Introduction:

Introduction to calculus of variations of geometric functionals Differential invariants of curves and surfaces Curve evolution - affine and euclidean invariant Surface evolution and the level set method (numerical aspects in a brief).

Applications:

Edge detection and integration (active contours and the Canny-Haralick connection. Fast marching on flat and curved domains (Eikonal solvers). Images as manifold (the Beltrami/NL-Means/Bilateral/TV/L1~Sparse filters - the metric

connection). Surfaces as metric spaces Multidimensional scaling, generalized MDS and Gromov-Hausdorff distances.

I plan to mention affine and scale invariants of curves and surfaces, and diffusion geometry. If we have time, I will also give a brief introduction to efficient computational tools for geometric capturing devices.