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JCT
2010
77views more  JCT 2010»
13 years 8 months ago
Obtainable sizes of topologies on finite sets
We study the smallest possible number of points in a topological space having k open sets. Equivalently, this is the smallest possible number of elements in a poset having k order ...
Kári Ragnarsson, Bridget Eileen Tenner
AAAI
1998
13 years 11 months ago
Integrating Topological and Metric Maps for Mobile Robot Navigation: A Statistical Approach
The problem of concurrent mapping and localization has received considerable attention in the mobile robotics community. Existing approachescan largely be grouped into two distinc...
Sebastian Thrun, Jens-Steffen Gutmann, Dieter Fox,...
ICPR
2002
IEEE
14 years 11 months ago
Building the Topological Tree by Recursive FCM Color Clustering
In this paper we define a Topological Tree (TT) as a knowledge representation method that aims to describe important visual and spatial features of image regions, namely the color...
Rita Cucchiara, Costantino Grana, Andrea Prati, St...
IJCAI
2007
13 years 11 months ago
Combining Topological and Directional Information for Spatial Reasoning
Current research on qualitative spatial representation and reasoning usually focuses on one single aspect of space. However, in real world applications, several aspects are often ...
Sanjiang Li
ISAAC
2009
Springer
93views Algorithms» more  ISAAC 2009»
14 years 4 months ago
Computing Multidimensional Persistence
Abstract. The theory of multidimensional persistence captures the topology of a multifiltration – a multiparameter family of increasing spaces. Multifiltrations arise naturally...
Gunnar Carlsson, Gurjeet Singh, Afra Zomorodian