S. Marcelja, "Mathematical description of the responses of simple cortical cells ". J. Opt. Soc. Amer., vol. 70, 1980, pp.1297-1300.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Typically, center surround receptive fields are modeled as the di#erence of two circular Gaussian kernels with di#erent widths (di#erence of gaussians model [130] whereas oriented receptive fields are most often fitted by Gabor functions (products of sinusoidal gratings and Gaussian envelopes) [28, 32, 65, 93, 129]; however, see also [142] It goes without saying that these linear models are drastic simplifications of the actual neural firing dynamics of these cells, but they are nevertheless useful starting points on which more detailed models can be built. Although these linear models are useful in ....

S. Marcelja, "Mathematical description of the responses of simple cortical cells," Journal of the Optical Society of America, vol. 70, no. 11, pp. 1297--1300, 1980.

.... Typically, center surround receptive fields are modeled as the di#erence of two circular Gaussian kernels with di#erent widths (di#erence of gaussians model [130] whereas oriented receptive fields are most often fitted by Gabor functions (products of sinusoidal gratings and Gaussian envelopes) [28, 32, 65, 93, 129]; however, see also [142] It goes without saying that these linear models are drastic simplifications of the actual neural firing dynamics of these cells, but they are nevertheless useful starting points on which more detailed models can be built. Although these linear models are useful in ....

S. Marcelja, "Mathematical description of the responses of simple cortical cells," Journal of the Optical Society of America, vol. 70, no. 11, pp. 1297--1300, 1980.

....for isolated target stimuli, measured before and after the practice sessions. Six adult observers, with typical contrast discrimination abilities [13] participated in the experiments. After measuring their performance in the contrast discrimination of an isolated foveal Gabor signal (GS) [14, 15], the observers practiced the same task in the presence of chains of high contrast lateral GS ankers (Fig. 1) The practice was organized in subsequent cycles of three daily sessions each, with 500 100 trials a day. During each experimental sub session, the contrast of the target stimulus was ....

Marcelja, S. Mathematical description of the responses of simple cortical cells. J Opt Soc Am 70, 1297-1300 (1980).

....the primary visual cortex in mammalian brains some thirty years ago, an enormous amount of experimental and theoretical research has greatly advanced our understanding of this area and the response properties of its cells. On the theoretical side, an important insight has been advanced by Marcelja [25] and Daugman [6] 7] that simple cells in the visual cortex can be modeled by Gabor functions. The 2D Gabor functions proposed by Daugman are local spatial bandpass filters that achieve the theoretical limit for conjoint resolution of information in the 2D spatial and 2D Fourier domains. Gabor ....

S. Marcelja, " Mathematical Description of the Responses of Simple Cortical Cells," J. Optical Soc. Am., vol. 70, pp. 1,297-1,300, 1980.

....exponential: G f,#,# (x, y) 1 2## 2 ( x 2 2# 2 y 2 2# 2 ) j2#f(x cos(#) y sin(#) 1) where f is the frequency, # the orientation and # the scale. These filters have the particularity to approximate the receptive field sensitivity of orientation sensitive cells of the retina [8, 5]. We then convolute the rendered image with a bank of Gabor filters obtained from particular orientations (# i = i# n ) and particular scales # i . If I orientation is the resulting orientation map, I orientation is given by: I orientation = S i=1 O j=1 I # G f,# j ,# i (2) with S ....

S. Marcelja. Mathematical description of the responses of simple cortical cells. Journal of Optical Society of America, 70:1297--1300, 1980.

....system of vertebrates. The convolution of the stereo images with oscillating local lters (Eq. 4) is a step quite commonly performed in the majority of technical approaches [Sanger, 1988, Fleet et al. 1991] and re ects the response of cortical simple cells which have Gaborlike receptive elds [Marcelja, 1980, Daugman, 1980, Jones and Palmer, 1987] It has been suggested that the evaluation of spatial phase di erences from such re12 ceptive eld responses could indeed be used to compute disparity in the brain [De Angelis et al. 1991] The dense coverage of the visual eld by cells with many di erent ....

