1. An apparatus for frame interpolation, the apparatus comprising: an initial motion vector determination unit to determine an initial motion vector of each of current blocks of an interpolation frame by performing forward motion estimation and backward motion estimation with respect to a current frame and a previous frame, wherein the initial motion vector determination unit comprises: a forward motion calculation unit to calculate a forward motion vector from the previous frame to the current frame; a backward motion calculation unit to calculate a backward motion vector from the current frame to the previous frame; and a motion vector difference calculation unit to calculate a motion vector difference between the forward motion vector and the backward vector for a current block of the interpolation frame; a filtering unit to filter the initial motion vector based on the motion vector difference between the forward motion vector and the backward motion vector; a result motion vector determination unit to determine a result motion vector which includes a rotation element by rotating a block of the current frame and the previous frame being determined according to the initial motion vector; and a frame generation unit to generate the interpolation frame according to the result motion vector, wherein the result motion vector determination unit comprises: a rotation element selection unit to select a rotation angle as the rotation element using a block matching error based on the rotating of the block of the current frame and the previous frame.