An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex

“contour of actor is obtained to generate spatiotemporal volume to obtain outer boundary information through 3D Gabor filters [165].”

“Such a kernel is a popular image processing choice for edge detection and texture classification (e.g., Petkov & Kruizinga 1997; Feichtinger & Strohmer 1998) and is thought to mimic some image processing functions of the mammalian brain (Jones & Palmer 1987).”

“…selectivity (Mastronarde, 1987; Saul and Humphrey, 1990, 1992b; Emerson et al., 1992), orientation, color or disparity selectivity, end-stopping, ON as well as OFF input, and Cartesian nonseparability of simple receptive fields (Jones and Palmer, 1987a,b; Reid et al., 1991; McLean et al., 1994).”

“retr Biology: Gabor kernels are commonly used to model image edge responses in the primary visual cortex, in humans and other mammals, to variations in frequency and orientation [43,44].”

“Marcelja [2] and Jones and Palmer [3] demonstrated that simple cells in the primary visual cortex have receptive fields that are restricted to”

“Our extensive usage of Gabor-type wavelets is the most obvious point of similarity to the visual system of higher vertebrates [Jones and Palmer, 1987].”

“Equation 2 gives the real (observable) part of a generalized 2D Gabor filter (Jones and Palmer 1987, p. 1236). a2 and b2 are variance in the x and y direction, respectively. x, y, U0 and V0 are spatial coordinates, K is a scale factor, and P can be interpreted as the relative spatial phase angle of…”

“A spike thresholding or “iceberg effect,” provoked by elevated inhibition, could account for these results (Jones and Palmer, 1987; Gardner et al., 1999).”

“Email: cslzhang@comp.polyu.edu.hk.”

“The receptive fields of the simple cells in the mammalian primary visual cortex have been hypothesized to be describable by Gabor-type functions (Daugman, 1980, 1985; Marcelja, 1980; Jones & Palmer, 1987 ), and the ASSOM process also produces Gabortype filters in the first-layer neurons.”

“One example of such decompositions are Gabor filters [40], [41].”

“Figure 2D shows that the distribution of these shapes in monkey (open circles) and cat (crosses; data from Jones & Palmer, 1987a).”

“The Gabor filter is a superior model of simple cell receptive fields in cat striate cortex (Jones & Palmer, 1987), and it grants exceptional basis for object recognition and face recognition (Lades et al., 1993; Wiskott, Fellous, Kruger, & vonderMalsburg, 1997).”

“The simplest plausible model consists of two stages: a spatiotemporal Gabor filter that represents a pool of area V1 simple and complex neurons (Adelson and Bergen, 1985; Jones and Palmer, 1987), and a linear pooling mechanism that selectively integrates information from a specific subset of putative V1 inputs.”

“Interestingly, the theoretical scale-space approach and the more empirical receptive field approach are to a certain extent in agreement; simple receptive fields in the mammalian retina and primary visual cortex are well described by Gaussian derivatives (Young, 1985, 1987; Jones and Palmer, 1987a, 1987b ) but also by…”

“There are some surprising parallels between the visual cortex and convolutional neural networks trained on natural images, like e.g. the emergence of Gabor-like filters in the first layer of processing (Marĉelja 1980; Daugman 1985; Jones & Palmer 1987; Krizhevsky et al. 2017; Cichy et al. 2016).”

“In recent years, the reverse correlation method has been applied to studies of the visual cortex, yielding detailed maps of the CRFs ( Jones & Palmer, 1987a, b; DeAngelis et al., 1993, 1995a; Alonso et al., 1996; Ohzawa et al., 1996).”

“To estimate the predicted feature selectivity from the ARF, the ARF was fitted and parameterized with a two-dimensional Gabor function using the Levenberg–Marquardt algorithm 37 .”

“Some previous studies have compared the tuning of spatial receptive fields with that derived from sinusoidal gratings by fitting Gabor functions to the RF structure (Jones and Palmer, 1987a; Ringach, 2002).”

