The relationship between CRF and Structured Perceptron

I would say the CRF and the structured perceptron are two closely related energy-based models. Given an energy function -- for instance, sum_t [x_t W y_t + y_t-1 A y_t] for linear-chain models -- CRFs and structured perceptrons minimize different loss functions to learn the parameters W and A. In particular, CRFs define a Gibbs distribution based on the energy and minimize the negative conditional log-likelihood, whereas structured perceptrons minimize something called the perceptron loss, which roughly has the form E(x, y) - max_y' E(x, y').

For fully observed models, it is possible to train the parameters using the structured perceptron and plug these into a CRF (or vice versa), as MAP-prediction amounts to exactly the same minimization, viz. minimization of the energy function over y. In the case when the model contains latent variables (such as in hidden, hidden-unit, or latent-dynamic CRFs), the two models become different. The difference is that latent-variable CRFs marginalize out the latent variables z and then optimize over y to obtain the MAP-prediction, whereas structured perceptrons would do a joint optimization over z and y. Empirically, I have experiences that in the case of latent-variable models, you can not plugin structured-perceptron parameters into the corresponding CRF model or vice versa.

Yann LeCun has a nice tutorial on energy-based models that you could use to read up on this stuff. Some of the papers on CRFs with latent variables may also be of interest to you.