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Extended Reeb Graphs for Surface Understanding and Description [chapter]

Silvia Biasotti, Bianca Falcidieno, Michela Spagnuolo
2000 Lecture Notes in Computer Science  
Theoretical approaches based on differential topology and geometry have been used for surface coding, for example Morse theory and Reeb graphs.  ...  In this paper, an Extended Reeb Graph representation (ERG) is proposed, which can handle degenerate critical points, and an algorithm is presented for its construction.  ...  Tosiyasu Kunii for the many helpful discussions on this topic, and to Corrado Pizzi for his helpful technical support.  ... 
doi:10.1007/3-540-44438-6_16 fatcat:tdu66x43avgbheqf6bvp4yrxhm

Surface Shape Understanding Based on Extended Reeb Graphs [chapter]

Silvia Biasotti, Bianca Falcidieno, Michela Spagnuolo
2006 Topological Data Structures for Surfaces  
The best example is the Morse theory, which sets the background for surface networks and Reeb graphs, both being effective tools for coding the surface shape.  ...  Computational topology techniques provide several tools and measures for surface analysis and coding [8]: Euler's equation, Morse theory, surface networks or Reeb graphs, for example, provide highly abstract  ...  Both graphs code the topological structure of a surface, with surface networks giving a surface-oriented view, while Reeb graphs giving a skeleton-like and volume-oriented description.  ... 
doi:10.1002/0470020288.ch6 fatcat:c2jeee3lrnerfpr2js64ar6rzi

Shape Abstraction Using Computational Topology Techniques [chapter]

S. Biasotti, B. Falcidieno, M. Spagnuolo
2002 From Geometric Modeling to Shape Modeling  
The resulting graph effectively represents the surface shape and has been successfully used as a basis for model compression and restoring purposes.  ...  In particular, a method is proposed for the extraction of a critical point configuration graph from a triangulated surface.  ...  Starting from Morse theory, it is possible to defme a graph, the Reeb graph, which represents a smooth surface by coding the evolution of its contours and which is particularly interesting for shape understanding  ... 
doi:10.1007/978-0-387-35495-8_16 fatcat:llpfcufv6fcphipx2ykl3vun3e

Reeb graphs for shape analysis and applications

S. Biasotti, D. Giorgi, M. Spagnuolo, B. Falcidieno
2008 Theoretical Computer Science  
Reeb graphs as shape descriptors have been proposed to solve different problems arising in Computer Graphics, and nowadays they play a fundamental role in the field of computational topology for shape  ...  This paper provides an overview of the mathematical properties of Reeb graphs and reconstructs its history in the Computer Graphics context, with an eye towards directions of future research.  ...  Landi and L. Papaleo for fruitful discussions. The authors also thank the anonymous reviewers for their helpful comments and suggestions.  ... 
doi:10.1016/j.tcs.2007.10.018 fatcat:k5rw4wtk2ff4ppi77kd2ux42oe

Volume data mining using 3D field topology analysis

I. Fujishiro, Y. Takeshima, T. Azuma, S. Takahashi
2000 IEEE Computer Graphics and Applications  
Acknowledgements We have benefited from continuous discussions with Xiaoyang Mao, Yoshihisa Shinagawa, Haruo Hosoya, Koji Koyamada, Sam Uselton, Karen Vierow, Yumi Yamaguchi, and research staff from Monolith  ...  Figure 1 shows two simple surfaces, an ellipsoid and a torus, and their corresponding Reeb graphs. Note that for the torus, changing the directions of the height axis may give different Reeb graphs.  ...  from computed tomography images. 2 They also applied the Reeb graph to represent the topological skeleton in their surface-coding system. 5 Others have used the Reeb graph and its variations for characterizing  ... 
doi:10.1109/38.865879 fatcat:leijqwqyl5esfnx27neqykwwri

Shape understanding by contour-driven retiling

M. Attene, S. Biasotti, M. Spagnuolo
2003 The Visual Computer  
Critical areas, which identify isolated and non-isolated critical points of the surface, are recognized and coded in the extended Reeb graph (ERG).  ...  Given a triangle mesh representing a closed manifold surface of arbitrary genus, a method is proposed to automatically extract the Reeb graph of the manifold with respect to the height function.  ...  The authors would like to thank all the people of the Computer Graphics Group at IMATI-CNR, and especially the reviewers for their helpful comments.  ... 
doi:10.1007/s00371-002-0182-y fatcat:cafdu3oc6fb2zjs45f5p5yavmq

Topology Dictionary for 3D Video Understanding

T. Tung, T. Matsuyama
2012 IEEE Transactions on Pattern Analysis and Machine Intelligence  
The model relies on 1) topology description and classification using Reeb graphs, and 2) a Markov motion graph to represent topology change states.  ...  Our approach serves to encode 3D video sequences, and can be applied for content-based description and summarization of 3D video sequences.  ...  Kinh Thang and Ms. Karine Tung for their support, as well as Ms. Bidda Camilla Solvang Poulsen for her graphic design work.  ... 
doi:10.1109/tpami.2011.258 pmid:22745004 fatcat:hn4vet5x7jcjxgijszcuxgxisu

