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Implicit B-Spline Surface Reconstruction

Mohammad Rouhani, Angel D. Sappa, Edmond Boyer
2015 IEEE Transactions on Image Processing  
Finally, a novel weighting technique has been introduced in order to blend small patches and smooth them in the overlapping regions.  ...  The whole framework is very fast and efficient and can handle large cloud of points with low computational cost.  ...  For all of these examples low degree IPs (d = 10 ∼ 20) and low resolution IBS (N = 20 ∼ 30) are used.  ... 
doi:10.1109/tip.2014.2366374 pmid:25373084 fatcat:as6qtv2p7rdeze225c2h2zreg4

Skeleton Marching-based Parallel Vascular Geometry Reconstruction Using Implicit Functions

Quan Qi, Qing-De Li, Yongqiang Cheng, Qing-Qi Hong
2019 International Journal of Automation and Computing  
A high-precision geometric vascular tree is then reconstructed by blending together these simple tubular-shaped implicit surfaces using the shapepreserving blending operations.  ...  These small point clouds are then fitted with a set of implicit surfaces in a parallel manner.  ...  To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.  ... 
doi:10.1007/s11633-019-1189-4 fatcat:gcsn744ylffkzb7i4edzxz2kw4

GPU-based rendering of sparse low-degree implicit surfaces

Takashi Kanai, Yutaka Ohtake, Hiroaki Kawata, Kiwamu Kase
2006 Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia - GRAPHITE '06  
In this paper, we propose a fast and a direct rendering method of SLIM (Sparse Low-degree IMplicit) surfaces using recent programmable GPUs.  ...  Geometric processes such as an intersection between a ray and an implicit surface and blending for PU (Partition of Unity) are performed in the fragment program on GPUs.  ...  Acknowledgements The models used in this paper are courtesy of California Institute of Technology (feline), the Stanford 3D Scanning Repository (armadillo, xyzrgb dragon, lucy, david), Aizu University  ... 
doi:10.1145/1174429.1174455 dblp:conf/graphite/KanaiOKK06 fatcat:pkie76dxs5colh4mmalnmgl2ve

Color Image Classification Through Fitting of Implicit Surfaces [chapter]

Raziel Álvarez, Erik Millán, Ricardo Swain-Oropeza, Alejandro Aceves-López
2004 Lecture Notes in Computer Science  
These color subspaces use implicit functions to create a bounding surface that will fit a set of characteristic color samples to define a particular color.  ...  The implicit subspace reconstruction allow to define clusters of arbitrary shape for a better approximation of the color distribution, reducing misclassification problems obtained when using predefined  ...  This work is part of a MsC Thesis at ITESM-CEM.  ... 
doi:10.1007/978-3-540-30498-2_68 fatcat:7iyyr2pvybb6tbpzviqjvm55za

High Precision Implicit modeling for Patient-specific Coronary Arteries

Qingqi Hong, Qingde Li, Beizhan Wang, Kunhong Liu, Quan Qi
2019 IEEE Access  
blending operation to form a complete coronary artery surface.  ...  High precision geometric reconstruction of patient-specific coronary arteries plays a crucial role in visual diagnosis, treatment decision-making, and the evaluation of the therapeutic effect of interventions  ...  In addition, a proper implicit blending operator is required to combine the set of implicit surfaces reconstructed locally corresponding to each sub-point cloud.  ... 
doi:10.1109/access.2019.2920113 fatcat:krdmibc6hzgnvgpvmufp6e73tq

Page 5695 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
The condition can be easily verified computationally.” 92j:65021 65D17 Kosters, Menno (NL-GRON) High-order implicit blending surfaces of low degree. Comput. Aided Geom.  ...  The extended method is able to produce blendings which are C*-continuous, where k may be chosen arbitrarily large. The blendings consist of piecewise algebraic surfaces of low degree.  ... 

N-ary implicit blends with topology control

C. Zanni, M. Gleicher, M.-P. Cani
2015 Computers & graphics  
Figure 1 : Topology control for implicit models can be used to prevent blending at distance and guarantee the topology of skeletonbased surfaces (left) or to control the dynamic topology of Manga-style  ...  Constructive implicit surfaces are attractive for modeling and animation because they seamlessly handle shapes with complex and dynamic topology.  ...  Low values of alpha lead to blend avoidance (objects deforming when they come in contact, and only blending when they overlap sufficiently). High values of alpha lead to blending at distance.  ... 
doi:10.1016/j.cag.2014.09.012 fatcat:yx6buha5ujakbbcon6ocq3lcpy

Reconstructing multi-scale variational partition of unity implicit surfaces with attributes

