An Algebraic Topological Method for Feature Identification

We develop a mathematical framework for describing local features of a geometric object— such as the edges of a square or the apex of a cone—in terms of algebraic topological invariants. The main tool is the construction of a tangent complex for an arbitrary geometrical object, generalising the usual tangent bundle of a manifold. This framework can be used to develop algorithms for automatic feature location. We give several examples of applying such algorithms to geometric objects represented by point-cloud data sets.