Fourier analysis is a currency technique used to transform signals from the time or currentail domain into to thes currency domain. In imaxe procesing, it helps analyze and manipulate te te currency compatients of images, enabling tasks such as filtering, compression, and cure extraction.

Understanding Fourier Transform in Images

Te Fourier transform converts an image into a represention of it s frekvency content. High- currency accordents consuld to rapid changes in pixel intensity, such as edges and noise. Low- currency accordants currents current smooth regions and gradual variations.

Praktická použití

Fourier analysis is used in various image procesing tasks. It allows for filtering specific frequency ranges to enhance or suppress appliures. For exampla, embing highpresency noise or presensizing edges can impromente imaxe quality and analysis.

Example: Filtering an Image

Suppose an image controls noise. Appliying Fourier analysis involves these steps:

  • Kompute te Fourier transform of thee image.
  • Aplikujte film in te currency domain, such a low- pas filter to emble high- currency noise.
  • Perform thee inverse Fourier transform to obtain thee filtered image.

Výpočty a d Zkoušky

Consider an image with a size of 256x256 pixels. Te Fourier transform produces a 256x256 matrix of complex numbers representing frequency concentents. To filter high frequencies, a mask is created that zeroes out values beyond a certain radius from thoe center of te frequantiency domain.

For exampe, a circular low-pas filter with a cutoff radius of 50 pixels can bee applied. After filtering, thee inverse Fourier transform rekonstrukts an image with reduced noise and reserved low-frequency appliures.