- If I have a rectangular chessboard (instead of square) then just need to make sure that the aspect ratio is preserved, whatever the actual L and W dimensions.
I believe that's correct.
- If I have to compensate for aspect ratio, then would elongate the side that has the larger DPI (so as to avoid losing detail.
To me DPI is only a concern when one is outputing to print, and I do all my image processing in image space. I would expect for perspective correction calculations, the largest edge of the quadrilateral I'm converting to a rectangle would have preserved the most information when going from real world to image. Since the image plane of your camera is probably very close to parallel to the plane of the page, I would probably begin by using the size of that side in pixels as the L dimension, and I'd stop there if the output quality was acceptable. 99 times out of 100, I expect it would be. If not, I would gradually reduce the L dimension (preserving the original L and W ratio) until the quality was acceptable.