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The number of views of piecewise-smooth algebraic objects [chapter]

Sylvain Petitjean
1995 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

3-D Surface Segmentation of Free-Form Objects Using Implicit Algebraic Surfaces

Rachid Benlamri, Yousuf Al-Marzooqi
2003 International Conference on Digital Image Computing: Techniques and Applications  
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

Page 3469 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
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.  ... 

MCMC-Based Multiview Reconstruction of Piecewise Smooth Subdivision Curves with a Variable Number of Control Points [chapter]

Michael Kaess, Rafal Zboinski, Frank Dellaert
2004 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

Reconstruction of objects with jagged edges through Rao-Blackwellized fitting of piecewise smooth subdivision curves

M. Kaess, F. Dellaert
2003 First IEEE International Workshop on Higher-Level Knowledge in 3D Modeling and Motion Analysis, 2003. HLK 2003.  
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

Differential geometry on simplicial spaces

Michael A. Penna
1975 Transactions of the American Mathematical Society  
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

Differential Geometry on Simplicial Spaces

Michael A. Penna
1975 Transactions of the American Mathematical Society  
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

A Study On Applications And Techniques Of Surface Re- Construction

Subhanga Kishore Das, Sabyasachi Pattnaik
2012 International journal of computer and communication technology  
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

New ideas about multiplication of tensorial distributions [article]

Jozef Skakala
2011 arXiv   pre-print
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

Dequantization of real algebraic geometry on logarithmic paper [article]

Oleg Viro
2000 arXiv   pre-print
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

Book Review: Embeddings in manifolds

James W. Cannon
2011 Bulletin of the American Mathematical Society  
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

Page 5591 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
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  ... 

Implicit Reconstruction of Vasculatures Using Bivariate Piecewise Algebraic Splines

Qingqi Hong, Qingde Li, Jie Tian
2012 IEEE Transactions on Medical Imaging  
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

Reconstructing Surfaces and Functions on Surfaces from Unorganized Three-Dimensional Data

C. L. Bajaj, F. Bernardini, G. Xu
1997 Algorithmica  
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

Homological techniques for the analysis of the dimension of triangular spline spaces

Bernard Mourrain, Nelly Villamizar
2013 Journal of symbolic computation  
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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