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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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“It is known that Gabor filters are well fitted to the receptive field profiles of the simple cells of the cat visual cortex [22].”
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“Gabor filters, which have been shown to fit well the receptive fields of the majority of simple cell in the primary visual cortex [11], are modulation products of Gaussian and complex sinusoidal signals.”
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ResultSpatiotemporal receptive fields of cells in V1 are optimally shaped for stimulus velocity estimation
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Phase estimation via riesz transform in laser speckle interferometry for large-area damage imaging
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“The spatial profile of receptive fields of simple cells in V1 can be modeled as Gabor functions [18], [58].”
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Dominant orientation patch matching for HMAX
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“The S1 units take the form of Gabor functions, which have been described as a model of cortical simple-cell RFs [27].”
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Tsushima, Y., Komine, K., Sawahata, Y., & Morita, T. (2016) · Frontiers in Psychology · doi:10.3389/fpsyg.2016.00242 · Cited by 12
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Bolc, L., Wojciechowski, K., Chmielewski, L. J., Tadeusiewicz, R., & 2010, I. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-15910-7 · Cited by 12
Fast Covariance Computation and Dimensionality Reduction for Sub-window Features in Images
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“For example, it is common to apply gradient or Gabor filters [11] to images for texture analysis as well as for computation of global scene features in the gist algorithm [21].”
MethodLiu, C., & Sun, F. (2015) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2015.7280677 · Cited by 12
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BackgroundBinocular disparity encoding cells generated through an Infomax based learning algorithm
Okajima, K. (2004) · Neural Networks · doi:10.1016/j.neunet.2004.02.004 · Cited by 12
Capturing hair assemblies fiber by fiber
Jakob, W., Moon, J. T., & Marschner, S. (2009) · ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia (SIGGRAPH Asia) · doi:10.1145/1661412.1618510 · Cited by 12
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Learning Object Representations Using A Priori Constraints Within ORASSYLL
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“PF1 Feature genetically determined orientation sensitive reduction of search space by forcing Selection Gabor{shaped neurons description by specic features (Wiesel and Hubel, 1974; Jones and Palmer, 1987 ) with symbolic meaning”
BackgroundFast Computation of the Gabor Wavelet Transform
Loy, G. (2002) · Cited by 12
Ursino, M., & Cara, G.-E. L. (2004) · Vision Research · doi:10.1016/j.visres.2004.02.005 · Cited by 12
Efficient pose estimation using view-based object representations
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Image Representation by Complex Cell Responses
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Giese, M. A. (2004) · Springer eBooks · doi:10.1007/978-1-4020-2092-6_20 · Cited by 12
A new image distortion measure based on a data-driven multisensor organization
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A Unifying Principle for the Functional Organization of Visual CortexPreprint
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A Generic Approach to Object Matching and Tracking
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Representational untangling by the firing rate nonlinearity in V1 simple cells
Gáspár, M. E., Polack, P., Golshani, P., Lengyel, M., & Orbán, G. (2019) · eLife · doi:10.7554/elife.43625 · Cited by 11
Exploitation of image statistics with sparse coding in the case of stereo vision
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Texton-based analysis of paintings
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“Yet, although RF creation in the currentmodel thus already, in some sense, share similarities with the approach of Blakeslee and McCourt (2004), we will implement Gaborfilters (Jones and Palmer, 1987) in future versions of ourmodel to simulate V1 responses even more accurately.”
MethodRetinal visual processing constrains human ocular following response
Sheliga, B. M., Quaia, C., FitzGibbon, E. J., & Cumming, B. G. (2013) · Vision Research · doi:10.1016/j.visres.2013.10.002 · Cited by 11
“A simple model: antagonistic center/surround RFs In order to evaluate the role of early visual neurons in generating our responses, we attempted to model the responses quantitatively with a simple Linear–Nonlinear (LN) model.”
InfluentialEfficient Dictionary Learning with Sparseness-Enforcing Projections
Thom, M., Rapp, M., & Palm, G. (2015) · International Journal of Computer Vision · doi:10.1007/s11263-015-0799-8 · Cited by 10
“We used the methods developed by Jones and Palmer (1987) and Ringach (2002) for a more detailed analysis.”
MethodMiao, S., Liao, R., & Pfister, M. (2013) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2012.12.024 · Cited by 11
A Differential Model of the Complex Cell
Hansard, M. E., & Horaud, R. (2011) · Neural Computation · doi:10.1162/neco_a_00163 · Cited by 11
“Indeed, these RFs can be well-represented by odd and even Gabor functions (Daugman, 1985; Jones and Palmer, 1987; Pollen and Ronner, 1983).”
