Question

Why can't a Bayesian network represent the probability distribution over assignments of all pixels to light or dark classes, for classifying pixels in an image as "dark" or "light"?

Answer 1

Bayesian networks have their own limitations in such situations. For pixels, it is hard to learn about the conditional probability links of different pixels. In certain cases when relationships might be cyclic, and deflection is dependent on other factors such as pressure field etc. these networks can't be used.

Bayesian networks are the best choice when there is reliable prior knowledge. In the given situation, the prior assumptions will distort the network and results will not be valid.