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Freeform Shape Representations for Efficient Geometry Processing

Leif Kobbelt
2003 Computer graphics forum (Print)  
While the algebraic complexity of volumetric representations S = {(x, y, z) | f (x, y, z) = 0} is independent from the shape complexity, the domain Ω of a parametric representation f : Ω → S usually has  ...  In this talk, a number of applications is presented and discussed where such a combination leads to efficient and numerically stable algorithms for the solution of various geometry processing tasks.  ...  Therefore it seems to be promising to combine an explicit mesh processing algorithm with an implicit global error representation.  ... 
doi:10.1111/1467-8659.00667 fatcat:iec4tj57lrefpnmuu4a525wqou

Topology preserving surface extraction using adaptive subdivision

Gokul Varadhan, Shankar Krishnan, TVN Sriram, Dinesh Manocha
2004 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
We present a novel topology preserving subdivision algorithm to generate an adaptive volumetric grid.  ...  Our algorithm ensures that every grid cell satisfies two local geometric criteria: a complex cell criterion and a star-shaped criterion.  ...  Acknowledgments We would like to thank David Applegate for providing us the QSOPT software and a modified dual LP formulation.  ... 
doi:10.1145/1057432.1057464 fatcat:7eh435u5tba6fliphbphvsng5e

Locality preserving KSVD for nonlinear manifold learning

Yin Zhou, Jinglun Gao, Kenneth E. Barner
2013 2013 IEEE International Conference on Acoustics, Speech and Signal Processing  
This paper proposes a novel algorithm called Locality Preserving KSVD (LP-KSVD), which can effectively learn a small number of dictionary atoms as locality-preserving landmark points on the nonlinear manifold  ...  Randomly selecting a subset of data points is very likely to place NML algorithms at the risk of local optima, leading to poor performance.  ...  This paper proposes a novel algorithm-Locality Preserving KSVD (LP-KSVD)-to learn a compact, representational, and locality-preserving dictionary.  ... 
doi:10.1109/icassp.2013.6638283 dblp:conf/icassp/ZhouGB13 fatcat:v227tiynq5citiwassdonqlcs4

Complex Functional Maps : a Conformal Link Between Tangent Bundles [article]

Nicolas Donati
2021 arXiv   pre-print
By first endowing and then exploiting the tangent bundle of each shape with a complex structure, the resulting operations become naturally orientationaware, thus favoring orientation and angle preserving  ...  A key property of these maps is their orientation awareness.  ...  Parts of this work were supported by the ERC Starting Grants No. 758800 (EXPROTEA) and No. 802554 (SPECGEO), and the ANR AI Chair AIGRETTE.  ... 
arXiv:2112.09546v1 fatcat:mliaivmn5nec7amjwbnrcaxzn4

Query processing of spatial objects: Complexity versus redundancy [chapter]

Michael Schiwietz, Hans-Peter Kriegel
1993 Lecture Notes in Computer Science  
A canonical model for a class of areal spatial objects Michael F.  ...  Brown 89 Indexing Mechanisms A hierarchical spatial index for cell complexes Elisabetta Bruzzone, Leila De Floriani, Monica Pellegrinelli 105 On optimal multiversion access structures Topology A small  ...  Complex and time^onsuming geometric algorithms evaluating the global shape of the objects have to be apptied.  ... 
doi:10.1007/3-540-56869-7_21 fatcat:wnfqnlwcujdffayomxao5atpwm

Edge- and Detail-Preserving Sparse Image Representations for Deformable Registration of Chest MRI and CT Volumes [chapter]

Mattias P. Heinrich, Mark Jenkinson, Bartlomiej W. Papież, Fergus V. Glesson, Sir Michael Brady, Julia A. Schnabel
2013 Lecture Notes in Computer Science  
Furthermore, we propose a new similarity criterion based on a binary shape representation of supervoxels, which improves the accuracy of single-modal registration and enables multimodal registration.  ...  Deformable medical image registration requires the optimisation of a function with a large number of degrees of freedom.  ...  We adapt a very recent algorithm, "simple linear iterative clustering" (SLIC) [1] for supervoxel clustering.  ... 
doi:10.1007/978-3-642-38868-2_39 pmid:24683991 fatcat:t2fh6hna4nhvrdlbsft74wqjei

Embedded deformation for shape manipulation

Robert W. Sumner, Johannes Schmid, Mark Pauly
2007 ACM Transactions on Graphics  
We present an algorithm that generates natural and intuitive deformations via direct manipulation for a wide range of shape representations and editing scenarios.  ...  One transformation is associated with each graph node and applies a deformation to the nearby space. Positional constraints are specified on the points of an embedded object.  ...  Acknowledgments We are grateful to Niloy Mitra for his assistance with the point sampling routine, Hao Li for editing the video, Richard Keiser for help with the fluid simulation, and Simone Riva for work  ... 
doi:10.1145/1239451.1239531 fatcat:oa4qchyforgilczdzcfbba2efy