BackgroundJoseph, P. R. B. (2015) · Cited by 11
A Metric Model for the Functional Architecture of the Visual Cortex
Montobbio, N., Sarti, A., & Citti, G. (2020) · SIAM Journal on Applied Mathematics · doi:10.1137/18m120141x · Cited by 11
“A well-estabilished model for the RPs of V1 simple cells is represented by Gabor filters ([24], [10], [26]): the whole bank of filters {ψx,y,θ}x,y,θ is obtained by translations of (x, y) ∈ R(2) and rotations of θ ∈ S(1) of a mother function”
BackgroundMethodMulti-scale pseudo labeling for unsupervised deep edge detection
Zhou, C., Yuan, C., Wang, H., Li, L., Oehmcke, S., Liu, J., & Peng, J. (2023) · Knowledge-Based Systems · doi:10.1016/j.knosys.2023.111057 · Cited by 14
“Bio-inspired meth-ods [33,34] also indicate that models constructed in a hierarchical and parallel way could not only perceive edges and contours in a straightforward and unsupervised manner, but also have the property of biological interpretability.”
BackgroundGabor feature based classification using statistical models for face recognition
Thiyagarajan, R., Arulselvi, S., & Sainarayanan, G. (2010) · Procedia Computer Science · doi:10.1016/j.procs.2010.11.011 · Cited by 11
“Because of their biological relevance and computational properties, Gabor wavelets were introduced into the area of image processing [15,16].”
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Casile, A., & Rucci, M. (2006) · Neural Computation · doi:10.1162/089976606775623270 · Cited by 11
A phase-based stereo vision system-on-a-chip
Díaz, J., Ros, E., Sabatini, S. P., Solari, F., & Mota, S. (2006) · Biosystems · doi:10.1016/j.biosystems.2006.09.028 · Cited by 11
“Stereo vision allows many biological systems to reconstruct depth information encoded within multiple ∗ Corresponding author at: Department of Computer Architecture and Technology, University of Granada, ETSI Informática, c/ Periodista Daniel Saucedo Aranda s/n, E-18071 Granada, Spain.”
BackgroundInvariant object recognition using a neural template classifier
Tang, H., Srinivasan, V., & Ong, S. H. (1996) · Image and Vision Computing · doi:10.1016/0262-8856(95)01065-3 · Cited by 11
Human Emotion Recognition from Body Language of the Head using Soft Computing Techniques
Zhao, Y. (2012) · uO Research (University of Ottawa) · doi:10.20381/ruor-6160 · Cited by 11
“Gabor filters [119] with eight orientations and six spatial frequencies were applied for feature extraction.”
MethodTemporal prediction captures key differences between spiking excitatory and inhibitory V1 neuronsPreprint
Taylor, L., Zenke, F., King, A. J., & Harper, N. S. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.05.12.593763 · Cited by 10
“We found the RF shapes to extend along a 1D-curve, from blob-like RFs at the origin (Figure 3A first row) to elongated bars with multiple subfields that are located further [32], mice [26], monkeys [33] and model units.”
BackgroundMethodInfluentialA Cortical Interpretation of ASSOMs
Mayer, N. M., Herrmann, J. M., Bauer, H.-U., & Geisel, T. (1998) · Perspectives in neural computing · doi:10.1007/978-1-4471-1599-1_150 · Cited by 11
A spatiotemporal energy model based on spiking neurons for human motion perception
Yedjour, H., & Yedjour, D. (2024) · Cognitive Neurodynamics · doi:10.1007/s11571-024-10068-2 · Cited by 10
“Studies have shown that the receptive field properties of simple cells can be effectively represented by linear filters, such as Gabor functions, which align well with their impulse responses (Andrews and Pollen 1979; Marcelja 1980; Daugman 1985; Jones and Palmer 1987).”
Face Recognition Using Independent GaborWavelet Features
Liu, C., & Wechsler, H. (2001) · Lecture notes in computer science · doi:10.1007/3-540-45344-x_3 · Cited by 10
“In most cases one would use Gabor wavelets at five different scales, � �{ 0,···,4}, and eight orientations, µ �{ 0,···,7} [9], [ 10 ], [3].”
Feature Decomposition Based Saliency Detection in Electron Cryo-Tomograms
Zhou, B., Guo, Q., Wang, K., Zeng, X., Gao, X., & Xu, M. (2018) · IEEE International Conference on Bioinformatics and Biomedicine (BIBM) · doi:10.1109/bibm.2018.8621363 · Cited by 10
Contextual Integration in Cortical and Convolutional Neural Networks
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“For example, the orientation selectivity of simple cells of primary visual cortex can be modeled with Gabor filters [3].”
MethodEfficient Hardware Architecture for Sparse Coding
Kim, J. K., Knag, P. C., Chen, T., & Zhang, Z. (2014) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2014.2333556 · Cited by 10
“In this work, we design custom hardware architectures for ef fi cient and high-performance implementations of a sparse coding algorithm called the sparse and independent local network (SAILnet).”
