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Filters
Construction of multiresolution triangular B-spline surfaces using hexagonal filters
2000
The Visual Computer
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We present multiresolution B-spline surfaces of arbitrary order defined over triangular domains. ...
The resulting basis functions are used to approximate triangular surfaces and possess many useful properties, such as multiresolution editing, local level of detail, continuity control, surface compression ...
Conclusion and Future Work We presented a novel approach for the construction of multiresolution B-spline surfaces over triangular domains. ...
doi:10.1007/s003710000073
fatcat:iecsy2xskvhxjdvgvlsmr7rrjy
Three Dimensional Face Recognition using Wavelet Decomposition of Range Images
2007
Proceedings of IEEE international conference on image processing
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In this technique, first the nose tip is automatically located on the range image, then the range data from a hexagonal region of interest around this landmark is decomposed using Barycentric wavelet kernels ...
The dimensionality of the extracted coefficients at each resolution level is reduced using principal component analysis (PCA). ...
[4] have constructed B-spline wavelets from tensor products of one dimensional B-spline wavelets and used them for multiresolution surface representation and compression. ...
doi:10.1109/icip.2007.4378912
dblp:conf/icip/JahanbinCBC07
fatcat:xd4edlvskjhq3cyzmyx53awj7u
Icosahedral Maps for a Multiresolution Representation of Earth Data
[article]
2016
Vision
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Our maps facilitate the execution of a multiresolution analysis on the ICON model. ...
We demonstrate this by applying a hexagonal version of the discrete wavelet transform in conjunction with our icosahedral maps to decompose ICON data to different levels of detail and to compress it via ...
We are therefore interested in a wavelet that is associated with the hexagonal lattice and makes use of the linear hexagonal box-spline kernel as the scaling function. ...
doi:10.2312/vmv.20161355
dblp:conf/vmv/JubairARCM16
fatcat:gel277dwtvhshldiv5cffmkwzy
BIORTHOGONAL WAVELETS WITH SIX-FOLD AXIAL SYMMETRY FOR HEXAGONAL DATA AND TRIANGLE SURFACE MULTIRESOLUTION PROCESSING
2011
International Journal of Wavelets, Multiresolution and Information Processing
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The constructed filter banks
have the desirable symmetry for hexagonal data processing, and they result in multiresolution
algorithms with the required symmetry for triangle surface processing ...
The filter banks with such a symmetry not only are
desirable for hexagonal image processing, but also can be used for triangle surface multiresolution
processing. ...
doi:10.1142/s0219691311004316
fatcat:izjjg7cisnf3tkpd3tih5gfitu
Highly symmetric3-refinement Bi-frames for surface multiresolution processing
2017
Applied Numerical Mathematics
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Multiresolution techniques for (mesh-based) surface processing have been developed and successfully used in surface progressive transmission, compression and other applications. ...
surface multiresolution processing. ...
The authors of [4] construct √ 3-refinement complex pre-wavelets (semi-orthogonal wavelets) on the hexagonal lattice with the scaling functions being the elementary polyharmonic hexagonal B-splines. ...
doi:10.1016/j.apnum.2017.02.005
fatcat:cffgih44cncvtdr76qe6snjgta
Optimal biorthogonal wavelet decomposition of wire-frame meshes using box splines, and its application to the hierarchical coding of 3-D surfaces
1999
IEEE Transactions on Image Processing
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Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces generated by box-splines. ...
Criterion of optimality is the minimization of the variance of the error difference between the original surface and its representation at each resolution level. ...
Triangular splines, on the other hand, can be used to construct smooth surfaces defined over arbitrary triangulation of the parameter domain. ...
doi:10.1109/83.736684
pmid:18262864
fatcat:uh4pcdyirvdnjomgfotw7et2am
Parameterization of triangle meshes over quadrilateral domains
2004
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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We use the parameterization for multiresolution Catmull-Clark remeshing and we illustrate two applications that take advantage of the resulting representation: interactive model editing and texture mapping ...
A combination of center-based clustering techniques is used to generate a partition of the model into regions suitable for remeshing. ...
Acknowledgements This work was performed as part of a collaboration with Dassault Systèmes. We would like to thank David Bonner and his team for their feedback and support. ...
doi:10.1145/1057432.1057459
fatcat:zm2tl4vf5fbvzdjd5na2vtsbta
Parameterization of Triangle Meshes over Quadrilateral Domains
[article]
2004
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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We use the parameterization for multiresolution Catmull-Clark remeshing and we illustrate two applications that take advantage of the resulting representation: interactive model editing and texture mapping ...
