In Liquid Resize, I selected the area of the picture that I DIDN'T want resized (Dan and his tripod), and let the program do the rest. As you can see, it created an almost perfect "scrunch job" of the image. Most of the image loss came from the path on the left, and from the trees. The large tree in the upper-right corner was scrunched a bit too much for my taste the first time, so I protected it too. The rest of the trees are mostly narrower, but you can't tell unless you're looking at the original.
In this image, I thought it'd be fun to try to take Dan out of the picture completely and see what happened. In LR, you can either choose to "protect" or "delete" an element of the picture. Protecting an area will cause the program to completely ignore the protected area when it's looking for elements to scrunch/stretch. Setting an area to "delete" will cause the area to be favored for deletion, so it'll scrunch into the deletion area as much as possible.
The result is pretty good, though you can definitely see some seams, and the big tree in the foreground has seen better days. Oh well; this isn't really what it's supposed to be used for.
Here's another fun shot. This is Kev, Dan, and Tim (and myself behind the camera) out golfing before Dan's wedding.
...and here's the square version. This one turned out really well. LR closed the gap between Kev and the other two, and brought in the left side. Remember that it's not cropping out ANYTHING; it's resizing the different elements so they all fit within the specified dimensions. The houses in the back do seem a little narrower, and of course the pond is a bit smaller, but you'd never notice that if you hadn't seen the original.
There is one minor issue though: Kev seems like he's a lot taller now, due to the change in perspective.
Hmm...why is Dan in every one of these pictures so far?
Anyway, this is Dan & Jenni after the wedding, when we were driving around on the bus through Stillwater. We stopped by an outdoor biker hangout and somebody let them pose for pictures on their bike.
Again, I had LR change it to be square. This one was tricky. I protected Dan, Jenni, and their motorcycle of course, and also Shelly on the right. I also protected the two motorcycles in the back, because they were too distorted the first time I tried this. I also had it delete the lady on the left. I may have protected the car in the back too; I don't remember.
As you can see, it brought the two bikes in the back (and Shelly) closer together. Some problems, which I could probably fix if I wasn't so lazy, are that the house in the back is kinda scrunched, as is the bike on the far left.
Now, let's play with a vertical picture, at 600x800. Here's a shot of some ducks on a frozen pond.
This time, rather than having the program scrunch the image down to a 600x600, I had it stretch it to 800x800. I didn't bother to have it protect any elements, and just decided to see what it would do.
Mostly, it just stretched the less-detailed area on the left. It also separated the ducks a little bit. Good solution.
This one is pretty funny, actually. I went back to the original image, and resized it down to 600x600. LR chose to shrink most of the background lake element, and as a result the ducks look gigantic. I definitely wouldn't have been chasing them with a stick that day if they were all 5 feet tall.
The horizon on the far right looks a little goofy too. It scrunched the skyline and treeline to make room for the branch.
Overall, I think this program/plugin is going to be a valuable tool in any photo manipulator's arsenal. Obviously it's not perfect for every situation, but it's very easy to use, and usually pulls off some impressive feats.
Here are a few more images I created. The first one is the original in each pair.