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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 first-layer Receptive Fields (RFs) (Fig 2B for the natural images database and Fig 2F for the face database) are similar to the V1 simple-cells RFs, which are oriented Gabor-like filters [46, 47].”
Plasticity of neuronal response properties in adult cat striate cortex
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MethodDiabetic Retinopathy detection using Weighted Filters and Classification using CNN
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MethodAction unit classification using active appearance models and conditional random fields
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“Gabor filters are local, high-frequency, oriented filters that resemble the filters implemented in the primate primal visual cortex V1 (Daugman 1985; Jones and Palmer 1987).”
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“Simple cells in the mammalian primary visual cortex (V1) are among the cells in the brain that are best functionally characterised [1–3].”
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“These detectors (see Appendix 1: Equations 8–10) were implemented using Gabor filters (Jones and Palmer, 1987) according to the classic motion-energy model (Adelson and Bergen, 1985).”
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MethodThe Berkeley Wavelet Transform: A Biologically Inspired Orthogonal Wavelet Transform
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“Gabor wavelets (Gabor, 1946; Daugman, 1980; Marcelja, 1980) provide an accurate description of the behavior of neurons in V1 ( Jones & Palmer, 1987; Smyth, Willmore, Baker, Thompson, & Tolhurst, 2003).,Their tuning can be described by an LN model where the linear filter is a two-dimensional generalization of the Gabor…”
BackgroundMethodInfluentialThe selection of natural scales in 2D images using adaptive Gabor filtering
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“The 2D Gabor functions give a good fit of the behavior of the receptive field of simple cells in mammals’ primary visual cortex [3], [4], [5], [ 6 ].”
BackgroundImage Representation with Gabor Wavelets and Its Applications
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A single functional model accounts for the distinct properties of suppression in cortical area V1
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“The RF of a simple cell in primary visual cortex can be accurately modelled by a 2-dimensional Gabor function (Daugman, 1980, 1988; Jones and Palmer, 1987; Lee, 1996; Marcelja, 1980).”
Perceptual learning in visual hyperacuity: A reweighting model
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MethodInternational Journal INFORMATION THEORIES & APPLICATIONS
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Learning Nonclassical Receptive Field Modulation for Contour Detection
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“Gabor function [63], [64] and sparse coding [65], [66] are usually used to mimic the simple-cell receptive field properties of V1 neurons in visual computing models.”
MethodZero-sum game theory model for segmenting skin regions
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Color contributes to object-contour perception in natural scenes
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“…the Sobel operators and and three biologically motivated algorithms which model simple cell responses in primary visual cortex (V1): Gabor filters (Jones & Palmer, 1987; Pollen & Ronner, 1983), a simple cell model with dominating opponent inhibition (SimpleCell; Hansen & Neumann, 2004a), and a…”
MethodTransfer of contrast sensitivity in linear visual networks
Watson, A. B. (1992) · Visual Neuroscience · doi:10.1017/s0952523800006507 · Cited by 34
“This has lead various authors to argue that the magnocellular system must be the substrate for psychophysical sensitivity (Hawken et al., 1988; Kaplan & Shapley, 1986).”
BackgroundThe DeepTune framework for modeling and characterizing neurons in visual cortex area V4Preprint
Abbasi-Asl, R., Chen, Y., Bloniarz, A. E., Oliver, M., Willmore, B. D. B., Gallant, J. L., & Yu, B. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/465534 · Cited by 33
“However, unlike existing studies using relatively simple Gabor wavelets (24, 25) or Fourier transform (8), complex nonlinear CNN features in our models make it extremely challenging to consistently interpret our models.”
MethodTranslation Invariant Directional Framelet Transform Combined With Gabor Filters for Image Denoising
Shi, Y. C., Yang, X., & Guo, Y. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2013.2285595 · Cited by 33
Lateral Inhibition Pyramidal Neural Network for Image Classification
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“2240295 detection [5] to texture analysis, such as the Gabor filter [6], [7].”
Robust detection of shady and highlighted roads for monocular camera based navigation of UGV
Mikšík, O., Petyovský, P., Žalud, L., & Jura, P. (2011) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2011.5979773 · Cited by 33
“Gabor wavelet filters are quite similar to the 2D receptive field profiles of the mammalian cortical simple cells, and shows suitable characteristics of spatial locality and orientation selectivity [21].”
