There is no need for feature extraction while using a neural network. Neural networks themselves compute the required features while they are trained. For signature verification what you should be looking for is to train your network to compute similarity index similar to what is applied in one of the face recognition techniques. Lets say you have 10 signatures of one person and you have 100 such persons. You trained your network to compute a similarity index between different signatures and for test signature you compute similarity index across existing 1000 signatures and based on average similarity which one gets the highest score, you can classify to which person the signature belongs. Now coming to the verification part you can compute similarity between the existing signatures and set a threshold, lets say similarity is 0.7 of test signature for a particular person while you want it to match as close as 0.9. In this case you can say signature does not match.
You can start reading about neural networks architectures that are used to compute similarity by going through Siamese Networks.