While the results above
Given a set of random
}, and the summations are over all the possible configurations of the sets
; in practice, the amount of computation involved in the evaluation of these summations makes the solution infeasible even for problems of relatively small
A Bayesian network for a set of variables
} is a probabilistic model
The ability to decompose the joint density into a product of local conditional probabilities allows the construction of efficient algorithms where inference takes place by propagation of beliefs across the nodes in the network [21,22].
Figure 3.7: A generic Bayesian architecture for content characterization. Even though only three layers of variables are represented in the figure, the network could contain as many as desired ( 1998 IEEE).
The visual sensors are tuned to visual features deemed relevant for the semantic content characterization. The network infers the presence/absence of the semantic attributes given these sensor measurements, i.e., P(
is a subset of A. The arrows indicate a
One of the strengths of Bayesian inference is that the sensors of Figure 3.7 do not have to be flawless since 1) the model can account for variable sensor precision, and 2) the network can integrate the sensor information to disambiguate conflicting hypothesis. Consider, for example, the simple task of detecting sky in a sports database containing pictures of both skiing and sailing competitions. One way to achieve such a goal is to rely on a pair of sophisticated water and sky detectors. The underlying strategy is to interpret the images first and then characterize the images according to this interpretation.
While such strategy could be implemented with Bayesian procedures, a more efficient alternative is to rely on the model of Figure 3.8. Here, the network consists of five semantic attributes and two simple sensors for large white and blue image patches. In the absence of any measurements, the variables sailing and skiing are independent. However, whenever the sensor of blue patches becomes active, they do become dependent (or, in the Bayesian network lingo, d-connected ) and the knowledge of the output of the sensor of white patches is sufficient to perform the desired inference.
Figure 3.8: A simple Bayesian network for the classification of sports ( 1998 IEEE).
This effect is known as the "explaining away" capability of Bayesian networks . Although there is no direct connection between the
sensor and the
variable, the observation of white
This second strategy relies more in modelling the semantics and the relationships between them than in the classification of the image directly from the image observations. In fact, the image measurements are only used to discriminate between the different semantic interpretations. This has two practical advantages. First, a much smaller