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In some filters of image processing, I see the image converted from spatial domain to frequency domain. My question is: why we do that? What is different between image in spatial domain and image in frequency domain ?
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Frequency domain gives you control over the whole images, where you can enhance(eg edges) and suppress (eg smooth shadow) different characteristics of the image very easily. Frequency domain has a established suit of processes and tools that be borrowed directly from signal processing in other domains.
Time domain signal processing enables an engineer to separate extraneous signals in time from the desired signal, thereby identifying the contaminated signals. In general, using a frequency domain will simplify analysis mathematically for the system running it.
Frequency domain representations are particularly useful when analyzing linear systems. EMC and signal integrity engineers must be able to work with signals represented in both the time and frequency domains. Signal sources and interference are often defined in the time domain.
This is usually only done for performance reasons. Filtering in the spatial domain is convolution, which is O(N^2), whereas in the frequency domain convolution becomes multiplication, which is O(N). For small filters (small N) the cost of the FFT to/from the frequency domain is relatively large, and so filtering is performed directly, using convolution. However for larger filters (larger N), the balance tips in favour of filtering in the frequency domain, since the cost of the FFT becomes relatively small compared to the O(N^2) operation.
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