Often, high dimensional data lie close to a low-dimensional submanifold and it is of interest to understand the geometry of these submanifolds. The homology groups of a manifold a...
Sivaraman Balakrishnan, Alessandro Rinaldo, Don Sh...
The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of to...
Abstract. We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms f...
Abstract. Qualitative reasoning uses a limited set of relevant distinctions of the domain to allow a flexible way of representing and reasoning about it. This work presents a conce...
Topological invariants are extremely useful in many applications related to digital imaging and geometric modeling, and homology is a classical one, which has not yet been fully e...
Samuel Peltier, Sylvie Alayrangues, Laurent Fuchs,...