On the Optimality of Motion-Based Particle Filtering

• Published in: IEEE transactions on circuits and systems for video technology Vol. 19; no. 7; pp. 1068 - 1072
• Main Authors: Bouaynaya, N., Schonfeld, D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive block matching; Applied sciences; Atoms & subatomic particles; Condensing; Density; Density measurement; Detection, estimation, filtering, equalization, prediction; Divergence; Exact sciences and technology; Filtering; Image processing; Information, signal and communications theory; Kullback-Leibler (KL) divergence; Mathematical analysis; Motion analysis; motion estimation; Optimization; particle filtering; Particle filters; Particle measurements; Particle tracking; Pattern recognition; Performance analysis; Performance enhancement; Proposals; Sampling methods; Sampling, quantization; Signal and communications theory; Signal processing; Signal, noise; Studies; Telecommunications and information theory; Video sequences; video tracking; Performance evaluation; Target tracking; Motion estimation; Similarity; Image processing; Video signal; Iterative method; video tracking; Kullback―Leibler (KL) divergence; Video signal processing; Block matching; Simulation; Image sequence; particle filtering; Object detection; Analytical method; Signal processing; Density function; Adaptive block matching; Sampling; Target detection; Particle filter
• ISSN: 1051-8215; 1558-2205
• DOI: 10.1109/TCSVT.2009.2020477

Particle filters have revolutionized object tracking in video sequences. The conventional particle filter, also called the CONDENSATION filter, uses the state transition distribution as the proposal distribution, from which the particles are drawn at each iteration. However, the transition distribution does not take into account the current observations, and thus many particles can be wasted in low likelihood regions. One of the most popular methods to improve the performance of particle filters relied on the motion-based proposal density. Although the motivation for motion-based particle filters could be explained on an intuitive level, up until now a mathematical rationale for the improved performance of motion-based particle filters has not been presented. In this letter, we investigate the performance of motion-based particle filters and provide an analytical justification of their superiority over the classical CONDENSATION filter. We rely on the characterization of the optimal proposal density, which minimizes the variance of the particles'weights. However, this density does not admit an analytical expression, making direct sampling from this optimal distribution impossible. We use the Kullback-Leibler (KL) divergence as a similarity measure between density functions and denote a particle filter as superior if the KL divergence between its proposal and the optimal proposal function is lower. We subsequently prove that under mild conditions on the estimated motion vector, the motion-based particle filter outperforms the CONDENSATION filter, in terms of the KL performance measure. Simulation results are presented to support the theoretical analysis.