92,743 research outputs found
Simultaneous Shape Tracking of Multiple Deformable Linear Objects with Global-Local Topology Preservation
This work presents an algorithm for tracking the shape of multiple entangling
Deformable Linear Objects (DLOs) from a sequence of RGB-D images. This
algorithm runs in real-time and improves on previous single-DLO tracking
approaches by enabling tracking of multiple objects. This is achieved using
Global-Local Topology Preservation (GLTP). This work uses the geodesic distance
in GLTP to define the distance between separate objects and the distance
between different parts of the same object. Tracking multiple entangling DLOs
is demonstrated experimentally. The source code is publicly released.Comment: 3 pages, 3 figures, presented at the 3rd Workshop on Representing and
Manipulating Deformable Objects at the IEEE International Conference on
Robotics and Automation. Video presentation [https://youtu.be/hfiqwMxitqA].
3rd Workshop on Representing and Manipulating Deformable Objects
[https://deformable-workshop.github.io/icra2023/
Describing images using qualitative models and description logics
Special Issue:Â Qualitative spatial and temporal reasoning: emerging applications, trends, and directionsOur approach describes any digital image qualitatively by detecting regions/objects inside it and describing their visual characteristics (shape and colour) and their spatial characteristics (orientation and topology) by means of qualitative models. The description obtained is translated into a description logic (DL) based ontology, which gives a formal and explicit meaning to the qualitative tags representing the visual features of the objects in the image and the spatial relations between them. For any image, our approach obtains a set of individuals that are classified using a DL reasoner according to the descriptions of our ontolog
Orbispaces and their Mapping Spaces via Groupoids: A Categorical Approach
In this paper, we give an accessible introduction to the theory of orbispaces
via groupoids. We define a certain class of topological groupoids, which we
call orbigroupoids. Each orbigroupoid represents an orbispace, but just as with
orbifolds and Lie groupoids, this representation is not unique: orbispaces are
Morita equivalence classes of orbigroupoids. We show how to formalize this
equivalence by defining the category of orbispaces as a bicatecory of fractions
from the category of orbigroupoids. We focus particularly on laying the
groundwork for future work in creating mapping objects for orbispaces which are
themselves orbispaces, and providing a concrete description of how this mapping
space construction will get its orbispace structure. Throughout this paper, we
illustrate our definitions and results with numerous examples which we hope
will be useful in seeing how the categorical point of view is used to study
these spaces
Comparing hierarchies of total functionals
In this paper we consider two hierarchies of hereditarily total and
continuous functionals over the reals based on one extensional and one
intensional representation of real numbers, and we discuss under which
asumptions these hierarchies coincide. This coincidense problem is equivalent
to a statement about the topology of the Kleene-Kreisel continuous functionals.
As a tool of independent interest, we show that the Kleene-Kreisel functionals
may be embedded into both these hierarchies.Comment: 28 page
Rational S^1-equivariant elliptic cohomology
For each elliptic curve A over the rational numbers we construct a 2-periodic
S^1-equivariant cohomology theory E whose cohomology ring is the sheaf
cohomology of A; the homology of the sphere of the representation z^n is the
cohomology of the divisor A(n) of points with order dividing n. The
construction proceeds by using the algebraic models of the author's AMS Memoir
``Rational S^1 equivariant homotopy theory.'' and is natural and explicit in
terms of sheaves of functions on A.
This is Version 5.2 of a paper of long genesis (this should be the final
version). The following additional topics were first added in the Fourth
Edition:
(a) periodicity and differentials treated
(b) dependence on coordinate
(c) relationship with Grojnowksi's construction and, most importantly,
(d) equivalence between a derived category of O_A-modules and a derived
category of EA-modules. The Fifth Edition included
(e) the Hasse square and
(f) explanation of how to calculate maps of EA-module spectra
4D topology optimization: Integrated optimization of the structure and self-actuation of soft bodies for dynamic motions
Topology optimization is a powerful tool utilized in various fields for
structural design. However, its application has primarily been restricted to
static or passively moving objects, mainly focusing on hard materials with
limited deformations and contact capabilities. Designing soft and actively
moving objects, such as soft robots equipped with actuators, poses challenges
due to simulating dynamics problems involving large deformations and intricate
contact interactions. Moreover, the optimal structure depends on the object's
motion, necessitating a simultaneous design approach. To address these
challenges, we propose "4D topology optimization," an extension of
density-based topology optimization that incorporates the time dimension. This
enables the simultaneous optimization of both the structure and self-actuation
of soft bodies for specific dynamic tasks. Our method utilizes multi-indexed
and hierarchized density variables distributed over the spatiotemporal design
domain, representing the material layout, actuator layout, and time-varying
actuation. These variables are efficiently optimized using gradient-based
methods. Forward and backward simulations of soft bodies are done using the
material point method, a Lagrangian-Eulerian hybrid approach, implemented on a
recent automatic differentiation framework. We present several numerical
examples of self-actuating soft body designs aimed at achieving locomotion,
posture control, and rotation tasks. The results demonstrate the effectiveness
of our method in successfully designing soft bodies with complex structures and
biomimetic movements, benefiting from its high degree of design freedom.Comment: 36 pages, 27 figures; for supplementary video, see
https://youtu.be/sPY2jcAsNY
Requirements for Topology in 3D GIS
Topology and its various benefits are well understood within the context of 2D Geographical Information Systems. However, requirements in three-dimensional (3D) applications have yet to be defined, with factors such as lack of users' familiarity with the potential of such systems impeding this process. In this paper, we identify and review a number of requirements for topology in 3D applications. The review utilises existing topological frameworks and data models as a starting point. Three key areas were studied for the purposes of requirements identification, namely existing 2D topological systems, requirements for visualisation in 3D and requirements for 3D analysis supported by topology. This was followed by analysis of application areas such as earth sciences and urban modelling which are traditionally associated with GIS, as well as others including medical, biological and chemical science. Requirements for topological functionality in 3D were then grouped and categorised. The paper concludes by suggesting that these requirements can be used as a basis for the implementation of topology in 3D. It is the aim of this review to serve as a focus for further discussion and identification of additional applications that would benefit from 3D topology. © 2006 The Authors. Journal compilation © 2006 Blackwell Publishing Ltd
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