Previsualization is a film making technique that uses 3D computer graphics to create rough versions of movie sequences - usually complex shots incorporating visual effects or stunts. This allows the film producers to see a rough version of the sequence before the costly full-scale production starts.
Cloverfield is mentioned in the Bios of Barry Howell and Nick Markel, and in the News section:
After being tapped by JJ Abrams’ production company to work on the super-secret “Cloverfield” trailer, (as seen in front of Transformers); The Third Floor delivered previs for the entire feature – coming soon (01-18-08?) to a theatre near you!The Third Floor's other works include: Fantastic Four: Rise of the Silver Surfer, Pirates of the Caribbean 3, Evan Almighty, Beowulf, Final Fantasy: The Spirits Within.
The Reel section has a six minute video of their work, including some very short scenes of the Cloverfield trailer.
UPDATE: The Third Floor has asked that I remove the YouTube video. However, you can still see the full six minute video on their site. The Cloverfield scenes are at 0:26, 1:39, and 5:36.
* Special thanks to Robbie for emailing about The Third Floor!