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I have an image and have been able to quantify its power across spatial frequencies, using Python. What I am interested in doing is creating some measure of how much of the image's information is low, medium and high SF.

I figured a good way to do this would be to take the average power within three bins of frequencies. This leads to two questions:

  1. Is that actually a good way to do it?
  2. Are there agreed upon ranges of "low", "medium" and "high" spatial frequency?

Thanks!

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  • $\begingroup$ Can I please ask if there was any resolution to this question? $\endgroup$ – A_A Aug 7 '16 at 13:02
  • $\begingroup$ Your question has beeen answered. Do not hesitate to vote for the useful ones and accept the most suitable $\endgroup$ – Laurent Duval Feb 9 '17 at 17:28
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The short answer is yes(1), no(2).

The quantification of the power spectrum is performed via the Fourier Transform over an image. An image is a matrix that describes the distribution of reflectance (or radiation more generally) across the field of view of the camera. It therefore has only a remote "relationship" with what is actually depicted in the image (the physical scene). Image resolution and spatial resolution are two different things. You can use a 50MP camera at the end of a telescope or at the end of a microscope. Both images will have the same image resolution but they will be "looking at" different spatial resolutions (actual space being sampled).

In other words, small objects correspond to high frequencies and large objects correspond to low frequencies but what is large and small depends on the context of the image (and the characteristics of the imaging equipment to an extent). Consequently, what is "high", "medium" and "low" spatial frequency can only be expressed in relative terms and either with a lot of assumptions or constraints.

The approach of dividing the available bandwidth into three bands and estimating the average power in each is, of course, reasonable.

An improvement would be to take a set of representative images, average their spectra and look at the actual bandwidth they occupy and its shape with a reference to the actual objects they represent to then decide at a different possible assignment between the low, med, high characterisations. But this implies specific scenes with a specific field of view, orientation, resolution and any other factor that affects the recorded spatial frequencies.

In case it is of any additional help, there is a concept in image histograms called "Adaptive Binning" where, the width of a given histogram bin is not fixed. The width is decided after an optimisation process over a criterion and it is image specific. For example, one criterion could be that each bin should represent at least N pixels. Although originally not defined over spectra, this adaptive concept might be useful here as well but applied over FFT bins. For more information please see this link.

Hope this helps.

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Not really, it depends a lot on the medium: microscope, naked eye, or with enhancement techniques... But if you decide to do so, remember to treat horizontal and vertical frequencies differently: the human (and terrestrial mammals) has a different eye sensitivity in the horizontal and vertical directions, as illustrated by the non-symmetric behavior of the JPEG baseline quantization matrix.

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