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The arc tree: An approximation scheme to represent arbitrary curved shapes
1990
Computer Vision Graphics and Image Processing
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This paper introduces the arc tree, a hierarchical data structure to represent arbitrary curved shapes. ...
Each tree level is associated with an approximation of the curve; lower levels correspond to approximations of higher resolution. ...
In this paper, we develop this theme of hierarchy of detail, focusing on the arc tree, a balanced binary tree that serves as an approximation scheme to represent arbitrary curved shapes. ...
doi:10.1016/0734-189x(90)90006-h
fatcat:is43nmgykne6zbboiu2md7bi2q
Strip trees: a hierarchical representation for curves
1981
Communications of the ACM
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The price paid for the improved performance is an increased storage cost. This is approximately 4n, where n is the storage needed to represent the xy coordinates. ...
Lower levels in the tree correspond to finer resolution representations of the curve. ...
Acknowledgements The author wishes to thank R. Peet and P. Meeker for their work in the preparation of this document. Thanks also go to H.
Tanaka and D. ...
doi:10.1145/358645.358661
fatcat:go6sp5woevelrgeijkorojn52e
Branching Gaussian Processes with Applications to Spatiotemporal Reconstruction of 3D Trees
[article]
2016
arXiv
pre-print
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We apply this prior to fit 3D trees directly to image data, using an efficient scheme for approximate inference based on expectation propagation. ...
The BGP prior's Gaussian form allows us to approximately marginalize over 3D trees with a given model structure, enabling principled comparison between tree models with varying complexity. ...
We develop an approximate inference scheme based on expectation propagation that exploits the BGP prior's Gaussian form to approximate the posterior as multivariate Gaussian. ...
arXiv:1608.04045v1
fatcat:gazfb4yksvfjnpnjfbbcsai3ym
Convolution surfaces for arcs and quadratic curves with a varying kernel
2002
The Visual Computer
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Xunnian Yang for his help on arc spline approximation, and the anonymous reviewers for their constructive suggestions. ...
The authors are grateful to Andrei Sherstyuk for his help on convolution surfaces, Dr. ...
method to approximate an arbitrary space polynomial curve by an arc spline to within a prescribed tolerance appears to be an interesting future research direction. ...
doi:10.1007/s00371-002-0161-3
fatcat:mdi7vhyh7jcwfkyq2pejrgxjs4
Tree balancing for mesh simplification
[article]
2002
Eurographics State of the Art Reports
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The shape of the individual triangles is evaluated by Guéziec's compactness value. Finally, a plot showing the shape distribution of all triangles in the mesh is given. ...
A well-balanced hierarchy is essential for data structures that explicitly represent vertices as the corresponding paths through the simplification hierarchy. ...
Finally, we show how Guéziec's compactness value c is related to the shape plot diagram by a set of curves for c ¢ 0 1 0 9.
) to 6(c). ...
doi:10.2312/egs.20021010
fatcat:bqznplpkevf3dibvobc7vc2s6u
Compact Shape Trees: A Contribution to the Forest of Shape Correspondences and Matching Methods
[article]
2015
arXiv
pre-print
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Finally, we propose a number of shape recognition experiments to test the efficacy of our concept. ...
points on the shape's boundary to the rest of the sample points on the boundary. ...
Further, on C, an arbitrary point p i is chosen from which arc lengths, are measured, say, counterclockwise. ...
arXiv:1506.02923v1
fatcat:2prtw5tiqrav7kxefx3r7hstsm
Fiedler trees for multiscale surface analysis
2010
Computers & graphics
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Namely, we utilize the first nontrivial eigenfunction of the Laplace-Beltrami operator to recursively decompose the surface. For this reason we coin our surface decomposition the Fiedler tree. ...
In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. ...
ACKNOWLEDGEMENTS We thank the anonymous reviewers for their detailed feedback in improving the paper. We also thank Tiago Etiene Queiroz for help in creating surface meshes. ...
doi:10.1016/j.cag.2010.03.009
fatcat:chye552kcvdstnfjnfqvbbfo6i
The Impact of Baryonic Cooling on Giant Arc Abundances
2008
Astrophysical Journal
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Using ray tracing for simple analytic profiles, we demonstrate that the lensing cross section for producing giant arcs has distinct contributions due to arcs formed through image distortion only, and arcs ...
This last effect can potentially increase the number of lensing clusters by an extra 50%. ...