MethodSensory optimization by stochastic tuning.
Jurica, P., Gepshtein, S., Tyukin, I., & van Leeuwen, C. (2013) · Psychological Review · doi:10.1037/a0034192 · Cited by 9
“The neurons were shown to implement an optimal tradeoff between the uncertainties associated with measurement of stimulus location and spatial frequency content (MacKay, 1981; Marčelja, 1980; Daugman, 1985; Glezer, Gauzel'man, & Iakovlev, 1986; J. P. Jones & Palmer, 1987).”
Spatial frequency components influence cell activity in the inferotemporal cortex
Bermúdez, M. A., Vicente, A. F., Romero, M. C., Perez, R., & González, F. (2009) · Visual Neuroscience · doi:10.1017/s0952523809990198 · Cited by 10
Two-tier self-organizing visual model for road sign recognition
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How Uncertainty Bounds the Shape Index of Simple Cells
Barbieri, D., Citti, G., & Sarti, A. (2014) · The Journal of Mathematical Neuroscience · doi:10.1186/2190-8567-4-5 · Cited by 10
“Remarkably, the same confinement was found also in cats [4, 5], and this suggests that this pattern can be associated with some criteria of optimality with respect to perceptive tasks.”
Selectivity, hyperselectivity, and the tuning of V1 neurons
Vilankar, K. P., & Field, D. J. (2017) · Journal of Vision · doi:10.1167/17.9.9 · Cited by 10
“This suggestion was supported by physiology (Field & Tolhurst, 1986; Jones & Palmer, 1987) and led to one of the standard models of visual processing, where images are represented by arrays of the Gabor functions that vary in location, orientation, and spatial frequency.”
BackgroundMethodA dual fast and slow feature interaction in biologically inspired visual recognition of human action
Yousefi, B., & Loo, C. K. (2017) · Applied Soft Computing · doi:10.1016/j.asoc.2017.10.021 · Cited by 10
“The methods, which have Gabor-like filters to model the detectors, have good constancy in simple cells [39].”
MethodLocal Operations: The Embodiment of Geometry
Koenderink, J.-J., Kappers, A. M. L., & van Doorn, A. J. (1992) · Springer eBooks · doi:10.1007/978-3-642-77840-7_1 · Cited by 10
Invariant Recognition Predicts Tuning of Neurons in Sensory Cortex
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A comparison of neural computations underlying stereo vision and sound localization
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Rasch, M. J., Chen, M., Wu, S., Lu, H. D., & Roe, A. W. (2012) · Journal of Neurophysiology · doi:10.1152/jn.00673.2012 · Cited by 11
Local autocorrelation of similarities with subspaces for shift invariant scene classification
Hotta, K. (2010) · Pattern Recognition · doi:10.1016/j.patcog.2010.11.003 · Cited by 10
Gabor filters for object localization and robot grasping
Walter, J., & Bert Arnrich, A. (2002) · Proceedings - International Conference on Pattern Recognition/Proceedings/International Conference on Pattern Recognition · doi:10.1109/icpr.2000.902879 · Cited by 10
“Biology gave us inspiration: 1987, Jones and Palmer [3] showed by cat visual cortex experiments, that receptive fields of simple cells fit well to a profile model, previously suggested by Daugman 1980 [1].”
BackgroundUnderstanding Visual Representation by Developing Receptive-Field Models
Kay, K. (2011) · The MIT Press eBooks · doi:10.7551/mitpress/8404.003.0009 · Cited by 10
Goyani, M. M., & Patel, N. M. (2017) · International Journal of Computers and Applications · doi:10.1080/1206212x.2017.1395134 · Cited by 11
Advances in Face Image Analysis
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A Novel Image Preprocessing by Evolvable Neural Network
Nam, M.-Y., Han, W. Y., & Rhee, P. K. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-30134-9_112 · Cited by 10
“Homomorphic filter: The Homomorphic filter[ 13 ] reduces brightness and emphasizes contrast in frequency domain in order to improve a reflectance effect and decrease a lighting effect.”
BackgroundImage perception and enhancement for the visually impaired
Myers, L. R., Rogers, S. K., Kabrisky, M., & Burns, T. J. (1995) · IEEE Engineering in Medicine and Biology Magazine · doi:10.1109/51.464776 · Cited by 10
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“filters (Eq. 4) is a step quite commonly performed in the majority of technical approaches (Sanger 1988; Fleet et al. 1991) and reflects the response of cortical simple cells which have Gabor-like receptive fields (Daugman 1980; Marcelja 1980; Jones and Palmer 1987 ).”
BackgroundGlezer, V. D. (2000) · Human Physiology · doi:10.1007/bf02760381 · Cited by 10
“The weight function of the linear area is described as a Gabor element [15, 16 ].”
