Given two shapes (say, two polygons in the plane), how similar are they? Can you translate, or maybe also rotate, one of them to be close to the other? And what does it mean at all for two shapes to be close to one another? There are many applications of shape matching, for example in robotics, computer graphics, image processing, and more.
Related projects:
Shape Matching of Curves Compare geometric shapes described by polygonal curves using adequate distance measures such as the "mandog" Fréchet distance. 

Fitting Prehistoric Stone Knives Archaeologists need to find out which prehistoric stone knives have been chopped from the same core stone. 

Geodesic Distances for Shapes Compare shapes on surfaces using shortest distances between points along the surface. This has high applicability in military and GIS applications in which objects traveling on various terrains are involved. 

MapMatching and Routing Algorithms for matching GPS curves to a given roadmap and reactive routing algorithms that adapt to dynamically changing traveltimes are essential technical components for Traffic Estimation and Prediction Systems. 

Analysis of 2D
Electrophoresis Gels Correctly modeling the shapes of protein spots in 2D electrophoresis gels as well as comparing two and more of such gels is highly important in Computational Proteomics. 

2D Frechet Distance The Frechet distance is a wellsuited distance measure for the comparison of surfaces. 