Entropy based Markov chains for multisensor fusion

This thesis proposes an entropy based Markov chain (EMC) fusion technique and demon-strates its applications in multisensor fusion. Multisensor fusion is a science in studying the methods for combining multiple sensory observations into a consensus output such that classification and estimation accuracy can be improved by reducing the measurement uncertainty. The consensus output can be either (a) one of the possible classes for the classification problem, or (b) a random variable for the parameter estimation problem. In recent years, a great deal of interests in multisensor fusion has been aroused in the fields of robotics, computer vision, remote sensing and medical imaging because of the general belief that multiple observations can help lower the uncertainty level, which can hardly be achieved by any individual observation. Therefore, a number of context dependent multisensor fusion techniques have been proposed recently. The most widely used measure of uncertainty, which is expressed in terms of the probabilistic function, is Shannon's entropy. It was originally employed in the measurement of randomness which in turn can be interpreted as the measurement of uncertainty. Self-emropy and conditional entropy, which measure how uncertain a sensor is about its own observation and joint observations respectively, are adopted. Markov chain has been used as an observation combination process because of two major reasons: (a) the consensus output is a linear combination of the weighted local observations which greatly simplifies the observation combination process; and (b) the weight is the transition probability assigned by one sensor to another sensor and can be intuitively related to the single observation distribution and the joint observation distribution between two sensors. Higher order distributions are not necessary. Because of these reasons, the Markov chain is employed. Experiments have been done to implement the entropy based Markov chain (EMC) fusion technique. The results show that the proposed approach can reduce the measurement uncertainty by aggregating multiple observations. The major benefits of this approach are as follows: (a) single observation distributions and joint observation distributions between any two sensors, which represent the interrelations between the sensory observations and the consensus output, can be represented in polynomial form, (b) the consensus output is the linear combination of the weighted observations, in which weights can be computed in polynomial time and (c) EMC is robust because it suppresses the noisy observation with high uncertainty level to minimize the contribution of the noisy and unreliable observations in the combination process