BackgroundMeasuring linear and quadratic contributions to neuronal response
Nykamp, D. Q. (2003) · Network Computation in Neural Systems · doi:10.1088/0954-898x/14/4/304 · Cited by 10
Recognizing Faces --- An Approach Based on Gabor Wavelets
Shen, L. (2005) · Nottingham ePrints (University of Nottingham) · Cited by 10
Domain Adaptive Oriented Object Detection From Optical to SAR Images
Huang, H., Guo, J., Lin, H., Huang, Y., & Ding, X. (2024) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2024.3515161 · Cited by 9
“D neural receptive fields in the visual cortex [16], [17].”
A novel biologically inspired local feature descriptor
Zhang, Y., Tian, T., Tian, J., Gong, J., & Ming, D. (2014) · Biological Cybernetics · doi:10.1007/s00422-013-0583-1 · Cited by 9
“3.1 S1-like response 2D Gabor filters are joint entropy minimizing frequency sensitive filters, which have been proved capable of modeling the 123 linear spatial summation properties of simple cells (Jones and Palmer 1987) and extensively used as convolution filters in many computer vision algorithms.”
MethodInfluentialLearning Invariance from Natural Images Inspired by Observations in the Primary Visual Cortex
Teichmann, M., Wiltschut, J., & Hamker, F. H. (2012) · Neural Computation · doi:10.1162/neco_a_00268 · Cited by 10
“The receptive fields of simple cells consist of excitatory and inhibitory regions (Hubel & Wiesel, 1962), and their arrangement can be well described by Gabor filters (Jones & Palmer, 1987).”
BackgroundMethodGabor-based Face Recognition With Illumination Variation Using Subspace-Linear Discriminant Analysis
Kusuma, H., Wirawan, N., & Soeprijanto, A. (2012) · TELKOMNIKA Indonesian Journal of Electrical Engineering · doi:10.11591/telkomnika.v10i1.661 · Cited by 9
Automated recognition of complex categorical emotions from facial expressions and head motions
Adams, A., & Robinson, P. (2015) · International Conference on Affective Computing and Intelligent Interaction and workshops · doi:10.1109/acii.2015.7344595 · Cited by 11
“Gabor wavelets [12], dynamic textures [13], optical flow [14]).”
BackgroundOne-Class Model for Fabric Defect Detection
Zhou, H. Y., Chen, Y., Troendle, D., & Jang, B. (2021) · Natural Language Processing · doi:10.5121/csit.2021.112314 · Cited by 9
“Gabor filter is a good model of simple cells in the human visual cortex and is capable of representing textures very well [13].”
BackgroundYadav, Y., Chand, S., Sahoo, R. C., Sahoo, B. M., & Kumar, S. (2022) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-212771 · Cited by 10
Strength of predicted information content in the brain biases decision behavior
Yan, Y., Zhan, J., Garrod, O., Cui, X., Ince, R. A. A., & Schyns, P. G. (2023) · Current Biology · doi:10.1016/j.cub.2023.10.042 · Cited by 12
Searching for optimal stimuli: ascending a neuron’s response function
Koelling, M. E., & Nykamp, D. Q. (2012) · Journal of Computational Neuroscience · doi:10.1007/s10827-012-0395-7 · Cited by 9
Retinal Image Simulation of Subjective Refraction Techniques
Perchés, S., Collados, M. V., & Ares, J. (2016) · PLoS ONE · doi:10.1371/journal.pone.0150204 · Cited by 9
“First, the software does not take into account chromatic aberration, pupil dynamics or eye accommodation, and nor does it consider the sampling of the cone mosaic or neural processing [21,22,23].”
MethodRueopas, W., Leelhapantu, S., & Chalidabhongse, T. H. (2016) · International Joint Conference on Computer Science and Software Engineering · doi:10.1109/jcsse.2016.7748907 · Cited by 9
“In V1, simple cells are tuned preferentially for different orientations and their receptive fields can be approximated with Gabor filter [14].”
Full-reference quality assessment for stereoscopic images based on binocular vision model
Lin, C., Chen, Z., & Liao, N. (2016) · Visual Communications and Image Processing · doi:10.1109/vcip.2016.7805596 · Cited by 9
“Finally, we map these features to final quality by SVR.”
Robotic astrobiology – prospects for enhancing scientific productivity of mars rover missions
Ellery, A. A. (2017) · International Journal of Astrobiology · doi:10.1017/s1473550417000180 · Cited by 9
“The simple receptive field of the cat striate cortex is well-modelled by 2D Gabor filters (Jones & Palmer 1987).”
MethodFixation Prediction and Visual Priority Maps for Biped Locomotion
Anantrasirichai, N., Daniels, K., Burn, J. F., Gilchrist, I. D., & Bull, D. (2017) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2017.2734946 · Cited by 9
“, 2-D receptive field profiles are well described by 2-D Gabor functions [47].”
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.
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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