1. An image coding apparatus for coding a video image comprising: a geometric-transformation motion compensation prediction unit configured to calculate, for each of a plurality of prediction modes, a motion vector and a prediction signal between a target block in a target image and a reference block in a reference image obtained by performing geometric transformation on the target block, to select pixels located at vertices constituting the target block, pixels located near the vertices, or interpolation pixels located near the vertices as representative pixels corresponding to the vertices in each prediction mode, to calculate the respective motion vectors of these representative pixels, and to calculate the respective motion vectors of pixels other than the representative pixels by interpolation using the motion vectors of the representative pixels so as to calculate the prediction signal; a prediction method determination unit configured to select any one of the plurality of prediction modes by the geometric-transformation motion compensation prediction unit for each target block in the target image; a prediction error signal generation unit configured to calculate a difference between a prediction signal calculated in a prediction mode selected by the prediction method determination unit and an image signal of the target block so as to generate a prediction error signal; a difference vector generation unit configured to calculate, using motion vectors inside and outside of the target block, prediction motion vectors of the respective motion vectors of the representative pixels calculated in the prediction mode selected by the prediction method determination unit and to calculate differences between the prediction motion vectors and the motion vectors of the representative pixels calculated in the selected prediction mode so as to generate respective difference motion vectors of the representative pixels; and a coding unit configured to code prediction method information for identifying the prediction mode selected by the prediction method determination unit, the difference motion vectors generated by the difference vector generation unit, and the prediction error signal generated by the prediction error signal generation unit, wherein the target block is an quadrangle region, and wherein the geometric-transformation motion compensation prediction unit includes at least two prediction modes out of four prediction modes: a first mode for calculating respective motion vectors, subject to coding, of four representative pixels of the target block; a second mode for calculating respective motion vectors, subject to coding, of two representative pixels in the vertical direction of the target block; a third mode for calculating respective motion vectors, subject to coding, of two representative pixels in the horizontal direction of the target block; and a fourth mode for calculating respective motion vectors, subject to coding, of three representative pixels of the target block.