3,067 research outputs found
Persistent homology for 3D reconstruction evaluation
Space or voxel carving is a non-invasive technique that is used to produce a 3D volume and can be used in particular for the reconstruction of a 3D human model from images captured from a set of cameras placed around the subject. In [1], the authors present a technique to quantitatively evaluate spatially carved volumetric representations of humans using a synthetic dataset of typical sports motion in a tennis court scenario, with regard to the number of cameras used. In this paper, we compute persistent homology over the sequence of chain complexes obtained from the 3D outcomes with increasing number of cameras. This allows us to analyze the topological evolution of the reconstruction process, something which as far as we are aware has not been investigated to date
3D Well-composed Polyhedral Complexes
A binary three-dimensional (3D) image is well-composed if the boundary
surface of its continuous analog is a 2D manifold. Since 3D images are not
often well-composed, there are several voxel-based methods ("repairing"
algorithms) for turning them into well-composed ones but these methods either
do not guarantee the topological equivalence between the original image and its
corresponding well-composed one or involve sub-sampling the whole image.
In this paper, we present a method to locally "repair" the cubical complex
(embedded in ) associated to to obtain a polyhedral
complex homotopy equivalent to such that the boundary of every
connected component of is a 2D manifold. The reparation is performed via
a new codification system for under the form of a 3D grayscale image
that allows an efficient access to cells and their faces
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
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Topological dualities in the Ising model
We relate two classical dualities in low-dimensional quantum field theory:
Kramers-Wannier duality of the Ising and related lattice models in
dimensions, with electromagnetic duality for finite gauge theories in
dimensions. The relation is mediated by the notion of boundary field theory:
Ising models are boundary theories for pure gauge theory in one dimension
higher. Thus the Ising order/disorder operators are endpoints of Wilson/'t
Hooft defects of gauge theory. Symmetry breaking on low-energy states reflects
the multiplicity of topological boundary states. In the process we describe
lattice theories as (extended) topological field theories with boundaries and
domain walls. This allows us to generalize the duality to non-abelian groups;
finite, semi-simple Hopf algebras; and, in a different direction, to finite
homotopy theories in arbitrary dimension
Designing a topological algorithm for 3D activity recognition
Voxel carving is a non-invasive and low-cost technique that is used for the reconstruction of a 3D volume from images captured from a set of cameras placed around the object of interest. In this paper we propose a method to topologically analyze a video sequence of 3D reconstructions representing a tennis player performing different forehand and backhand strokes with the aim of providing an approach that could be useful in other sport activities
Topological evaluation of volume reconstructions by voxel carving
Space or voxel carving [1, 4, 10, 15] is a technique for creating a three-dimensional reconstruction of an object from a series of two-dimensional images captured from cameras placed around the object at different viewing angles. However, little work has been done to date on evaluating the quality of space carving results. This paper extends the work reported in [8], where application of persistent homology was initially proposed as a tool for providing a topological analysis of the carving process along the sequence of 3D reconstructions with increasing number of cameras. We give now a more extensive treatment by: (1) developing the formal framework by which persistent homology can be applied in this context; (2) computing persistent homology of the 3D reconstructions of 66 new frames, including different poses, resolutions and camera orders; (3) studying what information about stability, topological correctness and influence of the camera orders in the carving performance can be drawn from the computed barcodes
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