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Consider we have an image like this:

enter image description here

After applying a Low Pass Filter (say Butterworth), the result is :

enter image description here

And after applying a High Pass Filter (Butterworth), the result is:

enter image description here

The text book (Gonzalez) explains everything clearly. But I still cannot catch the point why the background in LPF is white(gray) and in HPF is black. according to the book, it is because of convolution that averaging a neighbor pixel to calculate the center pixel. I know how convolution works, sliding a small kernel, but why the result from LP filtering has different background in comparison with HP filtering?

I think for HPF, it is because of High Pass Filtering in frequency domain is analogous to differentiation in the spatial domain? so all constants become zero (black)? what about Low pass filtering?

All pictures are from Gonzalez's Digital Image Processing,3rd Edtion,2008.

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It's very simple. White = 255, Black = 0. After high pass filtering, the pixels that don't change relative to their neighbors (low spatial frequency) get filtered out--meaning the pixel value is reduced. Thus, any solid color areas will be replaced by blackness, and only points of pixel value transition will be white.

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  • $\begingroup$ yes, it its true. in addition, the derivative can explain it. if we take derivative from a constant (solid intensity), the result is zero (black). But what about low pass filtering? I know the HPF is derivative in Spatial domain. but, what about low pass filtering? $\endgroup$
    – David
    Commented Sep 4, 2015 at 0:29
  • $\begingroup$ LPF attenuates high spatial frequencies, which appears to us as blurring edges. $\endgroup$
    – CMDoolittle
    Commented Sep 4, 2015 at 4:43
  • $\begingroup$ I know that LPF attenuates high frequencies. My question is whether LPF has a effect on background similar to HPF. $\endgroup$
    – David
    Commented Sep 4, 2015 at 20:39
  • $\begingroup$ No. Look, there is no "background", really. There are only pixel values. If the pixel values are unchanging relative to their neighbors, LPF has a minimal effect. $\endgroup$
    – CMDoolittle
    Commented Sep 5, 2015 at 1:54
  • $\begingroup$ Pay attention that HPF Filter enforces the sum of pixels is zero. $\endgroup$
    – Royi
    Commented Nov 3, 2015 at 7:43

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