2006/08/01 by Erik Carlsson, Gunnar Carlsson, Vin de Silva · 66 citations
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Digital Image Processing Techniques #Data Management and Algorithms #Mathematics #Feature (linguistics) #Point cloud #Manifold (fluid mechanics) #Tangent #Tangent bundle #Algebraic number #Object (grammar) #Point (geometry) #Topology (electrical circuits) #Algebra over a field #Algorithm #Tangent space #Computer science #Pure mathematics #Geometry #Artificial intelligence #Combinatorics #Mathematical analysis
paper · doi:10.1142/s021819590600204x
published in International Journal of Computational Geometry & Applications 16(04), 291-314 (World Scientific)
openalex publication_date 2006/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
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.