“Daugman et al.[20, 21] describe the response of stimuli in the CRF of simple cells which uses two-dimensional (2D) Gabor filters.”

“Early approaches consisting of hand-designed Gabor filters were successful in predicting V1 simple cell [46] and complex cell [47] responses to relatively simple stimuli.”

“We chose the parameters to match the shape, orientation, and spatial frequency selectivity of typical simple cells in monkey or cat V1 (DeValois et al., 1982, 1985; Foster et al., 1985; Jones and Palmer, 1987).”

“The linear filters are similar to Gabor functions (Field and Tolhurst Figure 1 shows the results when the letter R was used as 1986; Jones and Palmer 1987) except that, for reasons of computa-the training image.”

“for super-resolved LR images, first using the SVD-based SR algorithm [36], then using eigenfaces, the local binary pattern (LBP) [44], [45] feature, and the Gabor [46], [47] for face recognition.”

“The CRF can be well modeled with a Gaussian envelope (Jones and Palmer 1987).”

“These filters are based both on 2-D Gabor filters [26], which simulate the behavior of the simple cells of receptive fields (cells which respond to a line or edge of a certain orientation—directional cells) [27], and on the principle of matched filtering which determines that, in order to detect the presence of a know…”

“…cell receptive field is nearly perfectly described as a Gabor filter – which efficiently balances representation of both space and spatial frequency (Jones & Palmer, 1987); and the ‘efficient coding hypothesis’ applied to the statistics of natural images predicts oriented receptive fields…”

“Gabor functions have been shown to be solutions of an optimization problem that is minimizing simultaneously uncertainty in both position and spatial frequency [23] and to fit well with physiological data recorded from cat striate cortex [24].”

“In choosing these lengths, I have relied on the quantitative data of Jones and Palmer (1987a).”

“First, it is known that the spatial envelope of visual cortical RFs can be well characterized by 2D Gaussian functions (Jones and Palmer, 1987).”

“The receptive field profile (1) has the same form as the Gabor functions commonly used to model orientation selective cortical neurons [28], [ 29 ], except that the modulating function is not Gaussian.”

“According to the psychophysical and physiological experimental findings, the profiles of the receptive fields of the simple cells resided in the primary visual cortex of the mammal closely resemble the shapes of the frequency response of the Gabor filter [27], [28].”

“have been frequently used for modelling spatial receptive fields (Jones and Palmer 1987a,b; Ringach 2002) motivated by their property of minimizing the uncertainty relation. This motivation can, however, be questioned on both theoretical and empirical grounds. Stork and Wilson (1990) argue that (i) only complex-valued…”

“The filter is biologically motivated—it is a good model of observed receptive fields of simple cells in cat striate cortex ( Jones & Palmer, 1987 ).”

“In the V1, each eye's RF (simple cell) can be modeled using Gabor filter expressed as [56] G L ,R ( x, y; f, θ) = f 2 πγ η exp − f 2 γ 2 x 2 + f 2 η 2 y 2 + j 2π f x x = x cos θ + y sin θ y = −x sin θ + y cos θ (1) Here, f and θ are the RF's frequency and orientation, r and η and its bandwidth, and…”

“In a series of interesting studies, Daugman (1980, 1985), Marcelja (1980), and Jones and Palmer (1987) advanced the hypothesis that the receptive fields of the simple cells in the mammalian visual cortex are describable by Gabor-type functions.”

“[17] J. P. Jones and L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,”J. Neurophysiol., vol. 58, no. 6, pp. 1233–1258, Dec. 1987.”

“Our distribution of subregion aspect ratios is consistent with other extracellular mea- surements (Jones & Palmer, 1987a) but has a larger mean (4.3vs. 1.7) than aspect ratios measured intracellularly (Pei et al., 1994).”

