As far as I can see... They get their values later on in the sub, $infile and $outfile from the values passed to the sub, $image becomes the new image created from $infile, $x and $y it's dimensions, $width and $height the new dimensions, and $thumb the new image. Guess $error is a leftover from the ImageMagick version?

As for thumbnail_dimensions... $x and $y are passed to the sub, $ratio is their quotient, and $width and $height are the new dimensions. The mys just give them an undef value.

Hope this helps. Sorry if I misunderstood you.