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Construction of multiresolution triangular B-spline surfaces using hexagonal filters

A. Dreger, M.H. Gross, J. Schlegel
2000 The Visual Computer  
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

Sina Jahanbin, Hyohoon Choi, Alan C. Bovik, Kenneth R. Castleman
2007 Proceedings of IEEE international conference on image processing  
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]

Mohammad Imrul Jubair, Usman Alim, Niklas Röber, John Clyne, Ali Mahdavi-Amiri
2016 Vision  
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

QINGTANG JIANG
2011 International Journal of Wavelets, Multiresolution and Information Processing  
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

Qingtang Jiang, Dale K. Pounds
2017 Applied Numerical Mathematics  
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

S. Malassiotis, M.G. Strintzis
1999 IEEE Transactions on Image Processing  
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

Ioana Boier-Martin, Holly Rushmeier, Jingyi Jin
2004 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
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]

Ioana Boier-Martin, Holly Rushmeier, Jingyi Jin
2004 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
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

S. Danilov
2013 Ocean Modelling  
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

S. Ion, D. Marinescu, S.G. Cruceanu, V. Iordache
2014 Environmental Modelling & Software  
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

Igor Guskov, Andrei Khodakovsky, Peter Schröder, Wim Sweldens
2002 Proceedings of the eighteenth annual symposium on Computational geometry - SCG '02  
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  
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

L. Velho
Proceedings 13th Brazilian Symposium on Computer Graphics and Image Processing (Cat. No.PR00878)  
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]

Ali Mahdavi-Amiri, Erika Harrison, Faramarz Samavati, University Of Calgary, University Of Calgary
2016
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

Adhemar Bultheel, M. Jansen, J Maes, W Van Aerschot, E. Vanraes
2006
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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