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A cascadic geometric filtering approach to subdivision

U. Diewald, S. Morigi, M. Rumpf
2002 Computer Aided Geometric Design  
The approach closely connects subdivision to surface fairing concerning the geometric smoothing and to cascadic multigrid methods with respect to the actual numerical procedure.  ...  Such an evolution can be understood as a natural geometric filter process where time corresponds to the filter width.  ...  This leads to a suitable geometric smoothing filter on the initial mesh.  ... 
doi:10.1016/s0167-8396(02)00150-4 fatcat:uknna2kltnagxaxs6nmi75hjrq

Page 7848 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
(D-DUIS; Duisburg) A cascadic geometric filtering approach to subdivision. (English summary) Comput. Aided Geom. Design 19 (2002), no. 9, 675-694.  ...  The approach closely connects subdivision to surface fairing as regards the geometric smoothing and to cascadic multigrid methods with respect to the actual numerical procedure.  ... 

A Discrete Approach to Multiresolution Curves and Surfaces

Luke J. Olsen, Faramarz F. Samavati
2008 2008 International Conference on Computational Sciences and Its Applications  
In this paper, we investigate a discrete approach to multiresolution construction for a variety of subdivision schemes, based only on the subdivision rules.  ...  Noting that a compact representation can only afford to store a subset of the detail information, our construction enforces a constraint between locally adjacent detail terms.  ...  Acknowledgments The authors would like to thank the reviewers for their helpful comments. This research was supported in part by the National Science and Engineering Research Council of Canada.  ... 
doi:10.1109/iccsa.2008.65 dblp:conf/iccsa/OlsenS08 fatcat:ho4lhl6nwrh37oblrkl3fi6xme

A Discrete Approach to Multiresolution Curves and Surfaces [chapter]

Luke Olsen, Faramarz Samavati
2009 Lecture Notes in Computer Science  
In this paper, we investigate a discrete approach to multiresolution construction for a variety of subdivision schemes, based only on the subdivision rules.  ...  Noting that a compact representation can only afford to store a subset of the detail information, our construction enforces a constraint between locally adjacent detail terms.  ...  Acknowledgments The authors would like to thank the reviewers for their helpful comments. This research was supported in part by the National Science and Engineering Research Council of Canada.  ... 
doi:10.1007/978-3-642-10649-1_20 fatcat:eah4ya77k5egtfhxb7ouzrkeru

Topological and functional partitioning in EM analysis: Application to wafer-level chip-scale harmonic filters

Sidina Wane, James C. Rautio, Volker Muhlhaus
2009 2009 IEEE MTT-S International Microwave Symposium Digest  
Simulation is compared to measurement at both component and function-block levels. Limits of partitioning assumptions in comparison with fullelectromagnetic model approaches are discussed.  ...  Aggressively applied function and geometry oriented partitioning is proposed for design and analysis of RF harmonic filters.  ...  are cascaded for the divide-andconquer approach.  ... 
doi:10.1109/mwsym.2009.5166023 fatcat:gmp2rvqi5vdtvdwhqx3z3ibcmq

An Exact, Complete and Efficient Computation of Arrangements of BÉzier Curves

I. Hanniel, R. Wein
2009 IEEE Transactions on Automation Science and Engineering  
In order to avoid the prohibitive running times incurred by an indiscriminate usage of exact arithmetic, we make extensive use of the geometric properties of Bézier curves for filtering.  ...  It employs the exact computation paradigm in order to handle all degenerate cases in a robust manner.  ...  The authors wish to thank Gershon Elber and Dan Halperin for their useful comments and encouragement.  ... 
doi:10.1109/tase.2009.2014734 fatcat:gs5lerhjvfdghfqezpjkkmy26u

An exact, complete and efficient computation of arrangements of Bézier curves

Iddo Hanniel, Ron Wein
2007 Proceedings of the 2007 ACM symposium on Solid and physical modeling - SPM '07  
In order to avoid the prohibitive running times incurred by an indiscriminate usage of exact arithmetic, we make extensive use of the geometric properties of Bézier curves for filtering.  ...  It employs the exact computation paradigm in order to handle all degenerate cases in a robust manner.  ...  The authors wish to thank Gershon Elber and Dan Halperin for their useful comments and encouragement.  ... 
doi:10.1145/1236246.1236282 dblp:conf/sma/HannielW07 fatcat:52lkfqmkrrhcdlw36fpdufeaxa

Interactive multi-resolution modeling on arbitrary meshes

Leif Kobbelt, Swen Campagna, Jens Vorsatz, Hans-Peter Seidel
1998 Proceedings of the 25th annual conference on Computer graphics and interactive techniques - SIGGRAPH '98  
Within a multi-resolution framework, subdivision schemes provide a set of basis functions φ i¢ j £ φ ¤ 2 i ¥ § ¦ j¨which are suitable to build a cascade of nested spaces V i £ span ¤ © © u¤ v¤ n plus an  ...  ., the constrained minimization of discrete energy functionals, we obtain very fast mesh smoothing algorithms which are able to reduce noise from a geometrically specified frequency band in a multiresolution  ...  Due to the local smoothing properties of the fairing operators, we are able to define a geometric threshold for the wavelength up to which a low-pass filter should remove noise.  ... 
doi:10.1145/280814.280831 dblp:conf/siggraph/KobbeltCVS98 fatcat:zadxavkr4bdh5ml3ykkb7qww5y

