## Graduate Seminar on Numerical Simulation:

Shape spaces and shape representations

The course will be given by Dr. Behrend Heeren.

Where/When: **Tu 12.15-13.45, Room 2.040**.

Note that this is only a preliminary date - we can possibly agree on a different date in the first seminar meeting!

If you are interested in the seminar, please drop me an email!

There will be a first meeting at Thursday, September 28th, 2pm in room 2.040 to organize individual talks.

### Topics

First, we will discuss some papers on different representations of shapes, e.g.

- Curves: There are several papers by M. Bauer, M. Bruveris, P. Michor and D. Mumford which can be discussed
- Images: B. Berkels, A. Effland, M. Rumpf,
*Time discrete geodesic paths in the space of images*, 2015.
- Solid bodies: M. Fuchs, B. Jüttler, O. Scherzer, H. Yang,
*Shape metrics based on elastic deformations*, 2009.
- Measures: J.-D. Benamou and Y. Brenier,
*A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem*, 2000.

Second, we will discuss operations and applications on shape spaces, e.g.

- A geodesic calculus on generic shape spaces: M. Rumpf and B. Wirth,
*Variational time-discretization of geodesic calculus*, 2015.
- Statistical analysis based on elastic deformations: There are several papers by M. Rumpf and B. Wirth on elastic shape averaging and an elasticity-based covariance analysis of shapes, summarized e.g. in: M. Rumpf and B. Wirth,
* Variational methods in shape analysis*, 2011.
- Spline interpolation on general shape spaces: A. Trouve and F.-X. Vialard,
*Shape splines and stochastic shape evolutions: a second order point of view*, 2012.
- Regression analysis on shape spaces: There are several papers by T. Fletcher and co-workers, e.g. J. Hinkle, P. Muralidharan, P.T. Fletcher,
*Polynomial regression on Riemannian manifolds*, 2012.
- Principal geodesic analysis as a generalization of principal component analysis (PCA) to Riemannian manifolds