Marcelja, S. (1980). Mathematical description of the responses of simple cortical cells. J. Opt. Soc. Amer., 70:1297-1300. 14

....human visual system. At the retinal ganglion cells and the lateral geniculate nucleus (LGN) the receptive fields have a center surround property [3, 7] and further downstream in the primary visual cortex (V1) the receptive fields exhibit an orientation , phase , and frequency tuned properties [6, 9]. These early visual processes can be approximated by a sequence of convolutions with difference of Gaussian (DoG) and oriented Gabor filters (for instance, see [5] The resulting response level (called orientation energy) can be interpreted as visual cortical activity in response to visual ....

Marcelja, S. (1980). Mathematical description of the response of simple cortical cells. Journal of Optical Society of America A, 70(11):1297--1300.

....the FRAME theory [23] We address the problem of texture segmentation in the context of the Gabor feature space of images. The motivation for the use of Gabor filters in texture analysis is double fold. First, it is believed that simple cells in the visual cortex can be modeled by Gabor functions [13], 4] and that the Gabor scheme provides a suitable representation for visual information in the combined frequency position space [15] Second, the Gabor representation has been shown to be optimal in the sense of minimizing the joint two dimensional uncertainty in the combined spatial frequency ....

S. Marcelja, "Mathematical description of the response of simple cortical cells", J. Opt. Soc. Amer., 70, 1980, 1297-1300.

....5] and synthesis [6] motion [7] etc. Moreover, Gabor functions (frequently in the frame of multiscale filtering schemes) are often used in current models of image representation in the visual cortex [8 11] because they are a good approximation to the receptive fields of simple cortical cells [12, 13]. However, Gabor functions are not orthogonal and, as a consequence, the classic Gabor expansion is computationally expensive, having unusual dual basis functions [14] The reconstruction requires the use, among others, of iterative algorithms [15] neural networks [2] or the inversion of large ....

S. Marcelja, " Mathematical description of the response of simple cortical cells," J. Opt. Soc. Am., A 70, 1297-1300 (1980).

.... at different orientations similar to the receptive fields of simple cells in V1 [Hubel and Wiesel, 1962;1968; Palmer et al. 1991] see also [Olshausen and Field, 1996; Harpur and Prager, 1996; Bell and Sejnowski, 1996] These have previously been modeled as 2D Gabor functions [Daugman, 1980; Marcelja, 1980 ] or difference of 17 Gaussian operators [Young, 1985] The level 2 receptive fields were constructed by propagating a unit impulse response for each row of the weight matrix at the second level to level 0. These receptive fields appear to be tuned towards more complex shapes such as corners, ....

S. Marcelja. Mathematical description of the responses of simple cortical cells. Journal of the Optical Society of America, 70:1297--1300, 1980.

....the uniform distribution and the resulting vectors were normalized to length one. B) shows the same set of synaptic weights after training the neuron network on natural images (see text for details) The synaptic profiles at each time step resemble oriented Gabor wavelets [Daugman, 1980; Marcelja, 1980 ] C) depicts these synaptic weights using a classical 2D receptive field representation, where the dark regions are inhibitory and the bright regions are excitatory. The entire sequence of synaptic weights suggests that this neuron is tuned towards dark bars moving diagonally from the bottom ....

....impulse response functions for time steps . The receptive fields after learning resemble localized Gabor wavelets which have previously been shown to well approximate the receptive field weighting profiles of simple cells in the mammalian primary visual cortex [Daugman, 1980; Marcelja, 1980; Olshausen and Field, 1996 ] In addition, the model neuron can be seen to be tuned towards dark bars moving diagonally from the bottom left corner of the receptive field to the top right corner. A 12 2 3 4 5 6 8 7 t=1 2 3 4 5 6 8 7 t=1 (a) b) c) d) e) f) g) h) i) j) k) l) p) m) ....

S. Marcelja. Mathematical description of the responses of simple cortical cells. Journal of the Optical Society of America, 70:1297--1300, 1980.

....more random texture. To obtain texture features for a region we use Gabor filters, which are a particular type of filter tuned to respond to a specified range of spatial frequencies and orientations. Gabor filters have been to shown to have similar characteristics to simple visual cortical cells (Marcelja, 1980) and therefore sound psychophysical basis. Figure 8a shows an example of the real part of a complex valued Gabor filter in the spatial domain; the imaginary part is equal but subject to a 90 phase shift. In the spatial domain, the filter has the form of a complex sinusoid modulated with a Gaussian ....

