Classifying whether a chess board square contains a piece or not?
If it's a screenshot of a computer game, where each constituent has purely that box, that is by default any given box is white or black. then, any simple matrix operation like, variance of color in that box could be a feature in determining if there is a piece or not. 

If it's a hover cam image (Top view), then it's a different problem. you can simply do a kernel multiplication for edge detection, any empty box will have array of 0 as it's output. while it won't be the case if there is a piece.