Embedded deformation for shape manipulation

Robert W. Sumner, Johannes Schmid, Mark Pauly
2007 ACM Transactions on Graphics  
We present an algorithm that generates natural and intuitive deformations via direct manipulation for a wide range of shape representations and editing scenarios.  ...  One transformation is associated with each graph node and applies a deformation to the nearby space. Positional constraints are specified on the points of an embedded object.  ...  Acknowledgments We are grateful to Niloy Mitra for his assistance with the point sampling routine, Hao Li for editing the video, Richard Keiser for help with the fluid simulation, and Simone Riva for work  ... 
doi:10.1145/1276377.1276478 fatcat:c6xjau3fhjgujccaaprtwb6raa

Embedded deformation for shape manipulation

Robert W. Sumner, Johannes Schmid, Mark Pauly
2007 ACM SIGGRAPH 2007 papers on - SIGGRAPH '07  
We present an algorithm that generates natural and intuitive deformations via direct manipulation for a wide range of shape representations and editing scenarios.  ...  One transformation is associated with each graph node and applies a deformation to the nearby space. Positional constraints are specified on the points of an embedded object.  ...  Acknowledgments We are grateful to Niloy Mitra for his assistance with the point sampling routine, Hao Li for editing the video, Richard Keiser for help with the fluid simulation, and Simone Riva for work  ... 
doi:10.1145/1275808.1276478 fatcat:7x4rz4o26vfv5mnsotacq5df6a

On growth and formlets: Sparse multi-scale coding of planar shape

James H. Elder, Timothy D. Oleskiw, Alex Yakubovich, Gabriel Peyré
2013 Image and Vision Computing  
A generative model based on a composition of formlets applied to an embryonic shape, e.g., an ellipse, has the advantage of synthesizing only those shapes that could correspond to the boundaries of physical  ...  This paper presents a sparse representation of 2D planar shape through the composition of warping functions, termed formlets, localized in scale and space.  ...  We demonstrate that this formlet pursuit algorithm allows for an efficient and progressive approximation of shape, while preserving topological properties. 3.  ... 
doi:10.1016/j.imavis.2012.11.002 fatcat:6us4izlb5vcs5nzlg2namqibgy

On growth and formlets: Sparse multi-scale coding of planar shape

Timothy D. Oleskiw, James H. Elder, Gabriel Peyre
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
A generative model based on a composition of formlets applied to an embryonic shape, e.g., an ellipse, has the advantage of synthesizing only those shapes that could correspond to the boundaries of physical  ...  This paper presents a sparse representation of 2D planar shape through the composition of warping functions, termed formlets, localized in scale and space.  ...  We demonstrate that this formlet pursuit algorithm allows for an efficient and progressive approximation of shape, while preserving topological properties. 3.  ... 
doi:10.1109/cvpr.2010.5540179 dblp:conf/cvpr/OleskiwEP10 fatcat:n3xkhdxunrhsnasrvyjof7zilm

OBST-based segmentation approach to financial time series

Yain-Whar Si, Jiangling Yin
2013 Engineering applications of artificial intelligence  
A TP's degree of importance is calculated on the basis of its contribution to the preservation of the trends and shape of the time series.  ...  Comparison with existing approaches show that the time series reconstructed by the proposed method is able to maintain the shape of the original time series very well and preserve more trends.  ...  Acknowledgement This research is funded by the Research Committee of University of Macau, under grant MYRG041(Y1-L1)-FST13-SYW.  ... 
doi:10.1016/j.engappai.2013.08.015 fatcat:gel6csid6fdmhlxgk23yyyo6bu

Page 472 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
[Peta, Juan Manuel] (E-ZRGZ-AM; Zaragoza) A shape preserving representation with an evaluation algorithm of linear complexity. (English summary) Comput. Aided Geom. Design 20 (2003), no. 1, 1-10.  ...  The authors present an algorithm for evaluation of polynomial curves. The algorithm has linear time complexity and other desir- able properties. Reneta P.  ... 

MeshODE: A Robust and Scalable Framework for Mesh Deformation [article]

Jingwei Huang, Chiyu Max Jiang, Baiqiang Leng, Bin Wang, Leonidas Guibas
2020 arXiv   pre-print
Given a pair of shapes, our framework provides a novel shape feature-preserving mapping function that continuously deforms one model to the other by minimizing fitting and rigidity losses based on the  ...  leads to a better fitting quality compared with existing methods.  ...  pipeline for dealing with complex structures of CAD models, thus enabling a practical, robust and scalable deformation framework. • Evaluating deformation performance on a benchmark dataset, in which  ... 
arXiv:2005.11617v1 fatcat:ppqhjrm4znhzdhk3yuxsbfapee

Similarity-Aware Skill Reproduction based on Multi-Representational Learning from Demonstration [article]

Brendan Hertel, S. Reza Ahmadzadeh
2021 arXiv   pre-print
Given a demonstration of the skill, our framework constructs a similarity region around a point of interest (e.g., initial point) by evaluating individual LfD representations using the similarity metric  ...  However, when generalizing a learned skill over boundary conditions with higher variance, the similarity of the reproductions changes from one boundary condition to another, and a single LfD representation  ...  such that the system is critically damped, and f is a non-linear function which is learned using linear weighted regression to allow the generation of arbitrarily complex movements.  ... 
arXiv:2110.14817v1 fatcat:mblrtxcorvf2pga3nxbreyo3tq
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