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Surface compression using over-determined Laplacian approximation

Zhongyi Xie, W. Randolph Franklin, Barbara Cutler, Marcus A. Andrade, Metin Inanc, Daniel M. Tracy, Franklin T. Luk
2007 Advanced Signal Processing Algorithms, Architectures, and Implementations XVII  
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

Dilip Krishnan, Raanan Fattal, Richard Szeliski
2013 ACM Transactions on Graphics  
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

L. Váša, S. Marras, K. Hormann, G. Brunnett
2014 Computer graphics forum (Print)  
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

I. Kompatsiaris, D. Tzovaras, M.G. Strintzis
2001 IEEE Transactions on Image Processing  
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

Eduardo Sant'Ana Da Silva, Anderson Santos, Helio Pedrini
2018 Image Analysis and Stereology  
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]

Yu Wang, Mirela Ben-Chen, Iosif Polterovich, Justin Solomon
2018 arXiv   pre-print
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

Bruno Lévy, Hao (Richard) Zhang
2009 ACM SIGGRAPH ASIA 2009 Courses on - SIGGRAPH ASIA '09  
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

Bruno Lévy, Hao (Richard) Zhang
2010 ACM SIGGRAPH 2010 Courses on - SIGGRAPH '10  
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

Denis Kubasov, Christine Guillemot
2006 2006 International Conference on Image Processing  
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

Aamir Anis, Philip A. Chou, Antonio Ortega
2016 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
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

Fei Hou, Ying He, Hong Qin, Aimin Hao
2017 IEEE Transactions on Visualization and Computer Graphics  
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

Mario Botsch, Leif Kobbelt
2004 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
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]

Mario Botsch, Leif Kobbelt
2004 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
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

H. Zhang, O. Van Kaick, R. Dyer
2010 Computer graphics forum (Print)  
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

Bailin Yang, Xun Wang, Frederick W.B. Li, Binbo Xie, Xiaohui Liang, Zhaoyi Jiang
2016 International Journal of Advanced Robotic Systems  
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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