How do I fix the perspective while preserving the proportions

You can do a local repair with Perspective Warp, but it leaves the reflections wrong

This will work just fine as Gernot describes it. Correct the uprights with Distort, aided by guides or grid - then scale vertically to bring proportions back. Just stop when the tiles look square.

Yes, you lose some pixels in the final image, but you won't lose definition. You could go the other way, dragging the lower part outwards instead of the upper part inwards, but that involves upsampling which is usually best to avoid. Or you could compromise and do both.

Not to mention that that area you circled looks like it's not vertical to begin with, so trying to correct something that isn't plumb is going to be a real issue without messing up the rest of the photo.

In addition to what others have said, it's a give-and-take, nature-of-the-beast thing when it comes to images like this (or have the right lens like Semaphoric​ mentioned), i.e., correct the perspective and you'll more than likely need to crop. I like it as is as well.

I use Camera Raw's transform tool shift-T. Clicking on the last icon on the right allows you to draw line on the image to what you want vertical or horizontal.

CS6: Select All > Edit > Transform > Distort (not Perspective)

Move corners and adjust by appearance.

The correct scales sx, sz and the correct proportion sz:sx cannot be found automatically.

One would need gauges in the image: preferibly equal lengths Lx=Lz for the proportion and known

lengths Lx and Lz for accurate scales sx, sz.

Best regards --Gernot Hoffmann

I think it looks fine as is: shot with a wide-angle lens pointing slightly downwards. I would live with it, or accept the altered dimensions:

Or, you could invest in a tilt shift lens.

Hi please check this video hope it helps...Thanks.