S Marcelja (1980), "Mathematical description of the responses of simple cortical cells", Journal of the Optical Society of America, 70, 11, pp. 1297-1300.

....metric [26, 27] is obtained. If a given coding scheme uses some particular transform basis, specific incremental threshold data should be used [2, 3] However, as the impulse responses of the perceptual filter bank, T , closely resemble the basis functions used in image coding transforms [28, 29] a similar behavior can be expected 2 . Therefore the metric W can be considered a reasonable approximation with any generic local frequency transform. In some cases, it is also possible to obtain the behavior in the desired domain from the functions defined in other domains [26, 31] 3 Coder ....

S. Marcelja, "Mathematical description of the response of simple cortical cells," Journal of the Optical Society of America, vol. 70, no. 11, pp. 1297--1300, 1980. 15

....system of vertebrates. The convolution of the stereo images with oscillating local 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 [Marcelja, 1980, Daugman, 1980, Jones and Palmer, 1987] It has been suggested that the evaluation of spatial phase differences from such receptive field responses could indeed be used to compute disparity in the brain [De Angelis et al. 1991] The dense coverage of the visual field by cells with many different ....

Marcelja, S. (1980). Mathematical description of the responses of simple cortical cells. J. Opt. Soc. Amer., 70:1297--1300.

....allowing separate analysis of the magnitude (envelope) and phase characteristics in the spatial domain. The magnitude response of a Gabor function in the frequency domain is well behaved, having no sidelobes. Gabor functions appear to share many properties with the human visual system [25]. While Gabor functions are a good choice, the standard forms can be further improved. Under certain conditions, very low frequency effects (e.g. due to illumination and shading variations) can cause a significant response in a Gabor filter, leading to misclassification. An analytic form is ....

....angle of , and . In the spatial domain, is separable into two orthogonal 1 D Gabor functions from (1) that are, respectively, aligned to the and axes: 8) As in (3) an image is represented exactly [1] 2] 2 as (9) where , and are constants; and . Approximations to are obtained by using [25] (10) provided that the parameters are chosen appropriately. 2 The proofs in the references are based on the standard, not analytic, form of the Gabor function. D. Two Dimensional Gabor Function: Polar Form An alternative approach to extending the Gabor function into two dimensions is to ....

S. Marcelja, "Mathematical description of the responses of simple cortical cells," J. Opt. Soc. Amer., vol. 70, pp. 1297--1300, 1980.

.... scheme [47] obviously draws some inspiration from the measured responses of retinal ganglion cells [48] while the more complex coder devised by Daugman is based on the so called Gabor representation [44, 49] whose similarity to the responses of simple cortical neurons was noted by Marcelja [50] and also informed the original work of Granlund [51] There are therefore numerous ways in which the coding metaphor has been found productive. In all of these cases, the coder consists of a linear transformation, whose primary effect is to redistribute the energy in the image so that most of ....

S. Marcelja,"Mathematical Description of the Responses of Simple Cortical Cells",Jnl. Opt. Soc. Amer., 70, pp.1297-1300, 1980.

....detectors from this scheme are both derived from the image; ii) The response of the activated units (hereafter named as sensors) are given by complex Gabor filters. The 2D Gabor functions give a good fit of the behavior of the receptive field of simple cells in mammals primary visual cortex [3 6]. Also, these functions analyze the image simultaneously in both space and frequency domains, therefore we can use them to fit both frequential and spatial parameters. iii) The relative sharpness of the sensor response across scales is measured by a Gabor filter based criterion, and the natural ....

Marcelja S., "Mathematical description of the response of the simple cortical cells", J. Opt. Soc. Am., Vol. 70, pp. 1297-1399, (1980).

....are examined and compared in Section V in a series of computational experiments. In Section VI we summarize the results of the study and draw conclusions. II. GABOR FILTERS Gabor filters are closely related to the function of simple cells in the primary visual cortex of primates [26] 39] [40]. Since simple cells play a substantial role in the following, we first briefly introduce a computational model of this type of cell. The response of a simple cell which is characterized by a receptive field function to a luminance distribution image , is computed as follows ( denotes the visual ....

S. Marcelja, "Mathematical description of the response of simple cortical cells," J. Opt. Soc. Amer., vol. 70, pp. 1297--1300, 1980.