A combination of center-based clustering techniques is used to generate a partition of the model into regions suitable for remeshing. ...
Acknowledgements This work was performed as part of a collaboration with Dassault Systèmes. We would like to thank David Bonner and his team for their feedback and support. ...
doi:10.2312/sgp/sgp04/197-208
fatcat:nmpvclaqtnfszodzupokx7j5he
Ocean modeling on unstructured meshes
2013
Ocean Modelling
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Most of staggered discretizations on triangular or Voronoi meshes al-16 low spurious modes which are difficult to filter on unstructured meshes. ...
Among them, finite-volume models using the C-grid discretization on 9 Voronoi-centroidal meshes or cell-vertex quasi-B-grid discretization on trian-10 gular meshes work well and offer the multiresolution ...
Let us look from this perspective on the situation on triangular 600 and hexagonal meshes. ...
doi:10.1016/j.ocemod.2013.05.005
fatcat:4ayn5ogyhffwnjgihbr4exkkz4
A data porting tool for coupling models with different discretization needs
2014
Environmental Modelling & Software
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2014 pre-print arXiv:1407.2925v1 fatcat:3bi6mbq6unfdtcyvqa3wstvazi
The specific objective of this article is to provide the researchers a tool to build hexagonal raster using information from a rectangular raster data (e.g. GIS format), data porting. ...
The algorithm allows one to build the hexagonal raster with a cell size independent from the geometry of the rectangular raster. ...
Here, we compare ENO to filter reconstruction method (Catmull-Rom cubic spline (CRS), [9] ), well known and often used due to their efficiency in constructing smooth functions from discrete data. ...
doi:10.1016/j.envsoft.2014.09.012
fatcat:bsi7ef522vcw7nqo3qwpqzdxqq
Hybrid meshes
2002
Proceedings of the eighteenth annual symposium on Computational geometry - SCG '02
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A hybrid mesh is a multiresolution surface representation that combines advantages from regular and irregular meshes. ...
A preponderance of regular refinements allows for efficient data-structures and processing algorithms. ...
Since the Catmull-Clark scheme is a tensor product of two cubic 1D splines inside a regular patch, QMF filters are immediately generalized to the surface setting. ...
doi:10.1145/513400.513443
dblp:conf/compgeom/GuskovKSS02
fatcat:hoftd3v4jfa6ndnd5h6g2psaju
Subdivision methods for geometric design
2002
ChoiceReviews
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We wish to construct a function N(t) i n d-dimensional parameter domain using B. ...
= 1 2 A(z)B(z). 2 Using this theorem, the subdivision formula for the B-spline basis function N(t) of degree n can be derived. ...
doi:10.5860/choice.39-6470
fatcat:ink2sokkjrdddl6zyelcdwc2ni
Semi-regular 4-8 refinement and box spline surfaces
Proceedings 13th Brazilian Symposium on Computer Graphics and Image Processing (Cat. No.PR00878)
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It produces generalized four direction Box spline surfaces of class ½ . ...
In this paper we introduce a new mesh refinement method for subdivision surfaces. ...
Examples of surfaces produced by such scheme are constructed. The adaptation capabilities of the multiresolution 4-8 mesh representation is also demonstrated. ...
doi:10.1109/sibgra.2000.883905
dblp:conf/sibgrapi/Velho00
fatcat:3sgs5sjnnjeghdwgsssnaojhha
Hierarchical Grid Conversion
[article]
2016
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Hierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. ...
We also describe how patch-based data structures can be used for hexagonal cells and semiregular refinements. ...
One approach to construct multiresolution is to use surface subdivision (or refinement) [30, 31] . ...
doi:10.11575/prism/30991
fatcat:iohckuqx7bf5jgyrhg5ymedcgy
SUBDIVIDE AND CONQUER RESOLUTION
2006
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The second case is the use of Powell-Sabin splines to give a smooth multiresolution representation of a surface. ...
In this context we also illustrate the general method of construction of a spline wavelet basis using a lifting scheme. ...
The basis functions B ij constructed in this way are called B-splines (B stands for basis). The term was coined by Schoenberg [58] , the one we use here was given by Dierckx [17] . ...
doi:10.25643/bauhaus-universitaet.2909
fatcat:efplhybz6jgkbdsiwfighkfb34
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