We present a system to beautify curves: i.e. to take curves
that roughly depict some property of interest and make
them look more like what experts would draw. The focus
of our work is in applications for artistic drawings, but
our system can also be plugged into various other domains
where curves and trajectories play a dominant role such as
robot path planning, animation or edge-deblurring. Our approach
consists of learning properties from a database of
ideal example, which could be sketches or robot trajectories,
and transform a coarse input curve to make it look like
those in the database. The key scientific issue is: in what
sense are these curves 'like' one another? In our work, this
likeness is expressed statistically. Using Hidden Markov
Models in combination with multi-scale methods and mixture
models, we synthesize a new curve as a statistically
consistent mixture of the training set that best describes the
input. Additionally, our approach allows us to easily include
application specific biases to the system.