Invariant High Level Reeb Graphs of 3D Polygonal Meshes

Julien Tierny, Jean-Philippe Vandeborre, Mohamed Daoudi
2006 Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)  
Abstract Many applications in computer graphics need high level shape descriptions, in order to benefit from a global understanding of shapes.  ...  In this paper, we present a novel method for the construction of invariant high level Reeb graphs, topological entities that give a good overview of the shape structure.  ...  Invariant High Level Reeb Graphs of 3D Polygonal Meshes Abstract Many applications in computer graphics need high level shape descriptions, in order to benefit from a global understanding of shapes.  ... 
doi:10.1109/3dpvt.2006.84 dblp:conf/3dpvt/TiernyVD06 fatcat:lerbs6pxunaujp6xhwvhublm5u

Topological Visualisation Techniques for Volume Multifield Data [chapter]

Dean P. Thomas, Rita Borgo, Robert S. Laramee, Simon J. Hands
2018 Computer Graphics and Imaging [Working Title]  
This survey paper provides an overview of topological visualisation techniques for scalar data sets.  ...  Many techniques are discussed in detail, beginning with a review of algorithms working on scalar fields defined with a single variable, and then generalised to multivariate and temporal data.  ...  Hamish Carr for his advice and assistance throughout the duration of this work.  ... 
doi:10.5772/intechopen.82185 fatcat:f4pgvn2dvzauxp4l6vmje47itm

Topology dictionary with Markov model for 3D video content-based skimming and description

T. Tung, T. Matsuyama
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
It relies on an unsupervised 3D shapebased clustering of the dataset by Reeb graphs, and features a Markov network to characterize topological changes.  ...  Redundancies are detected and skipped based on a probabilistic discrimination process. Semantic description of video sequences is then automatically performed.  ...  Francis Schmitt from TELECOM ParisTech for the precious and insightful discussions.  ... 
doi:10.1109/cvprw.2009.5206823 fatcat:i57otwhidngqzhmxdagg33lyxa

Topology dictionary with Markov model for 3D video content-based skimming and description

Tony Tung, Takashi Matsuyama
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
It relies on an unsupervised 3D shapebased clustering of the dataset by Reeb graphs, and features a Markov network to characterize topological changes.  ...  Redundancies are detected and skipped based on a probabilistic discrimination process. Semantic description of video sequences is then automatically performed.  ...  Francis Schmitt from TELECOM ParisTech for the precious and insightful discussions.  ... 
doi:10.1109/cvpr.2009.5206823 dblp:conf/cvpr/TungM09 fatcat:kz642ambczfvzdrpsrjwapafda

Feature Tracking Using Reeb Graphs [chapter]

Gunther Weber, Peer-Timo Bremer, Marcus Day, John Bell, Valerio Pascucci
2010 Mathematics and Visualization  
Based on this information, a boundary surface between burning and non-burning regions is constructed. The Reeb graph of this boundary surface is the tracking graph for burning regions.  ...  Tracking features and exploring their temporal dynamics can aid scientists in identifying interesting time intervals in a simulation and serve as basis for performing quantitative analyses of temporal  ...  For more details on Reeb graphs and algorithms to construct them efficiently, we refer the reader to the description by Pascucci et al. [4] .  ... 
doi:10.1007/978-3-642-15014-2_20 fatcat:m5zy4xfoajesbffmllqf3iyw6u

3D object comparison based on shape descriptors

S. Biasotti, S. Marini
2005 International journal of computer applications in technology  
interpret the shape features through a graph representation, such as skeletal curves [46] and Reeb graphs [5][21] [42] .  ...  understanding.  ...  The authors would like to thank all the people of the Shape Modelling Group at IMATI-CNR, in particular Bianca Falcidieno and Michela Spagnuolo for their fruitful support.  ... 
doi:10.1504/ijcat.2005.006465 fatcat:2gt44aoajfcs7apwbvgjflx3xm

Output-Sensitive Construction of Reeb Graphs

H. Doraiswamy, V. Natarajan
2012 IEEE Transactions on Visualization and Computer Graphics  
The paper also describes a scheme for controlled simplification of the Reeb graph and two different graph layout schemes that help in the effective presentation of Reeb graphs for visual analysis of scalar  ...  Finally, the Reeb graph is employed in four different applications -surface segmentation, spatially-aware transfer function design, visualization of interval volumes, and interactive exploration of time-varying  ...  This work was supported by the Department of Science and Technology, India, under Grant SR/S3/EECE/048/2007. The silicium dataset used in the experiments is courtesy of the volvis repository [42] .  ... 
doi:10.1109/tvcg.2011.37 pmid:21301023 fatcat:54ydw7e675epbmalelbg5xvudy

Computational methods for understanding 3D shapes

M. Attene, S. Biasotti, M. Mortara, G. Patanè, M. Spagnuolo, B. Falcidieno
2006 Computers & graphics  
Understanding shapes has been a challenging issue for many years, firstly motivated by computer vision and more recently by many complex applications in diverse fields, such as medical imaging, animation  ...  This paper describes the historical evolvement of the research done at IMATI-GE / CNR in the field of shape understanding.  ...  The authors thank all the members of the Shape Modeling Group of the IMATI-GE/CNR, the co-authors and reviewers of the papers discussed, and the people that, through discussions and suggestions, made it  ... 
doi:10.1016/j.cag.2006.02.007 fatcat:ks6kiuldojetbosfffop3cqcv4
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