1. A motion image encoding apparatus for encoding a current image containing an object, the motion image encoding apparatus comprising: object extraction means for extracting the object contained in the current image from received current image data and outputting object contour data indicating a contour of the extracted object; predictive encoding means for performing a predictive encoding operation using the current image data, prestored data of a reference image, and control points of meshes which divide one of the current image and the reference image, and generating motion information relating to the control points, differential data between the current image and the reference image, and predictive image data; object difference generator means for selecting differential data in an object region among the differential data supplied from the predictive encoding means to encode the selected differential data based on the object contour data output from the object extraction means, and outputting the selected differential data and the encoded differential data; and adder means for receiving and adding the predictive image data output from the predictive encoding means and the selected differential data output from the object difference generator means to produce image data of an addition result, and updating the reference image data prestored in the predictive encoding means using the image data of the addition result.