.... investigating the role of localized phase in image representation is motivated by the manner in which biological visual systems process information [16, 17] According to neurobiological research, the visual system resembles Gabor like operators which are localized in both position and frequency [18, 19], thereby suggesting a localized frequency representation. In this paper, we examine the convergence rate of the algorithm for image reconstruction from Discrete Fourier Transform (DFT) phase. The importance of localized phase in signal representation is investigated. The convergence rate of the ....

S. Marcelja, "Mathematical Description of the Responses of Simple Cortical Cells" J. Opt. Soc. Am. 70, No. 11, pp.1297-1300, November 1980.

....transformation by each of these mechanisms and give rise to the pattern representation. Figure 14 illustrates this process. To implement a model of these mechanisms, we need to choose a particular set of mechanism response functions. A number of mathematical functions such as Gabor functions [Marcelja80], Cortex transforms [Watson87] and di#erencesof Gaussians (DOGs) Marr82] have been proposed to emulate these mechanisms. While all of these functions have been used to model visual processing, and some like the Cortex transform o#er greater computational e#ciency, we have chosen to use the DOG ....

Marcelja, S. (1980). Mathematical description of the responses of simple cortical cells. J. Opt. Soc. Am., 70, 1297-1300.

....5] and synthesis [6] motion [7] etc. Moreover, Gabor functions (frequently in the frame of multiscale filtering schemes) are often used in current models of image representation in the visual cortex [8 11] because they are a good approximation to the receptive fields of simple cortical cells [12, 13]. However, Gabor functions are not orthogonal and, as a consequence, the classic Gabor expansion is computationally expensive, having unusual dual basis functions [14] The reconstruction requires the use, among others, of iterative algorithms [15] neural networks [2] or the inversion of large ....

S. Marcelja, "Mathematical description of the response of simple cortical cells," J. Opt. Soc. Am., A 70, 1297-1300 (1980).

.... that biological neurons have evolved to be sensitive to elementary features occurring over a range of scales (frequency ranges) or equivalently, that images are decomposed by the cortical neurons into narrowband frequency channels that are highly spatially localized (sensitive to local features) Marcelja (1980) observed the highly oriented simple cell receptive fields in the cortex can be accurately modeled by 1 D Gabor functions, which are Gaussian modulated sine wave functions. The Gabor functions play an important role in functional analysis and in physics, since they are the unique functions that ....

S. Marcelja. Mathematical description of the responses of simple cortical cells, J. Opt. Soc. Am. 70, 1297-1300, 1980.

....one does not have to use the Gabor functions as the front end filters in our stereo vision model, there are good reasons to do so. The main reason, of course, is that the Gabor filters have been found to describe the spatial receptive field profiles of real primary visual cortical cells very well (Marcelja, 1980; Jones and Palmer, 1987; Ohzawa et al. 1990; Freeman and Ohzawa, 1990; DeAngelis et al. 1991) but see Stork and Wilson (1990) for a different point of view) There is, however, a hitherto unrecognized advantage of using Gabor filters as simple cell receptive field profiles in disparity ....

Marcelja, S. (1980). Mathematical description of the responses of simple cortical cells, J.

.... y) It might be expected that two dimensional signals could be represented in terms of two dimensional analogues of Gabor elementary functions, and in the early 1980s a number of researchers suggested Gaussian modulated sinusoids as models of the receptive fields of simple cells in visual cortex (Marcelja 1980; Daugman 1980; Watson 1982; Pribram Carlton 1986) Our presentation is based on Daugman (1985a, 1988) Daugman proved 12 two dimensional analogues of Gabor s Uncertainty Principle, Deltax Deltau 1 = 4 ; Deltay Deltav 1 = 4 12 Our own proofs can be found in Appendices A and B. where ....

Marcelja, S. "Mathematical Description of the Responses of Simple Cortical Cells." Journal of the Optical Society of America. Vol. 70 (1980), 1297-- 1300.

.... at different orientations similar to the receptive fields of simple cells in V1 [Hubel and Wiesel, 1962;1968; Palmer et al. 1991] see also [Olshausen and Field, 1996; Harpur and Prager, 1996; Bell and Sejnowski, 1996] These have previously been modeled as 2D Gabor functions [Daugman, 1980; Marcelja, 1980] or difference of Gaussian operators [Young, 1985] The level 2 receptive fields were constructed by propagating a unit impulse B C D E Input to Network Residual Top Down Prediction A Figure 3: Results from Experiment 1: Recognition of Simple Objects. A) The five objects used for training ....

