84,165 research outputs found

    On surfaces in digital topology

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    In R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, J. Rubio. A Polyhedral Approach to Digital Topology a new framework for digital topology has been proposed. This framework offers the possibility of transfering, in an easy way, definitions, statements and proofs from continuous topology to digital topology. In particular, it provides a straightforward definition of n-dimensional digital manifold. In this paper we prove that the class of digital 2-manifolds without boundary in the grid Z3 agrees with the class of (26, 6)-surfaces defined by Kong-Roscoe and other authors. As a consequence, the separation theorem for digital surfaces stated in D.G. Morgenthaler, A. Rosenfeld. Surfaces in threedimensional digital images. Information and Control, 51 (1981), 227-247] and G.M. Reed. On the Characterization of Simple Closed Surfaces in Three-dimensional Digital Images. Computer Graphics and Image Processing, 25 (1984), 226-235 is obtained.Dirección General de Investigación Científica y TécnicaUniversidad de La Rioj

    Digital dissection of the model organism Xenopus laevis using contrast-enhanced computed tomography

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    The African clawed frog, Xenopus laevis, is one of the most widely used model organisms in biological research. However, the most recent anatomical description of X. laevis was produced nearly a century ago. Compared with other anurans, pipid frogs – including X. laevis – exhibit numerous unusual morphological features; thus, anatomical descriptions of more ‘typical’ frogs do not detail many aspects of X. laevis skeletal and soft‐tissue morphology. The relatively new method of using iodine‐based agents to stain soft tissues prior to high‐resolution X‐ray imaging has several advantages over gross dissection, such as enabling dissection of very small and fragile specimens, and preserving the three‐dimensional topology of anatomical structures. Here, we use contrast‐enhanced computed tomography to produce a high‐resolution three‐dimensional digital dissection of a post‐metamorphic X. laevis to successfully visualize: skeletal and muscular anatomy; the nervous, respiratory, digestive, excretory and reproductive systems; and the major sense organs. Our digital dissection updates and supplements previous anatomical descriptions of this key model organism, and we present the three‐dimensional data as interactive portable document format (PDF) files that are easily accessible and freely available for research and educational purposes. The data presented here hold enormous potential for applications beyond descriptive purposes, particularly for biological researchers using this taxon as a model organism, comparative anatomy and biomechanical modelling

    Topological alterations of 3D digital images under rigid transformations

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    National audienceRigid transformations in R^n are known to preserve the shape, and are often applied to digital images. However, digitized rigid transformations, defined as digital functions from Z^n to Z^n do not preserve shapes in general\string; indeed, they are almost never bijective and thus alter the topology. In order to understand the causes of such topological alterations, we first study the possible loss of voxel information and modification of voxel adjacencies induced by applications of digitized rigid transformations to 3D digital images. We then show that even very simple structured images such as digital half-spaces may not preserve their topology under these transformations. This signifies that a simple extension of the two-dimensional solution for topology preservation cannot be made in three dimensions

    The KW-boundary hybrid digital waveguide mesh for room acoustics applications

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    The digital waveguide mesh is a discrete-time simulation used to model acoustic wave propagation through a bounded medium. It can be applied to the simulation of the acoustics of rooms through the generation of impulse responses suitable for auralization purposes. However, large-scale three-dimensional mesh structures are required for high quality results. These structures must therefore be efficient and also capable of flexible boundary implementation in terms of both geometrical layout and the possibility for improved mesh termination algorithms. The general one-dimensional N-port boundary termination is investigated, where N depends on the geometry of the modeled domain and the mesh topology used. The equivalence between physical variable Kirchoff-model, and scattering-based wave-model boundary formulations is proved. This leads to the KW-hybrid one-dimensional N-port boundary-node termination, which is shown to be equivalent to the Kirchoff- and wave-model cases. The KW-hybrid boundary-node is implemented as part of a new hybrid two-dimensional triangular digital waveguide mesh. This is shown to offer the possibility for large-scale, computationally efficient mesh structures for more complex shapes. It proves more accurate than a similar rectilinear mesh in terms of geometrical fit, and offers significant savings in processing time and memory use over a standard wave-based model. The new hybrid mesh also has the potential for improved real-world room boundary simulations through the inclusion of additional mixed modeling algorithms

    Topological characterization of simple points by complex collapsibility

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    International audienceThinning is an image operation whose goal is to reduce object points in a "topology-preserving" way. Such points whose removal does not change the topology are called simple points and they play an important role in any thinning process. For efficient computation, local characterizations have been already studied based on the concept of point connectivity for two-and three-dimensional digital images. In this paper, we introduce a new topological characterization of simple points based on collapsibility of polyhedral complexes. We also study their topological characteristics and propose a linear thinning algorithm

    Topology of structure in the Sloan Digital Sky Survey: model testing

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    We measure the three-dimensional topology of large-scale structure in the Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured with unprecedented statistical accuracy. The sample size is now sufficiently large to allow the topology to be an important tool for testing galaxy formation models. For comparison, we make mock SDSS samples using several state-of-the-art N-body simulations: the Millennium run of Springel et al. (2005)(10 billion particles), Kim & Park (2006) CDM models (1.1 billion particles), and Cen & Ostriker (2006) hydrodynamic code models (8.6 billion cell hydro mesh). Each of these simulations uses a different method for modeling galaxy formation. The SDSS data show a genus curve that is broadly characteristic of that produced by Gaussian random phase initial conditions. Thus the data strongly support the standard model of inflation where Gaussian random phase initial conditions are produced by random quantum fluctuations in the early universe. But on top of this general shape there are measurable differences produced by non-linear gravitational effects (cf. Matsubara 1994), and biasing connected with galaxy formation. The N-body simulations have been tuned to reproduce the power spectrum and multiplicity function but not topology, so topology is an acid test for these models. The data show a ``meatball'' shift (only partly due to the Sloan Great Wall of Galaxies; this shift also appears in a sub-sample not containing the Wall) which differs at the 2.5\sigma level from the results of the Millennium run and the Kim & Park dark halo models, even including the effects of cosmic variance.Comment: 13 Apj pages, 7 figures High-resolution stereo graphic available at http://www.astro.princeton.edu/~dclayh/stereo50.ep

    Dimension on Discrete Spaces

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    In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by means of axioms, and the axioms are based on an obvious geometrical background. This work presents some discrete models of n-dimensional Euclidean spaces, n-dimensional spheres, a torus and a projective plane. It explains how to construct new discrete spaces and describes in this connection several three-dimensional closed surfaces with some topological singularities It also analyzes the topology of (3+1)-spacetime. We are also discussing the question by R. Sorkin [19] about how to derive the system of simplicial complexes from a system of open covering of a topological space S.Comment: 16 pages, 8 figures, Latex. Figures are not included, available from the author upon request. Preprint SU-GP-93/1-1. To appear in "International Journal of Theoretical Physics

    Axiomatic Digital Topology

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    The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any connected and non-trivial LF space is isomorphic to an abstract cell complex. The paper demonstrates that in an n-dimensional digital space only those of the (a, b)-adjacencies commonly used in computer imagery have analogs among the LF spaces, in which a and b are different and one of the adjacencies is the "maximal" one, corresponding to 3n\"i1 neighbors. Even these (a, b)-adjacencies have important limitations and drawbacks. The most important one is that they are applicable only to binary images. The way of easily using LF spaces in computer imagery on standard orthogonal grids containing only pixels or voxels and no cells of lower dimensions is suggested
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