BackgroundNormative theory of visual receptive fields
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“…properties of the visual world that one may naturally require an idealized vision system, or a biological organism subject to strong evolutionary pressure, to be adapted to, to enable a consistent handling of receptive field responses in terms of provable covariance or invariance properties under…”
BackgroundThe Active Side of Stereopsis: Fixation Strategy and Adaptation to Natural Environments
Gibaldi, A., Canessa, A., & Sabatini, S. P. (2017) · Scientific Reports · doi:10.1038/srep44800 · Cited by 32
Liu, J., Zhao, S., Xie, Y., Gui, W., Tang, Z., Ma, T., & Niyoyita, J. P. (2020) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2020.3016317 · Cited by 33
“Constraint 2: The orientation of the complex sinusoid is equivalent to that of the Gaussian envelope [19]—namely, ω0 = θ.”
BackgroundInfluentialRole of homeostasis in learning sparse representations
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Real-Time Classification of Traffic Signs
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Bilateral symmetry analysis of breast MRI
Alterson, R., & Plewes, D. B. (2003) · Physics in Medicine and Biology · doi:10.1088/0031-9155/48/20/011 · Cited by 33
“Findings from neurophysiology suggest that Gabor wavelets have biological counterparts in the receptive field structures of cortical cells in the human visual system as they can effectively capture orientation and spatial frequency qualities ( Jones and Palmer 1987 ).”
BackgroundA Comparison of Natural-Image-Based Models of Simple-Cell Coding
Willmore, B. D. B., Watters, P., & Tolhurst, D. J. (2000) · Perception · doi:10.1068/p2963 · Cited by 32
“To provide a comparison with traditional models of simple-cell coding, we have also measured the sparseness and dispersal of a Gabor filter set (Gabor 1946; Daugman 1980 ; Marcelja 1980; Bossomaier and Snyder 1986). simple-cell receptive fields (Field and Tolhurst 1986; Jones and Palmer 1987).”
MethodA new robust circular Gabor based object matching by using weighted Hausdorff distance
Zhu, Z., Tang, M., & Lu, H. (2004) · Pattern Recognition Letters · doi:10.1016/j.patrec.2003.12.014 · Cited by 32
“Gabor filters, which have been shown to fit well the receptive fields of the majority of simple cell in the primary visual cortex (Jones and Palmer, 1987; Daugman, 1985, 1988), are modulation products of Gaussian and complex sinusoidal signals.”
BackgroundA recurrent dynamic model for correspondence-based face recognition
Wolfrum, P., Wolff, C. G., Lücke, J., & von der Malsburg, C. (2008) · Journal of Vision · doi:10.1167/8.7.34 · Cited by 37
“If we neglect color and binocularity, the response properties of neurons in primary visual cortex are commonly described by the well-known Gabor wavelets (Daugman, 1980; Jones & Palmer, 1987; Ringach, 2002).”
MethodPrimitive features by steering, quadrature, and scale
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“Filters similar to smoothed low-order directional derivatives have been identified in the primary visual cortex of the cat [2], [3], [4], [5], [6], [7].”
BackgroundQuantum holography and neurocomputer architectures
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Multi-modal estimation of collinearity and parallelism in natural image sequences
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“4) similar to what has been previously reported for cortical cells (Hubel and Wiesel, 1959, 1962, 1965, 1968; Schiller et al., 1976a,b,c; DeValois et al., 1982a,b; Jones and Palmer, 1987; Ringach, 2002).”
ResultDiabetic retinopathy detection by optimized deep learning model
Rachapudi, V., Rao, K. S., Rao, T. S. M., Dileep, P., & Roy, T. L. D. (2023) · Multimedia Tools and Applications · doi:10.1007/s11042-023-14606-8 · Cited by 31
Manifold Regularized Local Sparse Representation for Face Recognition
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“In [25], the computational cost is reduced by introducing Gabor features [23], which makes the occlu- 1051-8215 © 2014 IEEE.”
BackgroundInfluentialGeometrical optical illusion via sub-Riemannian geodesics in the roto-translation group
Franceschiello, B., Mashtakov, A., Citti, G., & Sarti, A. (2019) · Differential Geometry and its Applications · doi:10.1016/j.difgeo.2019.03.007 · Cited by 30
“The first models have been presented by Daugman [18] (1985), Jones and Palmer [39] (1987) in terms of Gabor filters.”
