https://sculpturetech.art.blog/2025/12/21/that-mona-lisa-smile/ The "Mona Lisa smile" has intrigued at lovers for centuries. She seems almost alive. This article explains how it is done technically, and dissects the portrait using Fourier analysis to show that the artist actually painted two different versions in distinct frequency bands. It explains how the eye switches between seeing two different facial expressions, producing that eerie feeling that she's alive.
I enjoyed the read, just added your blog to my rss reader. Keep posting!
Re: this specific post, I have to imagine every pro photo retoucher has practical experience with this — I wonder what % know the math behind it. You can definitely get a frequency separation in photoshop with some Apply Image trickery.
Slight tangent: I was playing around with Fourier transforms just the other day. I want to figure how the minimal set of brushes that will let me render the biggest variety of textures in Procreate. I’m at the point where I feel pretty confident with a big soft brush, roughing out the low frequency components, but I’m much less confident about detailed rendering.
I didn’t make a ton of headway because I got sidetracked by Gabor filters — they make for good brush tips! — but I feel like there’s potential. I assume that I’ll be able to slice and dice a bunch of images, compare their Fourier transforms, and find clusters of similar texture. Maybe sea foam and stucco have the same type of noise, that sort of thing.
If I get anywhere with it, I’ll be sure to send you a link. I want more tech/art blogs in the world.
Hey, my first and only reader so far! (I always fall down with actually trying to get this stuff out there.) I'm coming at it from an odd place as both an artist and a person with a long career in computer science, but little practical knowledge of workaday tools for image manipulation. You sound like you are skilled in the craft. It seems like it would be pretty easy to take two pictures of the same face making two different facial expressions, and use the blurring and sharpening features, to create different versions and then stack them on top of each other. I was thinking about just asking Claude to write a slightly different program to do it, but now that you mention it, I bet it could be done with Gimp or Photoshop, right?
I think Claude’s the better way to go for this one, the Photoshop method would be fiddly and require a whole bunch of menus… plus I don’t know off the top of my head how the compositing would work. The way that retouchers tackle it, there’s the low pass and high pass layers, and the “linear light” blending mode sums them up. But the registration needs to be perfect, otherwise you’ll get weird artifacting, so with two unrelated images, it might be tricky.