halftoning image processing penplotter Uncategorized

More Fourier Noise Contours

Previously, I used single-frequency Fourier noise to do some halftoning. This time, I’ll use broad-frequency noise.

I’ll filter 2D white noise with a gaussian with standard deviation \sigma. This reduces the high-frequency content. Let’s call the filtered noise h, and the gradient-scaled versionr. Skipping all the tedious probability work, the pdf of the gradient-scaled noise is

f_{r} = \frac{\sigma^2}{\left(2 \sigma^2+x^2 \right)^{3/2}} . .

So the curve length per unit area is f_r(x=0)=1/(\sigma 2 \sqrt{2}) \approx 0.3536/\sigma.

How’s this look in comparison to the other style?

Left: 50% darkness. Middle: Mono-frequency. Right: broad-spectrum. Same level of darkness in all.

The broad-spectrum noise is patchier, but kinda feels more ‘natural’ due to its unevenness. How about using it for halftoning?

Original, mono-frequency, broad-spectrum.

They patchiness isn’t helpful. It works, but the single frequency method looks better, I think.

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