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frequencies of sine wave gratings. When all of the visual cortex neurons that are influenced by a specific scene respond together, the perception of the scene is created by the summation of the various sine-wave gratings. (This procedure, however, does not address the problem of the organization of the products of the summation into figures, grounds, and so on. It effectively recovers the original (pre-Fourier analysis) distribution of photon intensity and wavelengths across the retinal projection, but does not add information to this original distribution. So the functional value of such a hypothesized procedure is unclear. Some other objections to the "Fourier theory" are discussed by
Westheimer (2001) ). One is generally not aware of the individual spatial frequency components since all of the elements are essentially blended together into one smooth representation. However, computer-based filtering procedures can be used to deconstruct an image into its individual spatial frequency components. Research on spatial frequency detection by visual neurons complements and extends previous research using straight edges rather than refuting it.
50:
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firing rate of a particular neuron as having a special significance with respect to its role in the perception of a particular stimulus, given that the neural code is known to be linked to relative firing rates. For example, in color coding by the three cones in the human retina, there is no special significance to the cone that is firing most strongly – what matters is the relative rate of firing of all three simultaneously. Teller (1984) similarly noted that a strong firing rate in response to a particular stimulus should not be interpreted as indicating that the neuron is somehow specialized for that stimulus, since there is an unlimited equivalence class of stimuli capable of producing similar firing rates.)
410:
proposed that low spatial frequencies represent global information about the shape, such as general orientation and proportions. Rapid and specialised perception of faces is known to rely more on low spatial frequency information. In the general population of adults, the threshold for spatial frequency discrimination is about 7%. It is often poorer in dyslexic individuals.
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than they do to edges or bars. Most neurons in the primary visual cortex respond best when a sine-wave grating of a particular frequency is presented at a particular angle in a particular location in the visual field. (However, as noted by Teller (1984), it is probably not wise to treat the highest
929:
The k-space domain and the space domain form a
Fourier pair. Two pieces of information are found in each domain, the spatial information and the spatial frequency information. The spatial information, which is of great interest to all medical doctors, is seen as periodic functions in the k-space
405:
The theory (for which empirical support has yet to be developed) states that in each functional module of the visual cortex, Fourier analysis (or its piecewise form ) is performed on the receptive field and the neurons in each module are thought to respond selectively to various orientations and
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Further research shows that different spatial frequencies convey different information about the appearance of a stimulus. High spatial frequencies represent abrupt spatial changes in the image, such as edges, and generally correspond to featural information and fine detail. M. Bar (2004) has
440:
It is very common that the raw data in k-space shows features of periodic functions. The periodicity is not spatial frequency, but is temporal frequency. An MRI raw data matrix is composed of a series of phase-variable spin-echo signals. Each of the spin-echo signal is a
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domain and is seen as the image in the space domain. The spatial frequency information, which might be of interest to some MRI engineers, is not easily seen in the space domain but is readily seen as the data points in the k-space domain.
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Image and its spatial frequencies: Magnitude of frequency domain is logarithmically scaled, and zero frequency is in the center. Notable is the clustering of the content on the lower frequencies, a typical property of natural
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in the cat. In support of this theory is the experimental observation that the visual cortex neurons respond even more robustly to sine-wave gratings that are placed at specific angles in their
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operates on a code of spatial frequency, not on the code of straight edges and lines hypothesised by Hubel and Wiesel on the basis of early experiments on
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as a raw data storage space. The value of each data point in k-space is measured in the unit of 1/meter, i.e. the unit of spatial frequency.
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358:. Sine-wave gratings also differ from one another in amplitude (the magnitude of difference in intensity between light and dark stripes),
1226:
Vision: How Global
Perceptual Context Changes Local Contrast Processing (Ph.D. Dissertation 2003). Updated for Computer Vision Techniques
1344:
Awasthi B, Friedman J, Williams MA (2011). "Faster, stronger, lateralized: Low spatial frequency information supports face processing".
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but not as the "spatial frequency", since "spatial frequency" is reserved for the name of the periodicity seen in the real space r.
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519:{\displaystyle {\text{Spin-Echo}}={\frac {M_{\mathrm {0} }\sin \omega _{\mathrm {r} }t}{\omega _{\mathrm {r} }t}}}
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Any visual stimulus can be represented by plotting the intensity of the light along lines running through it.
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When spatial frequency is used as a variable in a mathematical function, the function is said to be in
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Glezer, V. D. (1995). Vision and mind: Modeling mental functions. Lawrence
Erlbaum Associates, Inc.
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1389:"Sequential spatial frequency discrimination is consistently impaired among adult dyslexics"
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1457:"Webvision: Part IX Psychophysics of Vision. 2 Visual Acuity, Contrast Sensitivity"
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is the basic resonance frequency of the spin. Due to the presence of the gradient
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584:{\displaystyle \omega _{\mathrm {r} }=\omega _{\mathrm {0} }+{\bar {\gamma }}rG}
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Now, the spin-echo signal is in the k-space. It becomes a periodic function of
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The spatial-frequency theory of vision is based on two physical principles:
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Characteristic of any structure that is periodic across a position in space
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applications, spatial frequency is often expressed in units of cycles per
1211:
905:{\displaystyle {\text{Spin-Echo}}={\frac {M_{\mathrm {0} }\sin rk}{rk}}}
335:
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per metre (rad/m), is related to ordinary wavenumber and wavelength by
104:
73:
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677:. The periodicity seen in the MRI raw data is just this frequency
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89:
979:"ISO 80000-3:2019 Quantities and units — Part 3: Space and time"
434:
1006:
849:, the spin-echo signal is expressed in an alternative form
350:, spatial frequency is expressed as the number of cycles per
55:
Spatial frequency representation of the Green Sea Shell image
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Any curve can be broken down into constituent sine waves by
374:
The spatial-frequency theory refers to the theory that the
706:, which is basically the temporal frequency in nature.