Multiresolution analysis for surfaces of arbitrary topological type

Michael Lounsbery, Tony D. DeRose, Joe Warren
1997 ACM Transactions on Graphics  
Whereas previous two-dimensional methods were restricted to functions defined on ‫ޒ‬ 2 , the subdivision wavelets developed here may be applied to functions defined on compact surfaces of arbitrary topological  ...  In this article, we present a new class of wavelets, based on subdivision surfaces, that radically extends the class of representable functions.  ...  This cascade of analysis steps, referred to as a filter bank algorithm, culminates with the coarsest-level representation in Figure 1 (c), together with wavelet coefficients at each level.  ... 
doi:10.1145/237748.237750 fatcat:mxlign3or5glhaiqojlpqevjty

Integrated profiling of three dimensional cell culture models and 3D microscopy

Cemal Cagatay Bilgin, Sun Kim, Elle Leung, Hang Chang, Bahram Parvin
2013 Computer applications in the biosciences : CABIOS  
The strategy uses a cascade of geometric filters that are insensitive to spatial nonuniformity and partitions a clump of nuclei based on the grouping of points of maximum curvature at the interface of  ...  Motivation: Our goal is to develop a screening platform for quantitative profiling of colony organizations in 3D cell culture models.  ...  ACKNOWLEDGEMENTS We would like to thank Michelle Scott for her invaluable assistance in microscopy and the Bissell lab for biological reagents. Conflicts of Interest: none declared.  ... 
doi:10.1093/bioinformatics/btt535 pmid:24045773 pmcid:PMC3834800 fatcat:uxeukidjszezpe4ekfeyq4ymby

Spherical manifolds for adaptive resolution surface modeling

Cindy M. Grimm
2005 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia - GRAPHITE '05  
To manipulate these surfaces we describe a user-interface based on multiple, overlapping subdivision-style meshes.  ...  Figure 1: Creating a surface with spherical topology. a) Sketch mesh (22 faces) and first subdivision level mesh embedded in the spherical domain. b) Initial geometry of sketch mesh and resulting surface  ...  Acknowledgements Thanks to the reviewers for their helpful comments. Funded in part by NSF grant CCF 0429856 and CCF 0238062.  ... 
doi:10.1145/1101389.1101425 dblp:conf/graphite/Grimm05 fatcat:ywze53pnizajrcpcppddwtwa6y

Deep Learning 3D Shapes Using Alt-az Anisotropic 2-Sphere Convolution

Min Liu, Fupin Yao, Chiho Choi, Ayan Sinha, Karthik Ramani
2019 International Conference on Learning Representations  
A cascade set of geodesic disk filters rotate on the 2-sphere and collect spherical patterns and so to extract geometric features for various 3D shape analysis tasks.  ...  One of the main challenge in applying CNNs to 3D shape analysis is how to define a natural convolution operator on noneuclidean surfaces.  ...  The stride is applied accordingly to the subdivision frequency f. Fig. 3(c ) shows the icosahedron in different subdivision frequencies 1, 2, 4 and 8.  ... 
dblp:conf/iclr/LiuYCSR19 fatcat:ucvmvjnufvc4ni3vqddiv6w5qi

Infimaximal Frames: A Technique for Making Lines Look Like Segments

Kurt Mehlhorn, Michael Seel
2003 International journal of computational geometry and applications  
The technique can also be used to extend implementations of planar subdivisions to subdivisions with many unbounded faces.  ...  Many geometric algorithms that are usually formulated for points and segments generalize easily to inputs also containing rays and lines.  ...  Alternative Approaches We discuss projective geometry and the inclusion of the scene in a concrete geometric frames.  ... 
doi:10.1142/s0218195903001141 fatcat:teb444s7ufc7tkkzrevq2xnm6e

Rapid Detection of Many Object Instances [chapter]

Suwan Tongphu, Naddao Thongsak, Matthew N. Dailey
2009 Lecture Notes in Computer Science  
In a test on a challenging car detection problem using a relatively small training set, our implementation dramatically outperforms the detection performance of a standard AdaBoost cascade using Haar-like  ...  Our approach consists of first calculating frequency vectors for discrete feature vector clusters (visual words) within a sliding window as a representation of the image patch.  ...  In both the image patch and sparse feature approaches, a variety of ways to model geometric constraints between object parts have been proposed. Fergus et al.'  ... 
doi:10.1007/978-3-642-04697-1_40 fatcat:5eywzqqduvabjhfayvs3nrvysm

Scattering Parameters Characterization of Periodically Nonuniform Transmission Lines With a Perturbative Technique

Xiaokang Liu, Xinglong Wu, Flavia Grassi, Giordano Spadacini, Dries Vande Ginste, Sergio A. Pignari
2020 IEEE transactions on electromagnetic compatibility (Print)  
The procedure is based on a recentlyproposed perturbative technique, which is proven to be computationally more efficient than standard solution approaches, which are based on line subdivision into uniform  ...  cascaded sections (UCS).  ...  based on line subdivision into uniform cascaded sections (UCS).  ... 
doi:10.1109/temc.2020.2972844 fatcat:x3gziyje3rbwxbhe6fpkkawzoi
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