Topic
Spatial frequency
About: Spatial frequency is a research topic. Over the lifetime, 7426 publications have been published within this topic receiving 220996 citations.
Papers published on a yearly basis
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Papers
TL;DR: Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial-2D-spectral information resolution.
Abstract: Two-dimensional spatial linear filters are constrained by general uncertainty relations that limit their attainable information resolution for orientation, spatial frequency, and two-dimensional (2D) spatial position. The theoretical lower limit for the joint entropy, or uncertainty, of these variables is achieved by an optimal 2D filter family whose spatial weighting functions are generated by exponentiated bivariate second-order polynomials with complex coefficients, the elliptic generalization of the one-dimensional elementary functions proposed in Gabor’s famous theory of communication [ J. Inst. Electr. Eng.93, 429 ( 1946)]. The set includes filters with various orientation bandwidths, spatial-frequency bandwidths, and spatial dimensions, favoring the extraction of various kinds of information from an image. Each such filter occupies an irreducible quantal volume (corresponding to an independent datum) in a four-dimensional information hyperspace whose axes are interpretable as 2D visual space, orientation, and spatial frequency, and thus such a filter set could subserve an optimally efficient sampling of these variables. Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial–2D-spectral information resolution. The variety of their receptive-field dimensions and orientation and spatial-frequency bandwidths, and the correlations among these, reveal several underlying constraints, particularly in width/length aspect ratio and principal axis organization, suggesting a polar division of labor in occupying the quantal volumes of information hyperspace. Such an ensemble of 2D neural receptive fields in visual cortex could locally embed coarse polar mappings of the orientation–frequency plane piecewise within the global retinotopic mapping of visual space, thus efficiently representing 2D spatial visual information by localized 2D spectral signatures.
3,593 citations
TL;DR: The contrast thresholds of a variety of grating patterns have been measured over a wide range of spatial frequencies and the results show clear patterns of uniformity in the response to grating noise.
Abstract: 1. The contrast thresholds of a variety of grating patterns have been measured over a wide range of spatial frequencies.2. Contrast thresholds for the detection of gratings whose luminance profiles are sine, square, rectangular or saw-tooth waves can be simply related using Fourier theory.3. Over a wide range of spatial frequencies the contrast threshold of a grating is determined only by the amplitude of the fundamental Fourier component of its wave form.4. Gratings of complex wave form cannot be distinguished from sine-wave gratings until their contrast has been raised to a level at which the higher harmonic components reach their independent threshold.5. These findings can be explained by the existence within the nervous system of linearly operating independent mechanisms selectively sensitive to limited ranges of spatial frequencies.
3,285 citations
TL;DR: Spatial summation within cat retinal receptive fields was studied by recording from optic‐tract fibres the responses of ganglion cells to grating patterns whose luminance perpendicular to the bars varied sinusoidally about the mean level.
Abstract: 1. Spatial summation within cat retinal receptive fields was studied by recording from optic-tract fibres the responses of ganglion cells to grating patterns whose luminance perpendicular to the bars varied sinusoidally about the mean level.
2. Summation over the receptive fields of some cells (X-cells) was found to be approximately linear, while for other cells (Y-cells) summation was very non-linear.
3. The mean discharge frequency of Y-cells (unlike that of X-cells) was greatly increased when grating patterns drifted across their receptive fields.
4. In twenty-one X-cells the relation between the contrast and spatial frequency of drifting sinusoidal gratings which evoked the same small response was measured. In every case it was found that the reciprocal of this relation, the contrast sensitivity function, could be satisfactorily described by the difference of two Gaussian functions.
5. This finding supports the hypothesis that the sensitivities of the antagonistic centre and surround summating regions of ganglion cell receptive fields fall off as Gaussian functions of the distance from the field centre.
6. The way in which the sensitivity of an X-cell for a contrast-edge pattern varied with the distance of the edge from the receptive field centre was determined and found to be consistent with the cell's measured contrast sensitivity function.
7. Reducing the retinal illumination produced changes in the contrast sensitivity function of an X-cell which suggested that the diameters of the summating regions of the receptive field increased while the surround region became relatively ineffective.
2,624 citations
TL;DR: A new computer-based technique for automatic 3-D shape measurement is proposed and verified by experiments that has a much higher sensitivity than the conventional moire technique and is capable of fully automatic distinction between a depression and an elevation on the object surface.
Abstract: A new computer-based technique for automatic 3-D shape measurement is proposed and verified by experiments. In contrast to the moire contouring technique, a grating pattern projected onto the object surface is Fourier-transformed and processed in its spatial frequency domain as well as in its space-signal domain. This technique has a much higher sensitivity than the conventional moire technique and is capable of fully automatic distinction between a depression and an elevation on the object surface. There is no requirement for assigning fringe orders and interpolating data in the regions between contour fringes. The technique is free from errors caused by spurious moire fringes generated by the higher harmonic components of the grating pattern.
2,060 citations
TL;DR: In this paper, it was found that an occipital evoked potential can be elicited in the human by moving a grating pattern without changing the mean light flux entering the eye.
Abstract: 1. It was found that an occipital evoked potential can be elicited in the human by moving a grating pattern without changing the mean light flux entering the eye. Prolonged viewing of a high contrast grating reduces the amplitude of the potential evoked by a low contrast grating.
2. This adaptation to a grating was studied psychophysically by determining the contrast threshold before and after adaptation. There is a temporary fivefold rise in contrast threshold after exposure to a high contrast grating of the same orientation and spatial frequency.
3. By determining the rise of threshold over a range of spatial frequency for a number of adapting frequencies it was found that the threshold elevation is limited to a spectrum of frequencies with a bandwidth of just over an octave at half amplitude, centred on the adapting frequency.
4. The amplitude of the effect and its bandwidth are very similar for adapting spatial frequencies between 3 c/deg. and 14 c/deg. At higher frequencies the bandwidth is slightly narrower. For lower adapting frequencies the peak of the effect stays at 3 c/deg.
5. These and other findings suggest that the human visual system may possess neurones selectively sensitive to spatial frequency and size. The orientational selectivity and the interocular transfer of the adaptation effect implicate the visual cortex as the site of these neurones.
6. This neural system may play an essential preliminary role in the recognition of complex images and generalization for magnification.
2,035 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 47 |
| 2024 | 65 |
| 2023 | 114 |
| 2022 | 183 |
| 2021 | 151 |