effect of high pass filtering and low pass filtering on background color Consider we have an image like this:

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

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

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.
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.