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Surface compression using over-determined Laplacian approximation
2007
Advanced Signal Processing Algorithms, Architectures, and Implementations XVII
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Our approach first approximates the uncompressed terrain using an over-determined system of linear equations based on the Laplacian partial differential equation. ...
We describe a surface compression technique to lossily compress elevation datasets. ...
Hierarchical Triangulation Hierarchical Triangulation (HT) is a hierarchical triangle-based model for representing surfaces over sampled data proposed by De Floriani. 6 Similar to TIN, HT is based on subdividing ...
doi:10.1117/12.741224
fatcat:ow24ny63v5evbm2iw66mn67vta
Efficient preconditioning of laplacian matrices for computer graphics
2013
ACM Transactions on Graphics
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This speedup is achieved by the new method's ability to reduce the condition number of irregular Laplacian matrices as well as homogeneous systems. ...
It can therefore be used for a wide variety of computational photography problems, as well as several 3D mesh processing tasks, without the need to carefully match the algorithm to the problem characteristics ...
Figure 9 : 9 Example of mesh smoothing using an in homogenous Laplacian based on an inverse distance measure between vertices. ...
doi:10.1145/2461912.2461992
fatcat:zdth6wbvqvbrxozxklnw4zkowa
Compressing dynamic meshes with geometric laplacians
2014
Computer graphics forum (Print)
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We focus on sequences of triangle meshes with shared connectivity, avoiding the necessity of having a skinning structure. ...
A discrete geometric Laplacian of this average surface is then used to encode the coefficients that describe the trajectories of the mesh vertices. ...
with the vertices of a triangle mesh. ...
doi:10.1111/cgf.12304
fatcat:gokznjyhsfa3bcsn3s725afmdy
Hierarchical representation and coding of surfaces using 3-D polygon meshes
2001
IEEE Transactions on Image Processing
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Complete correspondence between triangles at each level is identified, resulting to an efficient hierarchical representation of the mesh. ...
Index Terms-Adaptive triangulation, minimum variance interpolation filters, quincunx sampling, 3-D hierarchical mesh representation, 3-D mesh compression. ...
Compression of the mesh information is necessary for efficient transmission and storage. 3) Progressive Transmission of the Mesh Information: Hierarchical representation of mesh information may be used ...
doi:10.1109/83.935030
pmid:18255531
fatcat:657oag635jdnrkz4llp7uegnru
Metrics for Image Surface Approximation Based on Triangular Meshes
2018
Image Analysis and Stereology
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Experiments on several data sets are performed to compare the quality of the resulting meshes. ...
The choice of metrics for building the triangular meshes is crucial to produce high quality models. ...
Rossignac (1999) developed a method for compressing 3D triangular meshes using 1.3 and 2 bits per triangle. ...
doi:10.5566/ias.1591
fatcat:ikj3xtjybzbi3esq33yfu2liaa
Steklov Spectral Geometry for Extrinsic Shape Analysis
[article]
2018
arXiv
pre-print
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large-scale meshes despite the density of the Dirichlet-to-Neumann discretization. ...
Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification ...
Meshes are courtesy of the AIM@Shape Repository, the TOSCA project, the Stanford Computer Graphics Laboratory, MIT, and the Princeton Segmentation Benchmark. ...
arXiv:1707.07070v2
fatcat:5m4jogjqyndvdeyvgurgdp35ki
Spectral mesh processing
2009
ACM SIGGRAPH ASIA 2009 Courses on - SIGGRAPH ASIA '09
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Geometry compression Karni and Gotsman [KG00c] proposed an approach to compress the geometry of triangle meshes. Firstly, the set of eigenvectors of the Tutte Laplacian is computed. ...
We present Laplacian smoothing and show how spectral processing based on 1D discrete Laplace operators can perform smoothing as well as compression. ...
doi:10.1145/1665817.1665834
dblp:conf/siggraph/LevyZ09
fatcat:3owm6apojnb5bi35prxd7mixj4
Spectral mesh processing
2010
ACM SIGGRAPH 2010 Courses on - SIGGRAPH '10
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Geometry compression Karni and Gotsman [KG00c] proposed an approach to compress the geometry of triangle meshes. Firstly, the set of eigenvectors of the Tutte Laplacian is computed. ...