Ireneusz Tobor, Patrick Reuter, Christophe Schlick
2006 Graphical Models  
For the evaluation of the defining function of the implicit surface at the desired scale, we hierarchically blend together the surface parts of the inner nodes by using a family of functions called partition  ...  In a short discussion, we evaluate the advantages and drawbacks of our reconstruction method compared to existing reconstruction methods for implicit surfaces.  ...  Acknowledgements The models are courtesy of the Stanford 3D Scanning Repository (Bunny, Dragon) and Cyberware (Isis, Igea, Chameleon, Male).  ... 
doi:10.1016/j.gmod.2005.09.003 fatcat:yjoky2hl5bcanipmybjig7cabi

Using particles to sample and control more complex implicit surfaces

John C. Hart, Ed Bachta, Wojciech Jarosz, Terry Fleury
2005 ACM SIGGRAPH 2005 Courses on - SIGGRAPH '05  
We have developed, implemented and tested techniques for automatic and numerical differentiation of the implicit surface function.  ...  In 1994, Witkin and Heckbert developed a method for interactively modeling implicit surfaces by simultaneously constaining a particle system to lie on an implicit surface and vice-versa.  ...  Acknowledgments The core of our implicit surface library was coded by CS497JCH students Ed Bachta, Lennie Brown, Nate Carr, Jeff Decker, Bill Nagel and Steve Zelinka.  ... 
doi:10.1145/1198555.1198657 dblp:conf/siggraph/HartBJF05 fatcat:uwluohimmrfpnj5w52jaes3p6a

Splines and geometric modeling [chapter]

Chandrajit Bajaj
2004 Handbook of Discrete and Computational Geometry, Second Edition  
Lodha Lod92 constructed low degree surfaces with both parametric and implicit representations and investigated their properties.  ...  Second, for the same polynomial of degree n, implicit algebraic surfaces have more degrees of freedom n+3n+2n+1 6 ,1 compared with 2n+2n+1,1 degrees of freedom for rational parametric surfaces.  ... 
doi:10.1201/9781420035315.ch53 fatcat:e7evq2b77ba5lj3vxlcxwxxzda

Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces

John C. Hart
1996 The Visual Computer  
Sphere tracing is a new technique for rendering implicit surfaces that uses geometric distance.  ...  It is an efficient direct visualization system for the design and investigation of new implicit models.  ...  I was greatly helped with the task of tracking down and deriving the distances in the appendix by conversations with A. Barr, C. Bajaj, C. Gunn,  ... 
doi:10.1007/s003710050084 fatcat:3ojremjrvbcqrf7usvlkqwjizu

Sparse Low-degree Implicits with Applications to High Quality Rendering, Feature Extraction, and Smoothing [article]

Yutaka Ohtake, Alexander Belyaev, Marc Alexa
2005 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
We propose a new surface representation delivering an accurate approximation to a set of points scattered over a smooth surface by Sparse Low-degree IMplicits (SLIM).  ...  The SLIM surface representation consists of a sparse multi-scale set of nonconforming surface primitives which are blended along view rays during the rendering phase.  ...  We are grateful to the authors of [JDD03] for making the source code of their mesh smoothing method available online.  ... 
doi:10.2312/sgp/sgp05/149-158 fatcat:tuauzhkkvjh7rdckr3swompdfe

Accurate Color Classification and Segmentation for Mobile Robots [chapter]

Raziel Alvarez, Erik Millan, Alejandro Aceves-Lopez, Ricardo Swain-Oropez
2007 Mobile Robots: Perception & Navigation  
One advantage of the implicit surfaces technique is the simplicity to modify the scale parameter for spherical primitives, and the blending degree ρ, in order to modify the amount of samples identified  ...  Besides, they present the property of being able to blend with other surfaces in order to produce a single one.  ...  aspects of a single robot and even for a group of robots.  ... 
doi:10.5772/4772 fatcat:lrbepvcdhzeevigetptwb6hxni

Piecewise approximate implicitization: experiments using industrial data [chapter]

Mohamed F. Shalaby, Jan B. Thomassen, Elmar M. Wurm, Tor Dokken, Bert Jüttler
2006 Mathematics and Visualization  
As demonstrated by the results, piecewise approximate implicitization is able to handle surfaces arising in industrial applications.  ...  as a part of MAPLE.  ...  ML, in the case of Surface 7x7, failed to give an implicit representation due to the low degree specified.  ... 
doi:10.1007/978-3-540-33275-6_3 fatcat:ezbxdm3lgfe7ndxwc57gv2piai

An Introduction to Guided and Polar Surfacing [chapter]

Jörg Peters, Kȩstutis Karčiauskas
2010 Lecture Notes in Computer Science  
An example construction generating guided C 2 surfaces from patches of degree bi-3 highlights the power of the approach.  ...  A key ingredient of high-quality constructions is a good layout of the surface pieces. Polar layout simplifies design and is natural where a high number of pieces meet.  ...  The images were generated with the surface analysis tool BezierView. This work was supported by the National Science Foundation Grant 0728797.  ... 
doi:10.1007/978-3-642-11620-9_20 fatcat:d7ou4xj4sbhoraouioiw2sagdi
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