Detecting regular patterns using frequency domain self-filtering

Filtering is often used in image processing to smooth noise, and to enhance or detect features within an image. Images which have regular patterns in the spatial domain have peaks in the frequency domain corresponding to the spatial frequencies of the regular patterns. When processing such images, it is often desirable to keep such peaks, enhancing the pattern and removing noise or irregularities. This is effectively a bandpass filtering operation. The problem with such filtering is that it requires a priori knowledge of the contents of the image so that the filter can be 'tuned' to select the appropriate frequencies. Self-filtering overcomes this by multiplying the frequency domain image with its own magnitude. This gives a bandpass filter that is automatically tuned to the frequency content of the image. Applications included detecting and enhancing regular patterns; interpolating or extrapolating regular patterns; and smoothing or reducing noise.