Image motion tracking by FRS state space model using SMC implementation of PHD filter

Abstract

This study is aimed at obtaining smoothed trajectory of feature points in dynamic image, where the feature points are extracted at each image frame with missing and false detection. The image scene contains independently moving multiple objects with occlusion and appearance. We develop a state space model using Finite Random Set (FRS) to cope with this situation since FRS is a set of random variables with the number of the variables also being random (integer) variable so it is suitable for representing the variable number of feature points caused by appearance/occlusion and missing/false detection. By estimating the state of the model using Sequential Monte Carlo (SMC) implementation of Probability Hypothesis Density (PHD) filter, we obtain smoothed trajectory of the feature points. PHD is 1st order moment of FRS, and it has a property that its integration yeilds the expected number of feature points in the integrated region. The SMC implementation gives approximated solution by weighted particles, where the number of particles varies depending on the number of feature points in the scene. Experiment of dynamic image demonstrates that proposed method successfully smoothed the trajectory of feature points responding to appearance and occlusion of objects without being affeted by missing and false detection.