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Spatial frequency

 

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Spatial frequency


 
 

In mathematicsMathematics

Mathematics is the discipline that deals with concepts such as quantity, structure, space and change....
, physicsFacts About Physics

Physics , the most fundamental physical science, is concerned with the underlying principles of the natural world....
, and engineeringEngineering

Engineering is the application of scientific and mathematical principles to develop economical solutions to technical proble...
, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often the structure repeats per unit of distance. The SISi

Si, si, or SI may stand for:...
 unit of spatial frequency is cycles per secondSecond

The second is the name of a unit of time, and today refers to the International System of Units base unit of time....
. In image processingImage processing Overview

In the broadest sense, image processing is any form of information processing for which both the input and output are images...
 applications, the spatial frequency often is measured as lines per millimeter, which is 1000 times smaller than the SI unit.

In wave mechanics, the spatial frequency is related to the wavelength by

Likewise, the wave number k is related to spatial frequency and wavelength by

Visual perception

In the study of visual perceptionVisual perception

Visual perception is the end product of vision, consisting of the ability to detect light and interpret the consequences of ...
, sinusoidalSine wave

The sine wave or sinusoid is a function that occurs often in mathematics, signal processing, alternating-current power...
 gratingFacts About Grating

A grating is any regularly spaced collection of essentially identical, parallel, elongated elements....
s are frequently used to probe the capabilities of the visual system. In these stimuli, spatial frequency is expressed as the number of cycles per degreeDegree (angle)

A degree, usually symbolized ', is a measurement of plane angle, representing 1/360 of a full rotation....
 of visual angleVisual angle

The visual angle is the angle that a visual stimulus subtends at the eye....
.

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 configural information and fine detail. Low spatial frequencies, on the other hand, represent global information about the shape, such as general orientation and proportions.
In the general population of adults, the threshold for spatial frequency discrimination is about 7%. It is often poorer in dyslexic individuals .

See also

  • Fourier transformFourier transform

    The Fourier transform, named after Joseph Fourier, is a reversible integral transform of one function into another....
  • Fourier analysis