An Extension of Least Squares Methods for Smoothing Oscillation of Motion Predicting Function

Abstract

A novel hybrid technique for detection and predicting the motion of objects in video stream is presented in this paper. The novelty consists in extension of Savitzky-Golay smoothing filter applying difference approach for tracing object mass center with or without acceleration in noised images. The proposed adaptation of least squares methods for smoothing the fast varying values of motion predicting function permits to avoid the oscillation of that function with the same degree of used polynomial. The better results are obtained when the time of motion interpolation is divided into subintervals, and the function is represented by different polynomials over each subinterval. Therefore, in proposed hybrid technique the spatial clusters with objects in motion are detected by the image difference operator and behavior of those clusters is analyzed using their mass centers in consecutive frames. Then the predicted location of object is computed using modified algorithm of weighted least squares model. That provides the tracing possible routes which now are invariant to oscillation of predicting polynomials and noise presented in images. For irregular motion frequently occurred in dynamic scenes, the compensation and stabilization technique is also proposed in this paper. On base of several simulated kinematics experiments the efficiency of proposed technique is analyzed and evaluated.