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# What Is Fourier Image Processing?

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• Written By: Andrew Kirmayer
• Edited By: Shereen Skola
2003-2018
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Fourier image processing typically breaks down a picture by representing each component as if it were part of a frequency. Points on the image are generally identified by their column and row placement, while the mathematical processing is typically performed based on a graphical frequency wave. The physical locations of image parts are usually the input. For the output, image processing algorithms called Fourier Transforms are often used by computers for image analysis, filtering, compression, and reconstruction. These operations in Fourier image processing are typically performed by using a series of mathematical formulas.

Vertical, or up and down, and horizontal positions going across, are generally accounted for numerically. Image processing algorithms can be used to transform the vertical columns and horizontal rows into equivalent representations of each section of the picture. Some parts of an image are represented at low frequencies, while others correspond to high-frequency patterns; a different image of a microscopic circuit, for example, can be formulated to show the magnitude, phase, or other aspect of the frequencies. Magnitude in Fourier image processing generally defines how much of a certain frequency there is, while the location of each of type can be shown by the phase.

Whether an image is clear or blurry can affect the resulting representation after Fourier image processing. Edges in an image often affect the patterns as well, while shapes such as letters sometimes display characteristic patterns with image filtering. An image with many objects of the same shape and size can form a symmetrical pattern, while less symmetrical objects tend to create a less defined structure in Fourier image processing.

Techniques that are related to this kind of image processing technology include optical diffraction. It is a common Fourier image processing technique, and is often the beginning of the analysis and processing of images. Optical diffraction has sometimes been used to analyze structural information in biological samples, for example. The process typically involves the use of a laser and an instrument called an optical diffractometer in a scientific laboratory. Related image processing applications can include visual inspection of photographs from microscopes, crystal analysis, and three-dimensional reconstruction.

Optical filtering is another form of Fourier image processing, typically performed on pictures with elements that can be divided by straight lines to produce identical components. Disturbances, called noise, can be removed from images to make microscope images clearer. Fourier image processing is also often applied to moving images, at up to 30 frames per second; the time it takes to complete such processing typically depends on the speed of the computer.