Wrapping up: Week 5

This week we have made a big leap into practical applications of shape modelling.

We have discussed Gaussian Process (GP) regression, which lets us incorporate knowledge about deformations that we may know at certain points of our reference shape. This knowledge could come from a medical expert, who annotates a reference and target shape with corresponding landmarks, from an automated machine learning algorithm, or it might be that we simply observe only a part of the shape. This latter situation occurs in clinical practice, when we have a part of a bone or organ from which we want to reconstruct the full shape.

The mathematics of Gaussian Process regression is as beautiful as one can hope for. GP regression provides us with a closed form solution, which can be computed efficiently using only linear algebra operations. Moreover, we do not only get the solution that matches the observation best, but obtain the full posterior distribution. This distribution is again a Gaussian Process. In our case this means that the posterior defines again a valid shape model, which represents the family of shapes that are consistent with the observed deformations.

In the practical application of this method in Scalismo Lab, we were able to compute a nose reconstructions for professor Vetter. Those of you who will take part in the course project next week will perform a similar task to reconstruct femur bones from fragments of various size. We are looking forward to seeing your work!