Object and image indexing based on region connection calculus and oriented matroid theory

In this paper a novel method for indexing views of 3D objects is presented. The topological properties of the regions of views of an object or of a set of objects are used to define an index based on region connection calculus and oriented matroid theory. Both are formalisms for qualitative spatial representation and reasoning and are complementary in the sense that, whereas region connection calculus characterize connectivity of couples of connected regions of views, oriented matroids encode relative position of disjoint regions of views and give local and global topological information about their spatial distribution. This indexing technique has been applied to hypothesis generation from a single view to reduce the number of candidates in 3D object recognition processes

Shape representation and indexing based on region connection calculus and oriented matroid theory

International Conference on Discrete Geometry for Computer Imagery (DGCI), 2003, Naples (Italy)In this paper a novel method for indexing views of 3D objects is presented. The topological properties of the regions of the views of a set of objects are used to define an index based on the region connection calculus and oriented matroid theory. Both are formalisms for qualitative spatial representation and reasoning and are complementary in the sense that whereas the region connection calculus encodes information about connectivity of pairs of connected regions of the view, oriented matroids encode relative position of the disjoint regions of the view and give local and global topological information about their spatial distribution. This indexing technique is applied to 3D object hypothesis generation from single views to reduce candidates in object recognition processes.Peer Reviewe

Shape representation and indexing based on region connection calculus and oriented matroid theory

International Conference on Discrete Geometry for Computer Imagery (DGCI), 2003, Naples (Italy)In this paper a novel method for indexing views of 3D objects is presented. The topological properties of the regions of the views of a set of objects are used to define an index based on the region connection calculus and oriented matroid theory. Both are formalisms for qualitative spatial representation and reasoning and are complementary in the sense that whereas the region connection calculus encodes information about connectivity of pairs of connected regions of the view, oriented matroids encode relative position of the disjoint regions of the view and give local and global topological information about their spatial distribution. This indexing technique is applied to 3D object hypothesis generation from single views to reduce candidates in object recognition processes.Peer Reviewe

Arrangements of Submanifolds and the Tangent Bundle Complement

Drawing parallels with the theory of hyperplane arrangements, we develop the theory of arrangements of submanifolds. Given a smooth, finite dimensional, real manifold $X$ we consider a finite collection \A of locally flat codimension $1$ submanifolds that intersect like hyperplanes. To such an arrangement we associate two posets: the \emph{poset of faces} (or strata) \FA and the \emph{poset of intersections} L(\A). We also associate two topological spaces to \A. First, the complement of the union of submanifolds in $X$ which we call the \emph{set of chambers} and denote by \Ch. Second, the complement of union of tangent bundles of these submanifolds inside $TX$ which we call the \emph{tangent bundle complement} and denote by M(\A). Our aim is to investigate the relationship between combinatorics of the posets and topology of the complements. We generalize the Salvetti complex construction in this setting and also charcterize its connected covers using incidence relations in the face poset. We also demonstrate some calculations of the fundamental group and the cohomology ring. We apply these general results to study arrangements of spheres, projective spaces, tori and pseudohyperplanes. Finally we generalize Zaslavsky\u27s classical result in order to count the number of chambers

Glosarium Matematika

273 p.; 24 cm

Dagstuhl News January - December 2002

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic

From dimers to webs

We formulate a higher-rank version of the boundary measurement map for weighted planar bipartite networks in the disk. It sends a network to a linear combination of $\textnormal {SL}_r$-webs and is built upon the $r$-fold dimer model on the network. When $r$ equals 1, our map is a reformulation of Postnikov's boundary measurement used to coordinatize positroid strata. When $r$ equals 2 or 3, it is a reformulation of the $\textnormal {SL}_2$- and $\textnormal {SL}_3$-web immanants defined by the second author. The basic result is that the higher-rank map factors through Postnikov's map. As an application, we deduce generators and relations for the space of $\textnormal {SL}_r$-webs, re-proving a result of Cautis-Kamnitzer-Morrison. We establish compatibility between our map and restriction to positroid strata and thus between webs and total positivity