The present invention seeks to provide a solution to the problem that motion compensation in an encoding method of the prior art involves decimal point picture element interpolation by means of fixed filters and therefore cannot realize interpolation of decimal point picture elements that accords with the nature and bit rate of a moving picture. A filter/interpolated image memory (101) interpolates picture elements of decimal point positions in a reference image by means of a plurality of sets of filters, a motion vector/filter detector (102) detects the combination of filter and motion vector that realizes the highest encoding efficiency, a prediction value generator (103) uses the detected combination of filter and motion vector to generate a prediction value, and motion vector/filter detector (102) supplies as output the information of the filter and information of the motion vector that generated the prediction value; whereby decimal point picture element interpolation that corresponds to the nature and bit rate of the moving picture can be realized and encoding of a moving picture can be improved.