Extracting pen trajectories from static signatures

Dr Emli-Mari Nel (PhD)


Handwritten signatures are still a common way of identifying yourself. Perhaps surprisingly, the verification of your signature is still mostly done by a human. Human interaction is required because automated signature verification systems are generally too unreliable to deal with skilled forgeries. The main problem is probably the number of false negatives, i.e. genuine signatures that are falsely rejected (which can potentially be annoying to the customer).

Be that is it may, there are two different types of signatures one has to consider—the static signature on a document, and the dynamic signature recorded on a special tablet. The latter is more secure than the former because dynamic information usually not available to the would-be forger, is also recorded. This includes, the pen trajectory (x and y coordinates), pen pressure, pen angle, and pen tilt.


Very effective systems typically based on Hidden Markov Models are available for dynamic signatures. Unfortunately the dynamic information is generally not available for static signatures, leaving them more vulnerable to attack by forgers. The question is whether it is possible to extract dynamic information from static signatures. For example is it clear which path the pen traced out in order to produce the signature on the right?

It is not easy to extract the pen trajectory from a static image, certainly not for a computer. Additional information is required. We assume that a dynamic exemplar of the individual’s signature is available. Typically this will be provided at the time of registration. The basic idea is to build an Hidden Markov Model of the static signature. Note that there is no training involved; all the transition probabilities as well as the emission pdf’s are obtained through trial and error. The dynamic exemplar is then matched to the HMM of the static signature. Using the Viterbi algorithm the optimal state sequence is extracted and this becomes the pen trajectory of the static signature.

In fact, the HMM is not build for the static signature but for a skeleton extracted from the static signature. This is not entirely straightforward since care must be taken that all possible connections through complicated areas (areas with a large number of intersections) are preserved.

The video shows the exemplar dynamic trajectory as well as the trajectory extracted from the static signature. The web-like structure of the skeleton might be of some interest—it can be easily removed but is retained in order to ensure that all the possible connections are preserved.

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