1. An image processing apparatus, comprising: a modeling unit, in video image data composed of a plurality of frame images where one direction in each of the frame images is defined as an X direction and a direction perpendicular to the one direction as a Y direction, separating a motion from a standard image, which is one frame before a reference image subjected to a process, until the reference image into a motion in the X direction and a motion in the Y direction and representing the motion in the X direction and the motion in the Y direction respectively as vector fields composed of a translation component composed of identical magnitude and direction regardless of positions in the X direction and the Y direction, an X dependent component primarily changing in correspondence with the position in the X direction, and a Y dependent component primarily changing in correspondence with the position in the Y direction; and a calculation unit respectively calculating the translation component, the X dependent component, and the Y dependent component corresponding to the X direction and the Y direction represented by the modeling unit.