DHT parabolic mask "checkerboard" effect

Posted by ericbarnhill on
URL: http://imagej.273.s1.nabble.com/Changing-fonts-in-macros-for-the-Series-Labeler-tp5000755p5000788.html

Hi all,

I'm wondering if anyone can give me insight into an effect I am  
getting in attempting to implement an algorithm.

The algorithm denotes a forward Laplacian operator as, dropping some  
constants,

FFT^-1[(p^2+q^2)FFT(f(x,y))]

and a corresponding inverse Laplacian operator as

FFT^-1[FFT(f(x,y)) / (p^2 + q^2)]

in short, forward and inverse Laplacians are obtained by multiplying  
and dividing the FFT by a parabolic mask.

x and y are row and column coordinates, p and q are fourier space  
coordinates with origin in the middle of the image.

I was quite interested in this algo because it's not too hard to get  
the Laplacian, but the inverse Laplacian? Hard.

However, the inverse is not quite working for me. I get a  
"checkerboarding" effect where pixels alternate positive-negative. For  
example, -55 might be right next to +55. If I take the Math.(abs) of  
the inverse it looks like it might be about right, though if so the  
algorithm doesn't work so great -- too much high pass on the way in  
and too much low pass on the way back. I can attach an image if that  
helps clarify anything.

I am wondering, is the checkerboarding a result of the nature of the  
DHT? Might I have more luck using some other kind of DFT, or a  
discrete cosine transform?

Thanks for any insights,
Eric

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