1. An image processing apparatus comprising: initial vector selecting means for selecting an initial vector used as an initial value for a gradient method for detecting a motion vector in a block of interest in a present frame; motion vector detecting means for using the gradient method to detect the motion vector in the block of interest by using the initial vector selected by said initial vector selecting means; shifted initial vector setting means for setting, as a shifted initial vector, a shifted motion vector having an initial point at the block of interest in said present frame being identical in position to a terminal point of the motion vector detected by said motion vector detecting means in a past frame with respect to said present frame; and candidate vector setting means for setting the shifted initial vector set by said shifted initial vector setting means as one of candidate vectors for selecting the initial vector in the block of interest by said initial vector selecting means; and wherein said shifted motion vector is identical in magnitude and in orientation to the motion vector detected by said motion vector detecting means.