313:{\displaystyle k=2\pi \xi ={\frac {2\pi }{\lambda }}.}
144:. Ordinary wavenumber is defined as the reciprocal of
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are frequently used to probe the capabilities of the
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1057:"Complex receptive fields in primary visual cortex"
433:. Two dimensional k-space has been introduced into
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92:. The spatial frequency is a measure of how often
100:) of the structure repeat per unit of distance.
1301:Bar M (Aug 2004). "Visual objects in context".
983:International Organization for Standardization
1250:Westheimer, G. "The Fourier Theory of Vision"
1121:"Spatial frequency maps in cat visual cortex"
84:is a characteristic of any structure that is
8:
1455:Kalloniatis, Michael; Luu, Charles (2007).
1168:Teller, DY (1984). "Linking propositions".
1104:De Valois, R. L.; De Valois, K. K. (1988).
236:{\displaystyle \xi ={\frac {1}{\lambda }}.}
1440:"Tutorial: Spatial Frequency of an Image"
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737:{\displaystyle \omega _{\mathrm {0} }=0}
620:is the gyromagnetic ratio constant, and
1442:. Hakan Haberdar, University of Houston
970:
1358:10.1016/j.neuropsychologia.2011.08.027
1119:Issa NP, Trepel C, Stryker MP (2000).
766:{\displaystyle \omega _{\mathrm {r} }}
699:{\displaystyle \omega _{\mathrm {r} }}
642:{\displaystyle \omega _{\mathrm {0} }}
1387:Ben-Yehudah G, Ahissar M (May 2004).
1212:https://doi.org/10.4324/9780203773932
7:
1108:. New York: Oxford University Press.
842:{\displaystyle k={\bar {\gamma }}Gt}
423:-space in magnetic resonance imaging
1037:is also used to represent temporal
445:of time, which can be described by
1137:10.1523/JNEUROSCI.20-22-08504.2000
801:{\displaystyle {\bar {\gamma }}rG}
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613:{\displaystyle {\bar {\gamma }}}
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1055:Martinez LM, Alonso JM (2003).
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657:is encoded onto the frequency
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1:
1406:10.1016/j.visres.2003.12.001
1182:10.1016/0042-6989(84)90178-0
107:of spatial frequency is the
1260:Blake, R. and Sekuler, R.,
1125:The Journal of Neuroscience
167:and is commonly denoted by
1503:
653:, the spatial information
417:
1223:Barghout, Lauren (2014).
119:(c/m) is also common. In
1073:10.1177/1073858403252732
1005:SPIE Optipedia article:
414:Spatial frequency in MRI
370:Spatial-frequency theory
160:{\displaystyle \lambda }
131:per millimeter (LP/mm).
670:{\displaystyle \omega }
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96:(as determined by the
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709:In a rotating frame,
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41:Green Sea Shell image
1482:Mathematical physics
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1030:{\displaystyle \nu }
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344:contrast sensitivity
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200:{\displaystyle \nu }
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180:{\displaystyle \xi }
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1284:, 6th ed. 293–294.
1229:. Scholars' Press.
1007:"Spatial Frequency"
243:Angular wavenumber
88:across position in
18:Spatial frequencies
1303:Nat. Rev. Neurosci
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808:. Just by letting
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1280:Pinel, J. P. J.,
1270:978-0-072-88760-0
1236:978-3-639-70962-9
1176:(10): 1233–1246.
1131:(22): 8504–8514.
955:Fringe visibility
950:Visual perception
924:k-space frequency
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773:is simplified to
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329:visual perception
323:Visual perception
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256:{\displaystyle k}
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98:Fourier transform
82:spatial frequency
16:(Redirected from
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356:visual angle
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1017:The symbol
360:orientation
346:. In these
78:engineering
70:mathematics
1476:Categories
1393:Vision Res
1262:Perception
996:(11 pages)
989:2019-10-23
966:References
380:V1 neurons
342:, such as
333:sinusoidal
146:wavelength
141:wavenumber
129:line pairs
125:millimeter
1331:205499985
1039:frequency
1025:ν
945:Superlens
883:
858:Spin-Echo
828:¯
825:γ
787:¯
784:γ
753:ω
718:ω
686:ω
665:ω
629:ω
605:¯
602:γ
570:¯
567:γ
550:ω
535:ω
500:ω
483:ω
479:
454:Spin-Echo
303:λ
299:π
287:ξ
284:π
226:λ
215:ξ
195:ν
175:ξ
155:λ
1446:22 March
1423:12605281
1415:15031099
1374:10037045
1366:21939676
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