Image processing based on discrete fourier transform
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I applied DFT to an image, as a result of which I got a real and an imaginary part. I wanted to know what information does the real and imaginary part of the image signify?
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Walter Roberson
2020-10-30
If you used fft() then by default fft() applies down columns.
For any one column, the first result will be the sum of the inputs, which is also (by definition) the mean times the length of the column. An entry of 0 would correspond to a mean of 0 (which is not likely for images as images are nearly always represented as non-negative values.)
Each row after that corresponds to an increasing number of complete cycles over the length of the column. Row 2 corresponds to one cycle per column; row 3 corresponds to 2 cycles per column; row 4 corresponds to 3 cycles per column, and so on. This keeps going until the middle row of output, after which for real input data the order reverses, decreasing in number of cycles per column -- but for real input data the output will be the complex conjugate of what it was in the mirror position in the first half.
For say the 7th row, that would correspond to 6 cycles per column. The absolute value would be the magnitude of the sine wave, and the angle of the value would be the phase.
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