BackgroundMaintaining filter structure: A Gabor-based convolutional neural network for image analysis
Molaei, S., & Abadi, M. E. S. A. (2019) · Applied Soft Computing · doi:10.1016/j.asoc.2019.105960 · Cited by 31
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“The sensory populations use two-dimensional Gabor filters as encoders [26,29,30].”
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David, S. V. (2017) · Hearing Research · doi:10.1016/j.heares.2017.12.021 · Cited by 33
“This general approach for studying neural encoding, developed in the auditory system, has since been applied to other sensory modalities (DiCarlo and Johnson, 2000; Jones and Palmer, 1987; Nagel and Wilson, 2011; Ramirez et al., 2014).”
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“Reverse-correlation technique (DeAngelis et al. 1993; Eckhorn et al. 1993; Jones and Palmer 1987) or a forward correlation technique equivalent to peristimulus time-histogram calculation was used to create spatial (x,y) RF maps separately for bright and dark dot stimulation.”
Detection of Blood Vessels in Fundus Images of the Retina using Gabor Wavelets
Oloumi, F., Rangayyan, R. M., Oloumi, F., Eshghzadeh-Zanjani, P., & Ayres, F. J. (2007) · Conference proceedings · doi:10.1109/iembs.2007.4353836 · Cited by 31
“Gabor functions have been found to provide good models for the receptive fields of simple cells in the striate cortex [14], [15].”
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“This allowed a direct comparison between the results of the simulations and neurophysiological data from cortical simple cells (Wilson and Sherman, 1976; Jones and Palmer, 1987b).”
MethodResultThe Problem of Sparse Image Coding
Pece, A. E. C. (2002) · Journal of Mathematical Imaging and Vision · doi:10.1023/a:1020677318841 · Cited by 31
“They are also similar to receptive fields of simple cells in the primary visual cortex [37].”
BackgroundGestalt perception in schizophrenia spectrum disorders.
Uhlhaas, P. J. (2003) · Stirling Online Research Repository (University of Stirling) · Cited by 31
Surround suppression sharpens orientation tuning in the cat primary visual cortex
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“A widely accepted model for the population of receptive fields is the one of space-time wavelet filterbank (Jones & Palmer, 1987; Field & Chichilnisky, 2007) which highlights the encoding properties and capabilities of the visual system, and can reproduce many properties of the ensemble response,…”
BackgroundMethodInfluentialAttention alters spatial resolution by modulating second-order processing
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“At central locations, RFs are predominantly small, which allows information to be integrated across narrow regions of space and mediates high-SF tuning (DeValois & DeValois, 1988; Jones & Palmer, 1987).”
BackgroundWSMN: An optimized multipurpose blind watermarking in Shearlet domain using MLP and NSGA-II
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The Maximal Causes of Natural Scenes are Edge Filters
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“It was found that the output of certain ganglion cells agrees with simple difference of Gaussian (DoG) filter responses [3] or more complex oriented Gabor filter results [4].”
BackgroundAdaptive weighting of local classifiers by particle filters for robust tracking
Hotta, K. (2008) · Pattern Recognition · doi:10.1016/j.patcog.2008.09.026 · Cited by 29
Does Sleep Really Influence Face Recognition Memory?
Sheth, B. R., Nguyen, N. T. T., & Janvelyan, D. (2009) · PLoS ONE · doi:10.1371/journal.pone.0005496 · Cited by 29
“This is tantamount to interference between memorized and perceived faces in brain areas or circuits prior to face processing, perhaps involving interactions between spatial filters in some low-level visual cortical area [20].”
BackgroundDirectional analysis of images with Gabor wavelets
Rangayyan, R. M., Ferrari, R. J., Desautels, J. E. L., & Frere, A. F. (2002) · Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI) · doi:10.1109/sibgra.2000.883910 · Cited by 29
Image Filtering and Analysis through the Wigner Distribution
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Recognizing faces with normalized local Gabor features and Spiking Neuron Patterns
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Universality in visual cortical pattern formation
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“The form of typical receptive fields can be described by Gabor functions with the form gðrÞ 1⁄4 cosðKrþWÞe rR r=2 [25], where the vector r is the location in the field of”
BackgroundFace Recognition Using Gabor Wavelets
Kumar, B. V., & Shreyas, B. S. (2006) · Asilomar Conference on Signals, Systems and Computers (ACSSC) · doi:10.1109/acssc.2006.354817 · Cited by 28
Fundamentals of Computer Vision
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No evidence for a common factor underlying visual abilities in healthy older people.
