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, wherein when a position in the X direction with a center of the frame image as an origin is x and a position in the Y direction as y, the modeling unit represents the translation component in the X direction as a translation parameter element u 0 , the X dependent component in the motion in the X direction as an X dependent parameter element u x and a multiplication value of x, the Y dependent component in the motion in the X direction as a Y dependent parameter element u y and a multiplication value of y, the translation component in the motion in the Y direction as a translation parameter element v 0 , the X dependent component in the motion in the Y direction as an X dependent parameter element v x and a multiplication value of x, and the Y dependent component in the motion in the Y direction as a Y dependent parameter element v y and a multiplication value of y, wherein when the vector fields are defined as (u(x, y), v(x, y)), the vector fields are modeled in accordance with an expression below: 
 (u(x,y), v(x,y))=(u 0+u x x+u y y,v 0 +v x x+v y y)  (1), and wherein by a local search searching an optimal solution while altering at least one or more of six parameter elements, composed of the translation parameter elements u 0 and v 0 , the X dependent parameter elements u x and v x , and the Y dependent parameter elements u y and v y , in steps of a search increase and decrease value, the calculation unit respectively calculates the six parameter elements.