Turning a circle into a wrapped ring shape (not masking!)

[srd1981]

I need to turn a simple letterbox-shaped image into a oval ring-shaped loop (but with 2 straight sides), and I can't figure out how to do it! Can anyone help please?

Here's the original image:

And here's what it needs to be:

Obviously they're different darknesses (due to an overlay placed on the ring-shaped version), and please ignore the redaction black boxes! The image repeats once (blended together) but I just can't figure out how to make it fit this kind of shape. A circular ring - fine - rectangle > circle polar co-ordinates - but this shape where the image is straight on the two long sides is beyond me! Any ideas would be really, really gratefully received! I'm trying to do this in Photoshop 2022 on MacOS, by the way...

Thanks!

[c.pfaffenbichler]

I think Puppet Warp or Illustrator’s Envelope Distort might provide options for this. 

Another option might be splitting up the panorama and threat the two curves as two halves for Polar Coordinates, but that seems pretty convoluted. 

[Semaphoric]

After making the ring via Polar Coordinates, set a horizontal guide on the center of the ring. Use the Single Row Marquee tool snapped to the guide, and Layer > New > Layer Via Cut. Select one of the (now separate) halves of the ring, drag it away from the other, and Layer > New > Layer Via Cut. Free Transform the Single Row layer to fit the space in between.

[Semaphoric]

One thing about the method I posted earlier is the sharp boundary between the stretched and round portions. Plus, the stretched portions look, well, stretched. If you wanted the image to "flow" around the straight sides, it would likely require planning how to cut it up properly, to modify and reassemble, as c.pfaffenbichler said.

When I first saw your Example pic, I thought it looked like the sort of thing Illustrator could do in an instant with its Art Brushes. Adobe had "Raster Art Brushes", if you will, in Adobe Sketch, but Sketch won't work anymore. As a mobile app, it relied on a touch interface; you would trace with your finger, and the brush graphic would fill the stroke. I still have several of these brushes in my Creative Cloud library they are orphans.

I think these would be great in Photoshop for stroking Paths, but they would probably be awkward to use with the Brush and a pointing device (mouse/tablet)