Abstract:

In the first part of the talk I will briefly review a computationally optimal
numerical answer to the question of how to compute the shortest path between
two points on a surface, also known as the `minimal geodesic problem'. 
It is based on efficiently solving `Eikonal equations' on triangulated curved domains. 

Next, we show how to use the method to compute:

1. Minimal geodesics on weighted curved domains,

2. Voronoi diagrams and offset curves on surfaces,  and

3. Applications of the technique to areas like:

   3.1. 3D shape reconstruction in computer vision,

   3.2. Path planning in robotic navigation,

   3.3. Texture mapping in computer graphics,    and

   3.4. Bending invariant signatures for isometric
        surface classification.
  
In the second part of the talk I'll give an overview of recent results in the
area of geometric image processing and analysis.