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Lecture Notes in Computer Science
In this paper, we study the complexity of aspect graphs of piecewise-smooth algebraic objects using the modern tools of algebraic geometry, i.e. intersection theory, multiple-point theory and enumerative ... We give a bound on the number of different appearances of such objects, an indication of the computational complexity of aspect graphs. ... Using Thom-Milnor's bound, we may conclude that a piecewise-smooth algebraic object has Ç´Ò ½¾ AE ½¾ µ views if orthographic projection is assumed (the viewpoint space may be modelled by a unit view sphere ...doi:10.1007/3-540-59042-0_106 fatcat:jvsl3f4cpvalhgcf7acfl4tas4
The aim is to derive a surface description of objects that may vary in shape and complexity without any restriction on the type of surfaces on the object. ... The proposed technique, not only reduces the number of used patches, but also preserves surface-depth and orientation continuity. ... This is because differential geometry is a theory for smooth differentiable surfaces, while free-form objects are not entirely smooth but piecewise smooth. ...dblp:conf/dicta/BenlamriA03 fatcat:unnc3ze46jch3ngfoahpctz7ke
The size of the view graph of a piecewise smooth algebraic surface N with transverse self- intersection curves and isolated triple-points and cross-caps is O(nK dim? ... (BR-SPL3-IC; Sao Carlos) Notes on the complexity of exact view graph algorithms for piecewise smooth algebraic surfaces. (English summary) Discrete Comput. Geom. 20 (1998), no. 2, 205-229. ...
Lecture Notes in Computer Science
We apply this general methodology to the reconstruction of piecewise smooth curves from multiple calibrated views, in which the object is segmented from the background using a Markov random field approach ... We investigate the automated reconstruction of piecewise smooth 3D curves, using subdivision curves as a simple but flexible curve representation. ... Acknowledgments We would like to thank Peter Presti from IMTC for providing the shard images and Zia Khan for valuable discussions on reversible jump MCMC. ...doi:10.1007/978-3-540-24672-5_26 fatcat:3nkap6pihzhzthuwavcecin7yi
We apply this general methodology to multi-view reconstruction of piecewise smooth curves from multiple calibrated views in which the object has been segmented from the background. ... In some applications objects are known to have nonsmooth or "jagged" edges, which are not well approximated by smooth curves. ... Acknowledgments We would like to thank Peter Presti from IMTC for providing the shard images. ...doi:10.1109/hlk.2003.1240857 dblp:conf/hlk/KaessD03 fatcat:lhylqkeovza53olzq2onxrnwuq
The cosimplicial bundle t(M) is a cotangent object since there is an .4(Af)-module isomorphism between the module E(M) of global piecewise smooth one-forms on M and the module Y(M, t(M)) of global sections ... To every simplicial space M a cosimplicial bundle t(M) over M is associated; t(M) is the cotangent object of M since there is an isomorphism between the module of global piecewise smooth one-forms on M ... The second approach is indirect: U is viewed as being patched together and A(U) is viewed as an algebra of compatible tuples of piecewise smooth functions defined on the components of U. ...doi:10.1090/s0002-9947-1975-0391146-5 fatcat:2r43facdwjcljbixvxxttaag3i
The cosimplicial bundle t(M) is a cotangent object since there is an .4(Af)-module isomorphism between the module E(M) of global piecewise smooth one-forms on M and the module Y(M, t(M)) of global sections ... To every simplicial space M a cosimplicial bundle t(M) over M is associated; t(M) is the cotangent object of M since there is an isomorphism between the module of global piecewise smooth one-forms on M ... The second approach is indirect: U is viewed as being patched together and A(U) is viewed as an algebra of compatible tuples of piecewise smooth functions defined on the components of U. ...doi:10.2307/1997109 fatcat:yealwvzg6jastcxelshygdy2ly
This paper describes a general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points. ... The surface reconstruction method has three major phases: Initial surface estimation, Mesh optimization, and piecewise smooth surface optimization. ... Phase 3: piecewise smooth surface optimization: In phase 3, the surface representation is changed from a piecewise linear one (meshes) to a piecewise smooth one. ...doi:10.47893/ijcct.2012.1156 fatcat:szsarzgnibdhvejv6e7m3ngtly
The big advantage of our approach lies also in the fact that it brings a physical insight into the mathematical concepts used and naturally leads to formulation of physics on (what we call) piecewise smooth ... Significant progress has been made through the concept of Colombeau algebras, and the construction of full Colombeau algebras on differential manifolds for arbitrary tensors. ... My research was supported by a Victoria University Vice-Chancellor's Strategic Research Scholarschip, and by the Marsden Fund administred by the Royal Society of New Zealand. ...arXiv:0908.0379v5 fatcat:lkarzqdu7fcmjclvd44gxrlsui
The corresponding deformation can be viewed as a quantization, in which the broken line is a classical object and the curves are quantum. ... On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover, the broken lines can be obtained as limits of those curves. ... of algebraic geometry over R and piecewise linear geometry. ...arXiv:math/0005163v3 fatcat:mvg2djdur5hi5pjtbgzjfgdoti
It seems to us that a more reasonable point of view is to accept these infinitely knotted embeddings as a necessary consequence of the completion process that passes from the rational numbers to the real ... Edwards noted that the method can be reinterpreted in terms of an infinite 2-dimensional complex that models the algebraic object that is a commutator of commutators of commutators, infinitely. D. R. ...doi:10.1090/s0273-0979-2011-01320-9 fatcat:4jt4mqbeffd3rbgc6bhwms7ak4
Simulation results showing the comparison between the actual and estimated pose parameters are included.” 96i1:68084 68U05 14399 14Q99 68U10 Petitjean, Sylvain The number of views of piecewise-smooth algebraic ... In this paper, we study the complex- ity of aspect graphs of piecewise-smooth algebraic objects using the modern tools of algebraic geometry, i.e. intersection theory, multiple-point theory and enumerative ...
In addition, both the qualitative and the quantitative validations have been performed to show that the reconstructed vessel geometry is of high accuracy and smoothness. ... With the proposed technique, an implicit geometry representation of the vascular tree can be accurately constructed based on the voxels extracted directly from the surface of a certain vascular structure ... ACKNOWLEDGMENT The authors would like to thank all the anonymous reviewers for their constructive comments. ...doi:10.1109/tmi.2011.2172455 pmid:22020672 fatcat:butr7f5t6nad5lq53gi2yudj7a
The problem of automatically reconstructing from this data a topologically consistent and geometrically accurate model of the object and of the sampled scalar field is the subject of this paper. ... It generates a representation of the surface and the field based on Bernstein-Bézier polynomial implicit patches (A-patches), that are guaranteed to be smooth and single-sheeted. ... The number of patches in the smooth reconstruction; (6) The error, as percentage of the diameter of the object. ...doi:10.1007/pl00014418 fatcat:uxxdhntxrvg6zo65pgqik7ssf4
The spline space C_k^r(Δ) attached to a subdivided domain Δ of ^d is the vector space of functions of class C^r which are polynomials of degree < k on each piece of this subdivision. ... The construction makes also possible to get a short proof for the dimension formula when k> 4r+1, and the same method we use in this proof yields the dimension straightaway for many other cases. ... ACKNOWLEDGEMENTS This thesis wouldn't have been concluded without the help of many persons. The purpose of these lines it to try to express my deep gratitude to all of them. ...doi:10.1016/j.jsc.2012.10.002 fatcat:3dmhmifvxrakdhjbwauk7ravwi
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