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Orientation Tuning Depends on Spatial Frequency in Mouse Visual Cortex
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“…there are studies showing that cells do not demonstrate only even or odd symmetry but also exhibit to a smaller extent various phases, which breaks the 1D symmetry that exists between the relative strength of each subfield (Kulikowski and Bishop, 1981; Jones and Palmer, 1987a; Ringach, 2002).”
BackgroundInfluentialDetection of fingertips in human hand movement sequences
Nölker, C., & Ritter, H. J. (1998) · Lecture notes in computer science · doi:10.1007/bfb0053001 · Cited by 28
“2D Gabor filters have been found by Jones and Palmer [3] to describe the response profile of simple cells in the visual cortex of cats.”
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Development of spatiotemporal receptive fields of simple cells: II. Simulation and analysis
Wimbauer, S., Wenisch, O. G., van Hemmen, J. L., & Miller, K. D. (1997) · Biological Cybernetics · doi:10.1007/s004220050406 · Cited by 28
“The notion of the phase of a spatial receptive field goes back to the modeling of simple cell receptive fields by Gabor functions, that is, by functions of the form J(α) = exp(−|α|2/(2A)) cos(k · α + θ) [10].”
BackgroundBiologically motivated approach to face recognition
Petkov, N., Kruizinga, P., & Lourens, T. (1993) · Lecture notes in computer science · doi:10.1007/3-540-56798-4_126 · Cited by 28
“A more precise study shows that tile receptive fields of the overwhelming majority of the simple cells in the primary cortex can be well fit by two-dimensional Gabor functions [ 23-26 ].”
BackgroundMethodReceptive Field Self-Organization in a Model of the Fine Structure in V1 Cortical Columns
Lücke, J. (2009) · Neural Computation · doi:10.1162/neco.2009.07-07-584 · Cited by 27
“For further analysis and as is customary in the literature, we match the real filters using Gabor wavelet functions (see, e.g., Jones & Palmer, 1987; Ringach, 2002).”
BackgroundMethodResultInfluentialNosrati, M., Karimi, R., Hariri, M., & Malekian, K. (2013) · Cited by 27
Introduction to Machine Learning
(2020) · Cambridge University Press eBooks · doi:10.1017/9781108690935.003 · Cited by 27
Patel, R. K., & Kashyap, M. (2023) · International Journal of Imaging Systems and Technology · doi:10.1002/ima.22865 · Cited by 27
“25 i. Gabor wavelets Here, f , θ , γ , η are known as frequency, angle of rotation, gamma, and eta, respectively.”
BackgroundMethodComputational approach for depth from defocus
Ghita, O., Whelan, P. F., & Mallon, J. (2005) · Journal of Electronic Imaging · doi:10.1117/1.1900743 · Cited by 27
“There are various psychophysical experiments which indicate that the simple cell operator acts as a line or edge detector, by responding to lines or edges with a specific orientation and spatial-frequency [11,20].”
BackgroundAllison, J. D., Casagrande, V. A., & Bonds, A. B. (1995) · Visual Neuroscience · doi:10.1017/s0952523800007999 · Cited by 27
Self-tuned Evolution-COnstructed features for general object recognition
Lillywhite, K. D., Tippetts, B. J., & Lee, D.-J. (2011) · Pattern Recognition · doi:10.1016/j.patcog.2011.05.012 · Cited by 27
Characterisation of nonlinear receptive fields of visual neurons by convolutional neural network
Ukita, J., Yoshida, T., & Ohki, K. (2019) · Scientific Reports · doi:10.1038/s41598-019-40535-4 · Cited by 30
Coding of the contrasts in natural images by visual cortex (V1) neurons: a Bayesian approach
Chirimuuta, M., Clatworthy, P. L., & Tolhurst, D. J. (2003) · Journal of the Optical Society of America A · doi:10.1364/josaa.20.001253 · Cited by 28
New color GPHOG descriptors for object and scene image classification
Sinha, A., Banerji, S., & Liu, C. (2013) · Machine Vision and Applications · doi:10.1007/s00138-013-0561-6 · Cited by 26
“The Gabor wavelet is considered to be a good model for human visual receptive fields and hence the Gabor waveletbased approach has been successfully used in image analysis [12,19,34].”
