3,067 research outputs found

    Persistent homology for 3D reconstruction evaluation

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    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

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    A binary three-dimensional (3D) image II 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 Q(I)Q(I) (embedded in R3\mathbb{R}^3) associated to II to obtain a polyhedral complex P(I)P(I) homotopy equivalent to Q(I)Q(I) such that the boundary of every connected component of P(I)P(I) is a 2D manifold. The reparation is performed via a new codification system for P(I)P(I) under the form of a 3D grayscale image that allows an efficient access to cells and their faces

    A graph-based mathematical morphology reader

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    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

    Designing a topological algorithm for 3D activity recognition

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    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

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    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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