The Corner Pin effect in Adobe After Effects
After ages trying to find a decent video filter in Premiere that would distort a clip in the same way as Photoshop's Distort transform, I decided to use the right tool for the job.
After Effects is the tool needed to do things like this, thanks to its Corner Pin effect.. You could copy the Corner Pin plugin from your After Effects installation to Premiere and use it directly. This isn't recommended as Premiere filters have fiddly settings editors.
This article describes using the plugin in its native environment and achieving the cool results seen above.