1. An image processing apparatus for estimating a motion of a plurality of predetermined feature points of a 3D object from a motion picture of the 3D object taken by a monocular camera, comprising: observation vector extracting means for extracting projected coordinates of the predetermined feature point onto an image plane, from each of frames of the motion picture; 3D model initializing means for making the observation vector extracting means extract from an initial frame of the motion picture, initial projected coordinates in a model coordinate arithmetic expression for calculation of model coordinates of the predetermined feature point on the basis of a first parameter, a second parameter, and the initial projected coordinates; and motion estimating means for calculating estimates of state variables including a third parameter in a motion arithmetic expression for calculation of coordinates of the predetermined feature point at a time of photography when a processed target frame of the motion picture different from the initial frame was taken, from the model coordinates, the first parameter, and the second parameter, and for outputting an output value about the motion of the predetermined feature point on the basis of the second parameter included in the estimates of the state variables, wherein the model coordinate arithmetic expression is based on back projection of the monocular camera, the first parameter is a parameter independent of a local motion of a portion including the predetermined feature point, and the second parameter is a parameter dependent on the local motion of the portion including the predetermined feature point, and wherein the motion estimating means: calculates predicted values of the state variables at the time of photography when the processed target frame was taken, based on a state transition model; applies the initial projected coordinates, and the first parameter and the second parameter included in the predicted values of the state variables, to the model coordinate arithmetic expression to calculate estimates of the model coordinates at the time of photography; applies the third parameter in the predicted values of the state variables and the estimates of the model coordinates to the motion arithmetic expression to calculate estimates of coordinates of the predetermined feature point at the time of photography; applies the estimates of the coordinates of the predetermined feature point to an observation function using a perspective transformation based on an observation model of the monocular camera to calculate estimates of an observation vector of the predetermined feature point; makes the observation vector extracting means extract the projected coordinates of the predetermined feature point from the processed target frame, as the observation vector; and filters the predicted values of the state variables by use of the extracted observation vector and the estimates of the observation vector to calculate estimates of the state variables at the time of photography, wherein each of the plurality of feature points represent each of a plurality of parts of the 3D object and are used for determining a local motion of each part of the 3D object when each part has different motion.