Finally, the dashed line represents the analytical solution for the point-source cross section of an SIS (not SIE). 9 We use the word ''merging'' to describe an arc formed by a source that overlaps the ...
doi:10.1086/589955
fatcat:qeilytqzx5dgpbnhcew4yewn6a
Analysis of Imaging Internal Defects in Living Trees on Irregular Contours of Tree Trunks Using Ground-Penetrating Radar
2021
Forests
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This method provides assistance to further study the defects of irregular living trees and prevents the misjudgment of targets as a result of hyperbolic distortion, resulting in a greater prospect of application ...
Finally, the influence of irregular detection routes on the geometry of the target reflection curve was investigated in detail through numerical simulations and actual experiments. ...
Conflicts of Interest: The authors declare no conflict of interest. ...
doi:10.3390/f12081012
fatcat:66y5tx4rszfpfpxxktgatcxwvy
Recognizing topological polynomials by lifting trees
[article]
2021
arXiv
pre-print
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If it is, the algorithm produces the Hubbard tree; otherwise, the algorithm produces the canonical obstruction. ...
We also give a new solution to Hubbard's twisted rabbit problem, and we state and solve several generalizations of Hubbard's problem where the number of post-critical points is arbitrarily large. ...
We are also grateful to Eko Hironaka and Sarah Koch for ...
arXiv:1906.07680v4
fatcat:i6diuuqa55emxpjamllm3genzm
Photogrammetric measurement of tree stems from vertical fisheye images
2016
Scandinavian Journal of Forest Research
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The XY coordinates of each stem define an arc shape, and these points are used as observations in a circle fitting by least squares. ...
The circle centre determines the tree position in a local reference system, and the estimated radius is used to calculate the DBH. ...
Acknowledgements The authors would like to thank the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and the Finnish Geospatial Research Institute (FGI) for assistance with the ground survey ...
doi:10.1080/02827581.2016.1273381
fatcat:ltxmlud2prejxjlvcfqedc5awi
Geometry-Experiment Algorithm for Steiner Minimal Tree Problem
2013
Journal of Applied Mathematics
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It is well known that the Steiner minimal tree problem is one of the classical nonlinear combinatorial optimization problems. ...
The approximate optimizing results are received by GEA and VEA for two examples. The validity of GEA was proved by solving practical problems in engineering, experiment, and comparative analysis. ...
Up to now they achieve the best approximation ratios of 1.644 in arbitrary metric and 1.267 in rectilinear plane, respectively. ...
doi:10.1155/2013/367107
fatcat:tn6rc3nn5rhqdjsien3ly3s5xy
A tool-path generation strategy for wire and arc additive manufacturing
2014
The International Journal of Advanced Manufacturing Technology
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This paper presents an algorithm to automatically generate optimal tool-paths for the wire and arc additive manufacturing (WAAM) process for a large class of geometries. ...
Abstract: This paper presents an algorithm to automatically generate optimal tool-paths for the wire and arc additive manufacturing (WAAM) process for a large class of geometries. ...
WAAM is by definition an arc-based process that uses either the Gas Tungsten Arc Welding (GTAW) or the Gas Metal Arc Welding (GMAW) process, and is considered to be a promising technology for fabricating ...
doi:10.1007/s00170-014-5808-5
fatcat:7unbttnxt5d3bbahjolrseoioa
Beamlet coder: a tree-based, hierarchical contour representation and coding method
2002
IIEEE International Conference on Acoustics Speech and Signal Processing
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Simulations are reported to evaluate the effectiveness of such an approach. This is a proof-of-concept study. The reported compression ratios are not the "best". ...
A quad-tree-based hierarchical contour representation and coding method is studied. This method is based on multiscale line segments-beamlets. ...
These works include discrete arcs [1] , polygonal curves [8] , and a lot more. Researchers have noticed that it is not necessary to exactly follow a curve given by a discrete image. ...
doi:10.1109/icassp.2002.1004929
fatcat:aajf54ld4zhlfnqntavykc5cym
Beamlet coder: A tree-based, hierarchical contour representation and coding method
2002
IEEE International Conference on Acoustics Speech and Signal Processing
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Simulations are reported to evaluate the effectiveness of such an approach. This is a proof-of-concept study. The reported compression ratios are not the "best". ...
A quad-tree-based hierarchical contour representation and coding method is studied. This method is based on multiscale line segments-beamlets. ...
These works include discrete arcs [1] , polygonal curves [8] , and a lot more. Researchers have noticed that it is not necessary to exactly follow a curve given by a discrete image. ...
doi:10.1109/icassp.2002.5745668
dblp:conf/icassp/ChenH02
fatcat:n5oqobf5prdh5b7e6qkxc2m75m
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