I specified the cut-off frequency in pixels to apply a high pass filter. "Pixels" is not a unit of frequency for sure, but a spatial position in the frequency domain representation of the image. This is typically done when performing frequency domain filtering, where an image is transformed into the frequency domain using a Fourier transform, filtered, and then transformed back into the spatial domain. In this context, the "frequency" of an image is a measure of how rapidly the pixel intensities are changing. Low frequencies correspond to slow changes in pixel intensity (e.g., large objects or smooth gradients), and high frequencies correspond to rapid changes (e.g., fine details or noise). Therefore, a high pass filter will allow these rapid changes, effectively enhancing the detail or noise in an image.
Accordingly, when I specified the cut-off frequency in terms of the number of pixels from the center of the frequency domain, I am essentially setting a radius around the center of the frequency domain image. All frequencies within this radius (low frequencies) are attenuated, and all frequencies outside this radius (high frequencies) are allowed to pass.
To sum up, this radial distance from the center to the cut-off frequency is not a frequency unit but a spatial position in the frequency domain representation. This is because the output of a Fourier transform while representing frequencies, is in the spatial domain. The center represents zero frequency, and frequencies increase as we move away from the center.
Do you think this concept is correct? Is there a procedure to interpret this radius in pixels to cycles per pixel? If the image is rectangular do I need 2 cut-off frequencies?
Many thank.