S. Marcelja. Mathematical description of the responses of simple cortical cells. Journal of the Optical Society of America, 70:1297--1300, 1980.

.... the focus of research: 1) Principal Components Analysis (PCA) based on information theory, as embodied by the eigenface approach; Turk and Pentland (1991) Kirby and Sirovich (1990) and (2) the Gabor wavelet transform motivated by psychophysical studies of the early mammalian vision system [Marcelja (1980), Daugman (1985) Daugman (1988) Lades et al. 1993) Wurtz (1995) These representation schemes are usually applied uniformly to an image without any explicit modelling 1 Funded by HCM Parallel Modelling of Neural Operators network 2 Mail address: Mile End Road, London. U.K. Email: ....

.... Gabor s theory leads to the idea that a visual system should analyse visual information most economically by using pairs of receptive fields of symmetrical (cosine) and asymmetrical (sine) response profiles in order to achieve minimum uncertainty in both spatial localisation and spatial frequency [Marcelja (1980), Kulikowski Bishop (1981) The following family of functions G(x; y) achieve the lower bound in joint 2 D entropy minimization: G(x; y) exp i Gamma h (x Gamma x 0 ) 2 a 2 (y Gamma y 0 ) 2 b 2 ij Theta exp ( Gamma2 i [u 0 (x Gamma x 0 ) v 0 (y Gamma y 0 ) where (x; y) ....

Marcelja, S. (1980) Mathematical Description of the Responses of Simple Cortical Cells, J. of the Optical Society of America 70.

....the primary visual cortex in mammalian brains some thirty years ago, an enormous amount of experimental and theoretical research has greatly advanced our understanding of this area and the response properties of its cells. On the theoretical side, an important insight has been advanced by Marcelja [25] and Daugman [6] 7] that simple cells in the visual cortex can be modeled by Gabor functions. The 2D Gabor functions proposed by Daugman are local spatial bandpass filters that achieve the theoretical limit for conjoint resolution of information in the 2D spatial and 2D Fourier domains. Gabor ....

S. Marcelja, "Mathematical Description of the Responses of Simple Cortical Cells," J. Optical Soc. Am., vol. 70, pp. 1,297-1,300, 1980.

.... a class of cells exist in the visual system whose response depends on the spatial frequency and the orientation of the stimulus (the so called simple cells of Hubel and Wiesel [9] It has been shown that the impulse response of this class of cells can be modeled very well by Gabor functions [3, 10, 13]. In addition to maintaining this property, wavelets based on these functions provide varying support sizes (or spreads) for the different frequencies and this corresponds well to the different receptive field sizes of biological neurons that are tuned to different frequencies. Biological ....

S. Marcelja. Mathematical description of the responses of simple cortical cells. Journal of the Optical Society of America, A 70(11):1297--1300, 1980.

....studies found cells in V 1 (simple cells) that are selectively tuned to orientation as well as to spatial frequency and phase. It was suggested that the response profile of a simple cell could be approximated by 2D Gabor like filters (Daugman, 1984; Daugman, 1985; De Valois and De Valois, 1990; Marcelja, 1980; Pollen and Ronner, 1981; Pollen and Ronner, 1983) or a set of m th ordered spatial derivatives of a Gaussian (Koenderink and van Doorn, 1990) Inspired by these findings, several artificial face recognition systems filter the grey level image by a set of 2D Gabor like functions before attempting ....

Marcelja, S. (1980). Mathematical description of the responses of simple cortical cells.

....LGN stage are D = 1, U = 1, L = 1, C = 100, oe c = 1:0, S = 10, oe s = 3:0, W = 0:16. Subscripts on parameters such as U; L; C and S are omitted in their several uses for simplicity. Simple and Complex Cell Layers The oriented cells used here are odd symmetric Gabor filters (Daugman, 1980; Marcelja, 1980). Including even Gabor cells may improve the system s boundary detection capabilities (Cruthirds et al. 1992; Pollen Ronner, 1981; Spitzer Hochstein, 1985) but adequate results were here obtained without them. Each odd cell has two subregions, A and B, that are symmetric about the cell s ....

