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Comment by woopsn | Hacker News Reader

In most photos with a recognizable subject, spectral energy will be concentrated around the origin (the upper left corner) as it is here

https://substackcdn.com/image/fetch/f_auto,q_auto:good,fl_pr...

The same is true for the DCT of the woman. Meanwhile, the subject of a photo is typically located towards the frame's center. This helps minimize interference between the space and frequency domain data in the composite, thus preserving kitty's expression when the transform is inverted

https://substackcdn.com/image/fetch/w_1456,c_limit,f_webp,q_...

(and vice versa for the woman)

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And this is only true of the DCT - 2D Fourier transforms of images usually concentrate the data near the center of the image.

its the same fundamental effect

It makes me think how the lens of the camera, is focusing the light/image at the center of the sensor, so it would make sense that data is also denser at the center, where the lens concentrated more light

So… I think you’re a bit confused about how lenses work and what they do (they don’t focus all the light into the middle, they focus light from one plane onto another one. They only focus light from the center of the frame onto the center of the image - that’s why it’s an image)

But… there is something interesting about what ‘focusing’ looks like in the frequency domain, and the difference between the frequency-space-transform of a sharply focused image and a blurred image - or of the same image focused at different focal planes - shows up as a predictable transformation in the frequency space; which means you can apply transformations in frequency space that cause focus changes in the image domain like a lens does.

your first paragraph is completely wrong. the lens concentrates collimated light parallel to its axis at its focal point, regardless of where it falls on the lens. (and, strictly speaking, only at a single wavelength.) collimated light coming from near-axial directions gets focused more or less to a point on more or less the focal plane. but light at a single point doesn't have a direction, being a wave. there is in fact a very profound connection between the action of a lens and the 2d fft; see my sibling comment for more details

your second paragraph is correct, and it is a special case of the convolution theorem; see https://en.wikipedia.org/wiki/Fourier_optics#The_2D_convolut...

I don't think the idea that (idealized, camera) lenses focus light from distinct points in one plane (or at infinity) onto distinct points in another plane is 'completely wrong', but I'm open to being educated on my error.

A lens focuses light parallel to its axis onto its focal point; it focuses parallel light coming in off-axis to other points on the focal plane.

Alternatively, and equivalently, it focuses divergent light coming from common points on planes closer than infinity, onto matching points on other planes behind its focal plane.

Lenses bring parallel rays of light (alternatively, light from infinitely far away) to the focal point. They don’t bring idealized points to points.

One consequence is you can’t use lenses to bring anything to a temperature higher than the temperature of the source light. For example you can’t use lenses + moonlight to light things on fire.

Here’s an HN thread going into the physics of it: https://news.ycombinator.com/item?id=18736700

What are you talking about?

yes, as it happens, the image on the focal plane of the camera resulting from light coming from a particular direction is in fact the 2d fourier transform of the spatial distribution of that light at the lens. this property has been used to build optical-computing military machine vision systems using spatial light modulators since the 01980s, because of some other useful properties of the fourier transform, that spatial shifts become phase shifts, so you can look for a target image everywhere in an image at once. as far as i know, these systems have never made it past the prototype stage

see https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transfo...

> is in fact the 2d fourier transform of the spatial distribution of that light at the lens. this property has been used to build optical-computing military machine vision systems

Amazing. Do you have any links/references about those systems and how they should work in theory?

yes, see the link above

that's sort of true and sort of false. here the origin is plotted in the upper-left-hand corner, and in the 2d fft images you're used to looking at, it's plotted in the center instead. but you can plot the dct that way too, so it's sort of false

it's sort of true in that if you plot the standard 2d fft in this coordinate system, the data will be concentrated not in one corner of the image but in all four of them. the dct really is unusual in putting all the low-frequency stuff at positive frequencies instead of equally at positive and negative frequencies

Considering the title of the article, this comment had me thinking of some supernatural. Took me way to long to realize what it was talking about...

Clarifying, the specter of a hidden animal will usually take the form of a diffuse sparkle or blur, typically hovering off to the person's side and somewhat above them, and as a result when carried through to the "other side" cannot possess what remains of the person in that domain (because they are returned to the origin in turn).

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