1. An image processing device that models, based on a plurality of frame images being results of time-sequential imaging of an object in motion, a motion of the object using a three-dimensional (3D) body configured by a plurality of parts, the device comprising: acquisition means for acquiring the frame images being the imaging results; estimation means for computing, based on a posture of the 3D body in any of the frame images selected for use as a reference, a first matrix of coordinates of a joint connecting the parts of the 3D body and a second matrix of coordinates of each of the parts of the 3D body, and generating a first motion vector with an estimation of a motion of each of the parts with no joint constraints based on the frame image subsequent to the reference frame image; computing means for computing, using the first and second matrixes being computation results by the estimation means and the first motion vector, a second motion vector with an estimation of the motion of each of the parts with the joint constraints for a predetermined objective function to satisfy predetermined requirements; and determination means for determining the 3D body corresponding to the subsequent frame image by transforming the 3D body in the reference frame image in accordance with the second motion vector being a computation result, wherein the predetermined requirements for the predetermined objective function are to minimize a difference between a posture of the 3D body being a result of transformation by the first motion vector and a posture of the 3D body being a result of the transformation by the second motion vector, and wherein the predetermined objective function is 
 (Δ*−Δ) t C (Δ*−Δ) the computing means computes the second motion vector for minimizing the predetermined objective function by 
 Δ*= V ( V t CV ) −1 V t CΔ where Δ* denotes the second motion vector, V denotes the first matrix, C denotes the second matrix, and, Δ denotes the first motion vector.