# Particle filter for visual tracking

## Kalman Filter

**Cons：**

Kalman filtering is inadequate because it is based on the unimodal Gaussian distribution assumption, and it can’t represent simultaneous alternative hypotheses.

It works relatively poorly in clutter which causes the density to be multi-modal and therefore non- Gaussian.

Kalman filter is based on the single Gauss model, and different components have different effects on the Gauss distribution, as follows:

- The deterministic component causes the density function to drift bodily.
- The random component of the dynamical model leads to spreading—increasing uncertainty.
- The effect of an external observation is to superimpose a reactive effect on the diffusion.

## Particle Filter

**The CONDENSATION Algorithm**

At the top of the diagram, the output from time-step t -1 is the weighted sample-set. The aim is to maintain, at successive time-steps, sample sets of fixed size N.

The first operation is to sample N times from the set , choosing a given element with probability. Some elements, especially those with high weights, may be chosen several times, leading to identical copies of elements in the new set. Others with relatively low weights may not be chosen at all.

- Each element chosen from the new set is now subjected to the predictive steps.First, an element undergoes drift and, since this is deterministic, identical elements in the new set undergo the same drift.
- The second predictive step, diffusion, is random and identical elements now split because each undergoes its own independent motion step. At this stage, the sample set for the new time-step has been generated but, as yet, without its weights;
Finally, the observation step is applied, generating weights from the observation density.

**Algorithm:**

## Color-based Particle Filter

Color histograms have many advantages for tracking non-rigid objects as they are robust to partial occlusion, are rotation and scale invariant and are calculated efficiently.

A target is tracked with a particle filter by comparing its histogram with the histograms of the sample positions using the Bhattacharyya distance.

**Bhattacharyya distance：**在统计学中，Bhattacharyya距离（以下称巴氏距离）测量的是两个离散或连续概率分布的相似性。计算方式和Bhattacharyya系数关系很密切。

**Algorithm:**

## Kernel-based Particle Filter

A PF does not perform well when the dynamic system has a very small system noise or if the observation noise has very small variance. In these cases, the particle set quickly collapses to one single point in the state space.

The standard PF often fails to produce a particle set that captures the “irregular” motion, leading to gradually drifting estimates and ultimate loss of target.

**to be done**

## A Boosted Particle Filter

The problem of **tracking a varying number of non- rigid objects** has two major difficulties:

- First, the observation models and target distributions can be highly
**non-linear and non- Gaussian**. - Second, the presence of a large, varying number of objects creates
**complex interactions with overlap and ambiguities**.

**Mixture particle filters and Adaboost：**

An effective way is to combine mixture particle filters and **Adaboost**. The crucial issues in mixture particle filters are the choice of the proposal distribution and the treatment of objects leaving and entering the scene.

The mixture particle filter is ideally suited to multi-target tracking as it assigns a mixture component to each player. The proposal distribution can be constructed by using a mixture model that incorporates information from the dynamic models of each player and the detection hypotheses generated by Adaboost.

**Methods：**

- Most multi-target tracking assumed
**a fixed number of objects**. - BraMBLe has an automatic object detection system that relies on modeling
**a fixed background**. - The authors will relax the assumption of a fixed background where the
**background changes**. - Particle filters may perform poorly when the posterior is multimodal for multiple targets. Vermaak et al introduce a
**mixture particle filter (MPF)**, where each component is modelled with an individual particle filter. BPF is based on MPF. - The authors adopt a multi-color observation model based on Hue-Saturation-Value (HSV) color histograms.

The boosted particle filter introduces **two important extensions of the MPF**:

- First, it uses Adaboost to construct the proposal distribution. It incorporates the recent observations in proposal distributions (through the Adaboost detections), and outperforms naive transition prior proposals considerably.
- Second, Adaboost provides a mechanism for obtaining and maintaining the mixture representation. It allows us to detect objects leaving and entering the scene efficiently.

## References

- M. Isard and A. Blake. Condensation–conditional density propagation for visual tracking. Int. J. Computer Vision, 29(1):5– 28, 1998.
- S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for on-line non-linear/non-Gaussian Bayesian tracking,” IEEE Transactions on Signal Processing, vol. 50, pp. 174–188, Feb. 2002.
- K. Nummiaroa, E. Koller-Meierb, L. V. Gool, “An adaptive color- based particle filter”, Image and Vision Computing 21 (2003) 99– 110.
- C.Chang, and R. Ansari, “Kernel Particle Filter for Visual Tracking”, IEEE SIGNAL PROCESSING LETTERS, VOL. 12, NO. 3, pp242-245, 2005.
- K. Okuma, et al., “A Boosted Particle Filter: Multitarget Detection and Tracking”, ECCV 2004 (2004), pp. 28-39.