MethodLiu, J., Zhou, J., Tang, Z., Gui, W., Xie, Y., He, J., Ma, T., & Niyoyita, J. P. (2019) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2019.2909763 · Cited by 26
“As reported in [22] and [24], the ULD model can be extended to a multivariate LD (MLD) model to depict the higher-order dependence of image pixel coefficients straightforward.”
MethodMice use robust and common strategies to discriminate natural scenes
Yu, Y., Hira, R., Stirman, J. N., Yu, W., Smith, I. T., & Smith, S. L. (2018) · Scientific Reports · doi:10.1038/s41598-017-19108-w · Cited by 29
May, K. A., & Hess, R. F. (2008) · Journal of Vision · doi:10.1167/8.13.4 · Cited by 26
“To arrive at this value, we examined the data of Jones and Palmer (1987), who fitted a Gabor model to the receptive fields of simple cells in the cat’s striate cortex.”
MethodInfluentialEffects of stimulus transformations on estimates of sensory neuron selectivity
Dimitrov, A. G., & Gedeon, T. (2006) · Journal of Computational Neuroscience · doi:10.1007/s10827-006-6357-1 · Cited by 26
“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; Simoncelli et al., 2004).”
Robust motion estimation using spatial Gabor-like filters
Bruno, E., & Pellerin, D. (2002) · Signal Processing · doi:10.1016/s0165-1684(01)00188-8 · Cited by 29
Weighted Feature Gaussian Kernel SVM for Emotion Recognition
Wei, W., & Jia, Q. (2016) · Computational Intelligence and Neuroscience · doi:10.1155/2016/7696035 · Cited by 26
Binocular combination of stimulus orientation
Yehezkel, O., Ding, J., Sterkin, A., Polat, U., & Levi, D. M. (2016) · Royal Society Open Science · doi:10.1098/rsos.160534 · Cited by 26
“Classical receptive fields of simple cells are closely matched by Gabor signals [29,30], similarly for behavioural and single-cell-level measurements [31].”
Background2D Gabor filters-based steganalysis of content-adaptive JPEG steganography
Song, X., Liu, F., Zhang, Z., Yang, C., Luo, X., & Chen, L.-J. (2016) · Multimedia Tools and Applications · doi:10.1007/s11042-016-4157-9 · Cited by 26
“A 2D Gabor filter approximates the receptive fields of a simple cell [21] and achieves the resolution limit in conjoint space [26], so it is suitable for image analysis.”
Model of Frequency Analysis in the Visual Cortex and the Shape from Texture Problem
Massot, C., & Hérault, J. (2007) · International Journal of Computer Vision · doi:10.1007/s11263-007-0048-x · Cited by 26
Idealized Computational Models for Auditory Receptive Fields
Tony Lindeberg, C., & Friberg, A. (2015) · PLoS ONE · doi:10.1371/journal.pone.0119032 · Cited by 26
“In the work by Qiu et al. [31], the measured biological receptive fields were fitted to Gabor functions as motivated by previous use of Gabor functions for modelling visual receptive fields (Marcelja [88]; Jones and Palmer [89, 90]).”
MethodThe central performance drop in texture segmentation: a simulation based on a spatial filter model
Kehrer, L. (1997) · Biological Cybernetics · doi:10.1007/s004220050391 · Cited by 26
“It closely resembles receptive field profiles found in the striate cortex of the cat and the monkey (e.g., Jones and Palmer 1987; Kulikowski and Bishop 1981; Kulikowski et al. 1982; Mullikin et al. 1984).”
Underestimation of visual texture slant by human observers: a model
Turner, M. R., Gerstein, G. L., & Bajcsy, R. K. (1991) · Biological Cybernetics · doi:10.1007/bf00206219 · Cited by 26
Tadmor, Y., & Tolhurst, D. J. (1989) · Visual Neuroscience · doi:10.1017/s0952523800005940 · Cited by 26
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.
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