We present Laplacian smoothing and show how spectral processing based on 1D discrete Laplace operators can perform smoothing as well as compression. ...
doi:10.1145/1837101.1837109
dblp:conf/siggraph/LevyZ10
fatcat:o2vdjdhr7vbg7pft2spbd5v72y
Mesh-Based Motion-Compensated Interpolation for Side Information Extraction in Distributed Video Coding
2006
2006 International Conference on Image Processing
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A hybrid block-based and mesh-based solution addressing the problem of motion discontinuities and occlusions is also described. ...
1 This paper addresses the problem of side information generation in distributed video compression (DVC) schemes. ...
Acknowledgements We are thankful to the IST and the Discover software development team for having provided the block-based DVC codec. ...
doi:10.1109/icip.2006.313175
dblp:conf/icip/KubasovG06
fatcat:cg2k5u6kizc65entgdqktmhypu
Compression of dynamic 3D point clouds using subdivisional meshes and graph wavelet transforms
2016
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
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Compression of such datasets is challenging because of the lack of efficient techniques for exploiting spatial and temporal correlations between the attributes. ...
In our approach, we create an intermediate high-resolution representation of the point clouds, using consistent subdivisional triangular meshes, that captures all the features of the underlying object ...
In particular, this constraint allows us to efficiently compute the mesh representation in a hierarchical manner from a very coarse base Fig. 1 : Subdivision of a triangular mesh mesh, which is the only ...
doi:10.1109/icassp.2016.7472901
dblp:conf/icassp/AnisCO16
fatcat:vk5txghivbd73di457uemd65zu
Knot Optimization for Biharmonic B-splines on Manifold Triangle Meshes
2017
IEEE Transactions on Visualization and Computer Graphics
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The new representation also facilitates optimization-driven knot selection for constructing biharmonic B-splines on manifold triangle meshes. ...
We prove that biharmonic B-splines have an equivalent representation, which is solely based on a linear combination of Green's functions of the bi-Laplacian operator. ...
Acknowledgements: We thank the reviewers for their detailed and constructive comments, which help us to improve the quality of the paper significantly. ...
doi:10.1109/tvcg.2016.2605092
pmid:27608469
fatcat:2jeowy73y5b77ijn7cxnhi73ge
A remeshing approach to multiresolution modeling
2004
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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The high regularity of the remeshed base surface further removes numerical problems caused by mesh degeneracies and results in a better discretization of the Laplacian operator. ...
In several approaches the modified base surface is computed by solving a linear system of discretized Laplacians. ...
As a consequence, a remeshing of the base surface should aim at well-shaped triangles. For the actual deformation of the base surface we have to solve a linear system based on Laplacians. ...
doi:10.1145/1057432.1057457
fatcat:aqtl2nuvzvc4vfmye3wfixf5nu
A Remeshing Approach to Multiresolution Modeling
[article]
2004
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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The high regularity of the remeshed base surface further removes numerical problems caused by mesh degeneracies and results in a better discretization of the Laplacian operator. ...
In several approaches the modified base surface is computed by solving a linear system of discretized Laplacians. ...
As a consequence, a remeshing of the base surface should aim at well-shaped triangles. For the actual deformation of the base surface we have to solve a linear system based on Laplacians. ...
doi:10.2312/sgp/sgp04/189-196
fatcat:sse7v5phofc7jo3gn3ke7iaueu
Spectral Mesh Processing
2010
Computer graphics forum (Print)
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Early work in this area can be traced back to the seminal paper by Taubin in 1995, where spectral analysis of mesh geometry based on a combinatorial Laplacian aids our understanding of the low-pass filtering ...
Over the past fifteen years, the list of applications in the area of geometry processing which utilize the eigenstructures of a variety of mesh operators in different manners have been growing steadily ...
We would like to thank Rong Liu for help in producing some of the images in the paper. ...
doi:10.1111/j.1467-8659.2010.01655.x
fatcat:jc5qxx4x6ncqhkbdayobyijjje
3D Mesh Compression and Transmission for Mobile Robotic Applications
2016
International Journal of Advanced Robotic Systems
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2016) '3D mesh compression and transmission for mobile robotic applications.', International journal of advanced robotic systems., 13 . p. 9. Further information on publisher's website: http://dx. ...
This paper proposes a qualitydriven mesh compression and transmission method to address this. ...
To address this problem, [13] developed a cluster-based random accessible compression scheme, which constructed and compressed independent clusters of a constant number of mesh triangles, as well as ...
doi:10.5772/62035
fatcat:r2omkq744fbs7nlxwuoi65amli
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