While pitching his beautiful Alien horror show to 20th Century Fox, director Ridley Scott scribbled up a collection of pre-production storyboards (known to the die-hard fans as Ridleygrams). These illustrations impressed the execs so much they would not only approve the movie but double the budget from $4.5 million to a whopping $8.5 million. Check out how the director originally envisioned his infinitely more naked cryo introduction. Warning slightly NSFW illustrations.
According to the Weyland-Yutani Archives the original cryo awakening moment was supposed to be much longer, and a lot more naked. It would start with the close up of Kane (John Hurt's) nostril. Kane's cryo tube pops open and he gets up and starts making coffee for the crew. One by one each member of the crew gets up and stumbles in for coffee. Alas the studio deemed the naked revival of the crew was too "pornographic" so the cast was given shorts. The actual filmed version does show Kane as the first to wake up from the joint slumber, but very little time is spent on the actual awakening.
And here's another take on that same sequence taken from the actual production boards, also from the Weyland-Yutani Archives. Feels like they were ready to run with this idea right up until actual filming.
As you can see the shot was filmed, but was never used. Ah well, we still think the final product is perfect, but it's cool to see it in the process.