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image-processingfilteringfrequency-domain

Apply parabolic filter in frequency domain

What would be the effect on initial image of applying this filter: enter image description here

in the frequency domain?

How can I determine the effect without using computer (on paper)?

This filter (H) is already in frequency domain.

Solution

  • You can try to see what you get for different values.

    First thing you can notice is because there is a 1 in the filter function the filter only amplify and don't waken the frequency.

    Second if we look at the two other terms: We amplify each spatial frequency as a function of the maximum frequency in each direction. Therefore for small frequencies the amplification will be minimal because (smallFreq/largeFreq) < 1 and the squaring this term will only make this value even smaller.

    For the large frequencies the amplification will be bigger. For uMax and vMax the amplification can be by a factor of 3 times the original value.

    If you want to know what will be the effect on the original image with out going back to the spatial domain you can say that areas with high frequencies (edges in the image) will have a very high value and areas with low frequencies( areas with a more or less a constant value) will stay the same.

    In conclusion it looks like your filter is a sharpening filter.