A SURVEY ON MOVING OBJECT TRACKING IN VIDEO <s> 2) Measurement equation <s> Abstract A non-Gaussian state—space approach to the modeling of nonstationary time series is shown. The model is expressed in state—space form, where the system noise and the observational noise are not necessarily Gaussian. Recursive formulas of prediction, filtering, and smoothing for the state estimation and identification of the non-Gaussian state—space model are given. Also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas. Significant merits of non-Gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples. A typical application of this non-Gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes. Simple Gaussian state—space modeling is not adequate for this situation. Here the model with small system noise variance cannot detect jump, whereas the one with large system noise variance yields unfavorable wiggle. To work... <s> BIB001 </s> A SURVEY ON MOVING OBJECT TRACKING IN VIDEO <s> 2) Measurement equation <s> The problem of tracking curves in dense visual clutter is challenging. Kalman filtering is inadequate because it is based on Gaussian densities which, being unimo dal, cannot represent simultaneous alternative hypotheses. The Condensation algorithm uses “factored sampling”, previously applied to the interpretation of static images, in which the probability distribution of possible interpretations is represented by a randomly generated set. Condensation uses learned dynamical models, together with visual observations, to propagate the random set over time. The result is highly robust tracking of agile motion. Notwithstanding the use of stochastic methods, the algorithm runs in near real-time. <s> BIB002
Where is measurement vector, is the Gaussian measurement noise vector and H is the measurement matrix. B. Particle Filters: The problem with Kalman filter is that the state variables are normally distributed (Gaussian). So, those state variables that do not follow Gaussian distribution Kalman filter will give poor estimations for those state variables. This problem of the kalman filter can be solved with the help of particle filtering BIB001 . In particle filtering, the conditional state density p(X t | Z t ) at time t is represented by a set of samples {s t (n) : n = 1, . . . , N} (particles) with weigh π t (sampling probability). The weights define the importance of a sample, that is, its observation frequency BIB002 . Particle filter uses a common sampling scheme i.e. importance sampling to find new samples. The importance sampling scheme can be done in three steps, i.e. selection (selection of random samples), prediction (generate new sample from selected sample) and correction (Weights corresponding to the new sample are computed using the measurements Z t ). C. Multiobject Data Association and State Estimation: Kalman filter, extended kalman filter and particle give very good results when the objects are not close to each other. For tracking multiple objects in the video sequences by using Kalman or particle filters, the most likely measurement for a particular moving object needs to be associated with the object's state. This is called the correspondence problem. So for multiple object tracking the most important step we have solve is the correspondence problem before kalman or particle filters are applied. Nearest neighbor approach is the very simplest method to solve the correspondence problem. Data Association algorithms are used to associate the objects state like position, velocity, size with the available filters. Some of the methods to solve the data association are Linear Assignment problem (LAP), Stable Marriage problem (SMP) and Munkers algorithm etc. However the correspondence problem is hard to deal with when the moving objects are close to each other, and then the correspondence shows incorrect results. These filters fail to converge when incorrectly associated measurement occurs. There exist several statistical data association techniques to tackle this problem. Two mostly used techniques for data association in this complex scenario are Joint Probability Data Association Filtering (JPDAF) and Multiple Hypothesis Tracking (MHT).