Randomness and geometric features in computer vision

It is often necessary to handle randomness and geometry in computer vision, for instance to match and fuse together noisy geometric features such as points, lines or 3D frames, or to estimate a geometric transformation from a set of matched features. However, the proper handling of these geometric features is far more difficult than for points, and a number of paradoxes can arise. We analyse in this article three basic problems: (1) what is a uniform random distribution of features, (2) how to define a distance between features, and (3) what is the "mean feature" of a number of feature measurements, and we propose generic methods to solve them.