On the Accuracy and Converence of 2-D Motion Models Using Minimum MSE Motion Estimation

Abstract

Two-dimensional (2-D) motion models make on image plane approximate motion descriptions of true motion made by 3-D motion model. This paper is concerned with several 2-D motion models and a 3-D motion model for 3-D planar object. The objectives of this work are in measuring accuracy of minimum MSE motion estimations based on 2-D motion models and in comparing convergence of an estimation process for different motion models. The accuracy is measured by numerical example using optimum motion description parameters for minimum MSE. The optimum description parameters are obtained by minimizing a mapping error function between the exact and approximate mappings. The convergence is examined for the gradient-based motion estimation algorithm on a test image sequence with or without random noise. It is shown that considering both the estimation accuracy and convergence, and the complexity of estimation procedure, 2-D motion model with either 6 or 4 description parameters can be a useful choice for motion description of planar objects nearly parallel to image plane and having translative and rotative motion. For the objects which are not parallel to image plane or undergo linear deformation, 2-D motion model with 6 parameters is required for an accurate description of motion.