“Visual neurophysiologists have used Gabor and Gamma functions as quantitative descriptors of visual STRFs (Cai et al. 1997; DeAngelis et al. 1993a, 1999; Jones and Palmer 1987a,b).”

“The choice of Gabor filter responses is biologically motivated since they model the response of human visual cortical cells [ 3 ].”

“These observations are predicted by thalamocortical models (Hubel & Wiesel, 1962; Palmer & Davis, 1981; Ferster, 1986, 1988; Jones & Palmer, 1987a,b; Chung & Ferster, 1998; Troyer et al. 1998).”

“Reverse correlation (de Boer and Kuyper 1968; Jones and Palmer 1987; Ringach and Shapley 2004) is an electrophysiological technique in which a randomly generated binary”

“Early tests of this notion showed that such functions did indeed provide an excellent fit to the receptive fields of cortical neurons (Webster & DeValois 1985; Field & Tolhurst 1986; Jones & Palmer 1987).”

“Such filters remove most of the variability in images due to variation in lighting and contrast, and closely model the response properties of visual cortical cells (Pollen and Ronner, 1981; Jones and Palmer, 1987; DeValois and DeValois, 1988; Daugman, 1988).”

“To make a comparison with other local descriptors, we implement two frequently used descriptors: Gabor feature [28] and SIFT feature [24].”

“The CRF was localized precisely by reverse correlation of responses to a dynamic sparse noise stimulus: black and white squares or bars positioned randomly on a gray background and randomly repositioned at 5–10 Hz (Jones and Palmer, 1987a; DeAngelis et al., 1993; Vinje and Gallant, 2002).”

“In addition, as they are shown to provide a good model of cortical simple cell receptive fields [Jones and Palmer 1987], Gabor filter banks are widely used in biologically motivated representations [Huang et al.”

“Area 18 was chosen for its higher from the neuron's measured receptive field profile (Field proportion of envelope-responsive neurons (Zhou and Baker and Tolhurst 1986; Jones and Palmer 1987; Kulikowski et 1996).”

“This is consistent with at least one study that showed parametrically increasing responses in FFA to scenes with increasingly nearby objects (Park et al., 2015).”

“However, the receptive fields of most simple cells are elongated along, rather than perpendicular to, the preferred orientatio”

“In this section, we provide details of each of the steps.”

“Gabor filters are widely used as texture descriptors, since they are shown to exhibit properties of low-level processing in human eyes [17].”

“That is, the cells in visual cortex are like edge detectors and spatial-frequency filters which respond to lines and spatiotemporal patterns modelled using the Gabor filter (Daugman 1985, Jones and Palmer 1987).”

“Linear classifiers were then used to assess the goodness of these populations in supporting positionand clutter invariant recognition.”

“Two-dimension (2D) Gabor filters, which resemble a human visual system, have been prevalently used in image texture extraction [44].”

“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].”

“Many other studies have compared grating responses to impulse responses (DeAngelis et al., 1993b; Shapley et al., 1991; Tadmor and Tolhurst, 1989; Jones and Palmer, 1987a; Jones and Palmer, 1987b; Jones et al., 1987; Field and Tolhurst, 1986; Dean and Tolhurst, 1983; Kulikowski and Bishop, 1981b;…”

“The 2D Gabor wavelets, whose kernels provide a useful and reasonably accurate description of most spatial aspects of simple receptive fields, exhibit desirable characteristics of spatial locality and orientation selectivity [5].”

“The first stage of processing extracts object edges using 2D Gabor filters (Kulikowski, Marcelja, & Bishop, 1982), which approximate the receptive fields of simple cells in the primary visual cortex (Jones & Palmer, 1987; Marcelja, 1980 ).”

“Classical studies focused on stimuli incident on the cell’s receptive field, and simple cells were modeled as cascades of a linear filter and a rectifying nonlinearity (Movshon, Thompson, & Tolhurst, 1978; Jones & Palmer, 1987 ).”