Cropping for encoding

Theory

The image on the DVD has width D_w and height D_h. The movie itself occupies a width of M_w and a height of M_h. When scaled for display, the image from the DVD is D′_w wide and D′_h high and the movie itself occupies M′_w wide and M′_h high. The display aspect ratio is D′_a. These values are linked by:

• (1) M_w ⁄ D_w = M′_w ⁄ D′_w
• (2) M_h ⁄ D_h = M′_h ⁄ D′_h
• (3) D′_a = D′_w ⁄ D′_h

From this you easily get:

• M′_h = M′_w × D_w × M_h ⁄ (D′_a × D_h × M_w)
• M′_w = D′_a × M′_h × D_h × M_w ⁄ (D_w × M_h)

Using MPlayer with this

The values here are for -vop scale=M′_w:M′_h,crop=M_w:M_h.

You may find this article (also available here) more easy to understand.