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Comment by danilor | Hacker News Reader

I have difficulty understanding what the transformed image is equivalent to. This makes it feel like the picture was taken at a difference distance and focal length, but[1] it would look different if that were the case because the perspective would be different. Does this have any "physical" interpretation that would make it easier for me to understand? Like, cropping an image is equivalent to changing the focal length; what would this be equivalent to? A type of rectilinear lens?

[1] With the exception maybe for a single plane in focus?

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> I have difficulty understanding what the transformed image is equivalent to.

As a non-photographer with zero knowledge about photography, the fixed image, with straight lines, feels much more natural to me.

I'd say it reminds me of 3D games like, say, 3D game simulators?

Are 3D games not reproducing lens deformation more or less correct from a "physics" point of view? I happen to be on vacation atm in an apartment on the beach on the ninth floor with a clear view: what I see is much closer to the "corrected" (not my word but TFA's author's one) version than to the other one.

The author is saying "wide angle lens" but means what people would conventionally call a "fish eye lens." Normally when someone says wide angle, it's still assumed to be a rectilinear image projection, same as what you get with 3D game rendering. And if you're talking about a curvy fisheye projection, you specify that.

The iPhone's ultrawide lens is a good example of a rectilinear projection with lots of example photos available.

It can produce weird feeling images with stuff at the edges looking stretched out, and parallel lines being at significant angles to each other, but it does not make straight lines curved like the effect that the author is removing.

Example ultrawide photo with straight lines from reddit https://www.reddit.com/r/iPhoneography/comments/ena7s5/bosto...

That is how the brain wants to see. When I got a new pair of glasses everything looked very curvy. After a week every line was straight again because the brain learned the new transformation

As an artist, this the transformed image is what I would draw using 1-point perspective. Basically making everything straight lines. It intuitively feels a lot more natural and fits into our mental model of how the human world is shaped (i.e. everything is a rectangle)

https://m.youtube.com/watch?v=qOojGBEsWQw

I’ve done some work on implementing this as a coder, not a mathematician. So, the following description is just how the process looks while you are implementing it :P

Take the original curved image and put it on a super stretchy rubber sheet. Pull all four corners out diagonally until the curves look straight. You have to pull really hard and the corners will be stretched out into thin spikes.

But, no one wants to see an image that’s 80% long, thin spikes with lots of empty space between them. So, go to the center and crop down to the biggest rectangle you can that doesn’t have empty space around the edges.

I would draw an analogy to map projections.

Or, take an image of a soccer ball (the kind with pentagons and hexagons), you can see all of one hemisphere. But it’s a “fisheye” view. If you take the half soccer ball and cut up the shapes and rearrange them on a flat surface, you are adjusting the projection

It sounds like you know this already, but as any portrait photographer would note, changing the focal length is not equivalent to cropping. It's roughly equivalent, at best.

ie, Telephoto lenses bring a different perspective which includes distance compression. It's very apparent when photographing human faces.

Changing the focal length doesn't inherently change the perspective, and (resolution and lens aberations aside) is exactly equivalent to cropping.

What changing the focal length does do is (e.g.) make you stand further back, and that changes the perspective, causing distance compression, etc.

True. A change in focal length is exactly equivalent to moving the vanishing points further away/closer to the picture plane. See the vid at the bottom of this page:

https://rmit.instructure.com/courses/87565/pages/perspective...

Ahh, you're right. Thanks.

If you take a shot with a 35mm and take same shot with a 85mm and then crop the 35mm to the same fov as the 85m the image will look _identical_ (not withstanding lens characteristics etc) the compression you talk about is due to the _distance_ between the subject and then lens changing . You will get the same compression effect if you shoot with a 50mm from 30 feet away …

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