Search results for "Discrete space"
showing 6 items of 6 documents
Representing 2D Digital Objects
2000
The paper describes the combination a multi-views approach to represent connected components of 2D binary images. The approach is based on the Object Connectivity Graph (OCG), which is a sub-graph of the connectivity graph generated by the Discrete Cylindrical Algebraic Decomposition(DCAD) performed in the 2D discrete space. This construction allows us to find the number of connected components, to determine their connectivity degree, and to solve visibility problem. We show that the CAD construction, when performed on two orthogonal views, supply information to avoid ambiguities in the interpretation of each image component. The implementation of the algorithm is outlined and the computati…
Toward a real-time tracking of dense point-sampled geometry
2012
4 pages; International audience; In this paper, we address the problem of tracking temporal deformations between two arbitrary densely sampled point-based surfaces. We propose an intuitive and efficient resolution to the point matching problem within two frames of a sequence. The proposed method utilizes two distinct space partition trees, one for each point cloud, which both are defined on a unique discrete space. Our method takes advantage of multi-resolution concerns, voxel adjacency relations, and a specific distance function. Experimental results obtained from both simulated and real reconstructed data sets demonstrate that the proposed method can handle efficiently the tracking proces…
K-theory of function rings
1990
AbstractThe ring R of continuous functions on a compact topological space Xwith values in R or C is considered. It is shown that the algebraic K-theory of such rings with coefficients in ZkZ, k any positive integer, agrees with the topological K-theory of the underlying space X with the same coefficient rings. The proof is based on the result that the map from Rδ (R with discrete topology) to R (R with compact-open topology) induces a natural isomorphism between the homologies with coefficients in ZkZ of the classifying spaces of the respective infinite general linear groups. Some remarks on the situation with X not compact are added.
A PARALLEL ALGORITHM FOR ANALYZING CONNECTED COMPONENTS IN BINARY IMAGES
1992
In this paper, a parallel algorithm for analyzing connected components in binary images is described. It is based on the extension of the Cylindrical Algebraic Decomposition (CAD) to a two-dimensional (2D) discrete space. This extension allows us to find the number of connected components, to determine their connectivity degree, and to solve the visibility problem. The parallel implementation of the algorithm is outlined and its time/space complexity is given.
Quantum Field Theory on a Discrete Space and Noncommutative Geometry
2001
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams of the corresponding theory in four dimensions is worked out explicitly. Special emphasis is put on the motivation as well as the presentation of some well-known basic notions of quantum field theory which in the zero-dimensional theory can be studied without being spoiled by technical complications due to the absence of divergencies.
Laplacian versus Adjacency Matrix in Quantum Walk Search
2015
A quantum particle evolving by Schr\"odinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete space, this is replaced by the discrete or graph Laplacian, which gives rise to a continuous-time quantum walk. Besides this natural definition, some quantum walk algorithms instead use the adjacency matrix to effect the walk. While this is equivalent to the Laplacian for regular graphs, it is different for non-regular graphs, and is thus an inequivalent quantum walk. We algorithmically explore this distinction by analyzing search on the complete bipartite graph with multiple marked vertices, using both the Lapla…