientists for many years [13], [14].”
BackgroundMethodBaruzzi, V., Indiveri, G., & Sabatini, S. P. (2025) · Nature Communications · doi:10.1038/s41467-024-55749-y · Cited by 7
Understanding Human Amygdala Function with Artificial Neural Networks
Jang, G., & Kragel, P. A. (2025) · Journal of Neuroscience · doi:10.1523/jneurosci.1436-24.2025 · Cited by 9
Arm-Hand Behaviours Modelling: From Attention to Imitation
Fanello, S., Gori, I., & Pirri, F. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-17274-8_60 · Cited by 6
Sparse coding generates curvature selectivity in V4 neurons
Hatori, Y., Mashita, T., & Sakai, K. (2016) · Journal of the Optical Society of America A · doi:10.1364/josaa.33.000527 · Cited by 7
Extraction of GGO candidate regions from the LIDC database using deep learning
Hirayama, K., Tan, J. K., & Kim, H. (2016) · International Conference on Control, Automation and Systems (ICCAS) · doi:10.1109/iccas.2016.7832398 · Cited by 7
“In addition, the visual cortex of mammals have been found to learn the characteristics similar to Gabor filter [6].”
From receptive profiles to a metric model of V1
Montobbio, N., Citti, G., & Sarti, A. (2019) · Journal of Computational Neuroscience · doi:10.1007/s10827-019-00716-6 · Cited by 8
Nature Inspiration for Support Vector Machines
Anguita, D., & Sterpi, D. (2006) · Lecture notes in computer science · doi:10.1007/11893004_57 · Cited by 7
“Two-dimensional Gabor filters are a simple model for the responses of simple cells in the primary visual cortex [12].”
BackgroundVideo sequence-based iris recognition inspired by human cognition manner
Liu, Y., He, F., Zhu, X., Chen, Y., Han, Y. S., & Fu, Y. (2014) · Journal of Bionic Engineering · doi:10.1016/s1672-6529(14)60060-3 · Cited by 7
Binocular Energy Estimation Based on Properties of the Human Visual System
Bensalma, R., & Larabi, M. (2012) · Cognitive Computation · doi:10.1007/s12559-012-9187-7 · Cited by 7
“2 Comparison between measured responses of simple cells and their Gabor modeling [29] Cogn Comput (2013) 5:589–609 591”
BackgroundVideo based indoor exploration with autonomous and mobile robots
Florczyk, S. (2005) · Journal of Intelligent & Robotic Systems · doi:10.1007/s10846-005-3508-y · Cited by 7
“Algorithms, which used Gabor filter [19], highpass filter [21], and Sobel filter [18], reached a good rating.”
MethodApplication of Phase Congruency for Discriminating Some Lung Diseases Using Chest Radiograph
Rijal, O. M., Ebrahimian, H., Noor, N. M., Hussin, A., Yunus, A., & Mahayiddin, A. A. (2015) · Computational and Mathematical Methods in Medicine · doi:10.1155/2015/424970 · Cited by 7
Cope, D. K., Blakeslee, B., & McCourt, M. E. (2009) · Journal of the Optical Society of America A · doi:10.1364/josaa.26.002067 · Cited by 7
“However, the Gabor model has withstood the test of repeated physiological [15, 16, 4, 17], and psychophysical [18, 19] verification, and has therefore emerged as the most commonly accepted mathematical description of cortical simple cell receptive field structure.”
BackgroundEvidence for elongated receptive field structure for mechanisms subserving stereopsis
Chen, C., & Tyler, C. W. (2006) · Vision Research · doi:10.1016/j.visres.2006.02.009 · Cited by 7
“The sensitivity profile of the luminance specific RFs is known to be well fit by a Gabor function, which is the product of a Gaussian envelope and a sinusoid (Marcelja, 1980; Daugman, 1985; DeAngelis, Ohzawa, & Freeman, 1991; Jones & Palmer, 1987).”
Image patches analysis for text block identification
Zhong, G., & Cheriet, M. (2012) · International Conference on Information Science, Signal Processing and their Applications (ISSPA) · doi:10.1109/isspa.2012.6310482 · Cited by 7
“Due to their biological relevance and computational properties, Gabor features are widely used in the image processing area [24, 25, 26, 27].”
BackgroundSenescent changes in photopic spatial summation
Malania, M., Devinck, F., Kenneth Knoblauch, B., Delahunt, P. B., Hardy, J. L., & Werner, J. S. (2011) · Journal of Vision · doi:10.1167/11.10.15 · Cited by 7
Lee, Y.-C., & Chen, C. (2009) · International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) · doi:10.1109/iih-msp.2009.210 · Cited by 7
“First, we use the Gabor wavelet representation to capture the local structure corresponding to spatial frequency, spatial localization, and orientation selectivity [2], [5].”
MethodLearning visual object detection and localisation using icVision
Leitner, J., Harding, S., Chandrashekhariah, P., Frank, M., Förster, A., Triesch, J., & Schmidhuber, J. (2013) · Biologically Inspired Cognitive Architectures · doi:10.1016/j.bica.2013.05.009 · Cited by 7
“The choice is also motivated by the fact that they have a similar shape as the receptive field of simple cells found in the visual cortex of vertebrate animals (Jones and Palmer, 1987; Pollen and Ronner, 1981).”
BackgroundA method for feature extraction of traffic sign detection and the system for real world scene
Park, J.-G., & Kim, K.-J. (2012) · IEEE International Conference on Emerging Signal Processing Applications (ESPA) · doi:10.1109/espa.2012.6152433 · Cited by 7
Analysis of Cluttered Scenes Using an Elastic Matching Approach for Stereo Images
Eckes, C., Triesch, J., & von der Malsburg, C. (2006) · Neural Computation · doi:10.1162/neco.2006.18.6.1441 · Cited by 7
“These features have been shown to be more robust with respect to small translations and rotations than raw pixel values, and they are heavily used in biological vision systems (Jones & Palmer, 1987).”
MethodSensitivity of V1 Neurons to Direction of Spectral Motion
Wang, C., & Yao, H. (2010) · Cerebral Cortex · doi:10.1093/cercor/bhq176 · Cited by 7
“The location and the size of the CRF were measured using 16 3 16 grid sparse noise stimuli consisting of white or black squares flashed for 25 ms in a randomized order (Jones and Palmer 1987).”
Inhibition-augmented trainable COSFIRE filters for keypoint detection and object recognition
Guo, J., Shi, C., Azzopardi, G., & Petkov, N. (2016) · Machine Vision and Applications · doi:10.1007/s00138-016-0777-3 · Cited by 7
“Similarly, simple cells in area V1, whose properties provided the inspiration for Gabor filters [16,23], derivative of Gaussians [18] and CORF [3,7] filters, have receptive fields that consist of inhibitory and excitatory regions.”
BackgroundCoding Schemes in the Archerfish Optic Tectum
Reichenthal, A., Ben-Tov, M., & Segev, R. (2018) · Frontiers in Neural Circuits · doi:10.3389/fncir.2018.00018 · Cited by 7
“…investigation of the cellular receptive fields structures has been conducted on a variety of terrestrial mammals such as the monkey (Ringach, 2002), cat (Hubel and Wiesel, 1962; Jones and Palmer, 1987a,b), rat (Girman et al., 1999), mouse (Niell and Stryker, 2008), and ferret (Usrey et al., 2003).”
Background
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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