Computational Geometry for Shape Matching and Shape Approximation - Literature and Supplementary Material

Sequence of five lectures given by Günter Rote as part of the 2nd Winter School on Computational Geometry, Amirkabir University of Technology, Tehran, March 2–6, 2010.

General Literature

H. Alt and L. J. Guibas. Discrete geometric shapes: Matching, interpolation, and approximation. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 121–153. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000. doi:10.1016/B978-044482537-7/50004-8

Congruence and similarity of geometric figures (Day 1)

The most basic question in shape matching is to test whether two objects are equal, possibly after translation, rotation, scaling, or other geometric transformations. We show how to test whether two point sets in the plane or in space can be tested for exact congruence. Further Reading

The Hausdorff distance between geometric figures (Day 2)

The Hausdorff distance is the most basic measure for comparing two point sets. We will discuss how the Hausdorff distance between two plane geometric objects can be computed efficiently, using the plane-sweep technique and Voronoi diagrams of sets of line segments.

The Fréchet distance (Day 3)

The Fréchet distance is a natural distance between curves that does not just regard them as point sets but takes their order into account. We will see how the Fréchet distance can be computed. Further References

Convex Approximation (day 5A)

A basic data processing task is to replace a complicated geometric object by a simpler approximation. We will discuss and analyze the Sandwich algorithm for a simultaneous inner and outer approximation of convex plane shapes by polygons. Further References

Pseudotriangulations (Day 5B)

Pseudotriangulations are a nice geometric structure and also a useful data structure. We will review the basic definitions and properties of Pseudotriangulations, and see how they arise in applications such as ray shooting, kinetic collision detection, lower approximation and locally convex hulls.
Günter Rote
Last modified: Mon Mar 15 16:27:36 CET 2010