Marcelja, S. (1980). Mathematical description of the responses of simple cortical cells. Journal of the Optical Society of America, 70, 1297--1300.

....cells preferentially respond to oriented edges or lines, they can be viewed as edge or line detectors. Their joint localisation in both the spatial domain and the spatial frequency domain has led to the suggestion that they mimic Gabor filters, minimising uncertainty in both domains (Daugman 1980, Marcelja 1980). More recently, the match between the operations performed by simple cells and the wavelet transform has attracted attention (e.g. Field 1993) The approaches based on Gabor filters and wavelets basically consider processing by the visual cortex as a general image processing strategy, relatively ....

Marcelja, S. 1980 Mathematical description of the responses of simple cortical cells. J.Opt.Soc.Am. 70, 1297-1300.

....Our previous analysis (Qian, 1994) and simulations (Qian, Andersen and Adelson, 1994b) confirm that this is indeed the case. There is, however, one major problem with this formulation: while the spatial receptive fields of cortical simple cells can be modeled accurately by Gabor functions (Marcelja, 1980; Daugman, 1985; Jones and Palmer, 1987; Freeman and Ohzawa, 1990) the temporal responses of the cells are clearly not Gabor like 3 (DeAngelis, Ohzawa and Freeman, 1993) The integrated model we developed using spatiotemporal Gabor filters is therefore not completely physiologically realistic. ....

Marcelja, S. (1980). Mathematical description of the responses of simple cortical cells, J.

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S. Marcelja, "Mathematical description of the responses of simple cortical cells ". J. Opt. Soc. Amer., vol. 70, 1980, pp.1297-1300.

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S. Marcelja. Mathematical description of the responses of simple cortical cells. J. Opt. Soc. Am., 70:1297--1300, 1980.

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S. Marcelja, Mathematical description of the responses of simple cortical cells, Journal of the Optical Society of America 70 (1980) 1297-1300

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S. Marcelja. Mathematical description of the response of simple cortical cells. J. Opt. Soc. Amer., 70:1297--1300, 1980.

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S. Marcelja. Mathematical description of the response of simple cortical cells. J. Opt. Soc. Amer., 70:1297--1300, 1980.

No context found.

S. Marcelja, "Mathematical description of the responses of simple cortical cells," Journal of Optical Society of America, vol. 70, pp. 1297--1300, 1980.

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S. Marcelja, "Mathematical description of the responses of simple cortical cells," Journal Opt. Soc. Amer., vol. 70, pp. 1297--1300, 1980.

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S. Marcelja, "Mathematical description of the responses of simple cortical cells," Journal Opt. Soc. Amer., vol. 70, pp. 1297--1300, 1980.

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S. Marcelja. Mathematical description of the responses of simple cortical cells. Journal of Optical Society of America, 70:1297--1300, 1980.

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S. Marcelja, "Mathematical description of the responses of simple cortical cells," J. Opt. Soc. Am, 70(11):1297--1300, Nov 1980.

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S. Marcelja, "Mathematical description of the responses of simple cortical cells," Journal of Optical Society of America, vol. 70, pp. 1297--1300, 1980.

No context found.

S. Marcelja. Mathematical description of the response of simple cortical cells. J. Opt. Soc. Amer., 70:1297--1300, 1980.

No context found.

S. Marcelja. Mathematical description of the response of simple cortical cells. Journal of Optical Society of America, 70:1297--1300, 1980.

No context found.

S. Marcelja, "Mathematical description of the response of simple cortical cells", J. Opt. Soc. Am., vol. 70, No. 11, pp 1297-1300, November 1980.

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S. Marcelja, "Mathematical description of the response of simple cortical cells," J. Opt. Soc. Am. A 70, 1297--1300 ~1980!.

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S. Marcelja, Mathematical Description of the Responses of Simple Cortical Cells, Journal of the Optical Society of America 70(11), 1297-1300 (1980).

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Marcelja S., "Mathematical description of the response of the simple cortical cells", J. Opt. Soc. Am., Vol. 70, pp. 1297-1399, (1980).

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S. Marcelja (1980). Mathematical description of the responses of simple cortical cells, J. Opt. Soc. Am., Vol. 70, No. 11, 1297--1300.

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