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Enhancing 3D mesh topological skeletons with discrete contour constrictions

Julien Tierny, Jean-Philippe Vandeborre, Mohamed Daoudi
2007 The Visual Computer  
Constriction approximations enable Reeb graphs refinement into more visually meaningful skeletons, that we refer as enhanced topological skeletons.  ...  The key idea of the algorithm is that discrete contourscurves carried by the edges of the mesh and approximating the continuous contours of a mapping function -encode both topological and geometrical shape  ...  This work is partially supported by the European Network of Excellence Delos No. 507618 -http://www.delos.info.  ... 
doi:10.1007/s00371-007-0181-0 fatcat:vcbzgnxrzjbkxfqn4y5mjpfvua

3D Mesh decomposition using Reeb graphs

Stefano Berretti, Alberto Del Bimbo, Pietro Pala
2009 Image and Vision Computing  
In this paper, an approach is proposed for decomposition of 3D objects based on Reeb-graphs.  ...  by manual decomposition of 3D objects.  ...  However, Reeb-graphs reported in their work are induced by the height function using a set of slicing planes.  ... 
doi:10.1016/j.imavis.2009.02.004 fatcat:vd7dbuablzfjxlw2wf6y32esqm

Interactive shape modeling using a skeleton-mesh co-representation

J. Andreas Bærentzen, Rinat Abdrashitov, Karan Singh
2014 ACM Transactions on Graphics  
A PAM is a mesh-skeleton co-representation designed for the modeling of 3D organic, articulated shapes.  ...  We further present a PAM-based multi-touch sculpting application in order to demonstrate its utility as a shape representation for the interactive modeling of organic, articulated figures as well as for  ...  Models are from the Princeton Segmentation Database, the Stanford 3D Scanning Repository, the AIM@Shape Repository, and Thingiverse.  ... 
doi:10.1145/2601097.2601226 fatcat:wkr4yu37kjeqlaloumiii7d77i

Describing shapes by geometrical-topological properties of real functions

S. Biasotti, L. De Floriani, B. Falcidieno, P. Frosini, D. Giorgi, C. Landi, L. Papaleo, M. Spagnuolo
2008 ACM Computing Surveys  
The fundamental idea behind Morse theory is that of combining the topological exploration of a shape with quantitative measurement of geometrical properties provided by a real function defined on the shape  ...  The added value of approaches based on Morse theory is in the possibility of adopting different functions as shape descriptors according to the properties and invariants that one wishes to analyze.  ...  Project SHALOM funded by the Italian Ministry of Research under contract number RBIN04HWR8 and by the National Science Foundation under grant number CCF-0541032.  ... 
doi:10.1145/1391729.1391731 fatcat:yg6k2lwerfd63nuhhxxypcnzju

Topological methods reveal high and low functioning neuro-phenotypes within fragile X syndrome

David Romano, Monica Nicolau, Eve-Marie Quintin, Paul K. Mazaika, Amy A. Lightbody, Heather Cody Hazlett, Joseph Piven, Gunnar Carlsson, Allan L. Reiss
2014 Human Brain Mapping  
In addition, these findings underscore the potential of TDA as a powerful tool in the search for biological phenotypes of neuropsychiatric disorders.  ...  Fragile X syndrome (FXS), due to mutations of the FMR1 gene, is the most common known inherited cause of developmental disability as well as the most common single-gene risk factor for autism.  ...  Access to Iris software was provided by Ayasdi, Inc., of which Gunnar Carlsson is a co-founder.  ... 
doi:10.1002/hbm.22521 pmid:24737721 pmcid:PMC4113391 fatcat:47tkqpxhxzfybj2k5njuiwxsji

3D Skeletons: A State-of-the-Art Report

Andrea Tagliasacchi, Thomas Delame, Michela Spagnuolo, Nina Amenta, Alexandru Telea
2016 Computer graphics forum (Print)  
This survey presents an overview of 3D shape skeletonization. We start by presenting the definition and properties of various types of 3D skeletons.  ...  a) (b) (c) (d) Figure 1: Four alternative definitions of medial skeletons: (a) centers of maximally-inscribed balls; (b) shock graph of the grassfire surface flow; (c) as points with more than one corresponding  ...  Acknowledgments This work was partially funded by the advanced grant no. 291184 EXPRESSIVE from the European Research Council (ERC-2011-ADG_20110209), and by the H2020 EC Project GRAVITATE (RE-FLECTIVE7  ... 
doi:10.1111/cgf.12865 fatcat:dpyylsn5kffwxkjw4cza3zzcyu

Deformable Model Retrieval Based on Topological and Geometric Signatures

Gary K.L. Tam, Rynson W.H. Lau
2007 IEEE Transactions on Visualization and Computer Graphics  
R. (2007) 'Deformable model retrieval based on topological and geometric signatures.', IEEE transactions on visualization and computer graphics., 13 (3), 470 -482.  ...  is made to the original source a link is made to the metadata record in DRO the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of  ...  Instead of using the skeletal graph, [26] analyzes models based on the component graph. A model is first split by mesh decomposition with each component node described by one primitive.  ... 
doi:10.1109/tvcg.2007.1011 pmid:17356214 fatcat:2thm4vxrh5cffnoimpllxxn3ee

Kinematic skeleton extraction from 3D articulated models

Jaehwan Ma, Sunghee Choi
2014 Computer-Aided Design  
Ideas based on topological features such as the Reeb graph and the Morse complex are suitable for detecting such joints.  ...  t a r t i c l e i n f o a b s t r a c t We propose a method to extract a kinematic skeleton from an articulated 3D model.  ...  using structures such as Reeb graphs [21] [22] [23] , contour trees [24] , and Morse complexes [25, 26] .  ... 
doi:10.1016/j.cad.2013.08.036 fatcat:26lgjkhj7nagzekac4ryd5tx3i

Feature-based similarity search in 3D object databases

Benjamin Bustos, Daniel A. Keim, Dietmar Saupe, Tobias Schreck, Dejan V. Vranić
2005 ACM Computing Surveys  
Over the last few years, a strong interest in methods for 3D similarity search has arisen, and a growing number of competing algorithms for content-based retrieval of 3D objects have been proposed.  ...  We survey feature-based methods for 3D retrieval, and we propose a taxonomy for these methods. We also present experimental results, comparing the effectiveness of some of the surveyed methods.  ...  ACKNOWLEDGMENTS We thank the editors of ACM Computing Surveys and the anonymous referees for their helpful comments on the earlier version of this article.  ... 
doi:10.1145/1118890.1118893 fatcat:qci4gin7j5buzezfetwvbu7oei

Modeling and Correspondence of Topologically Complex 3D Shapes [article]

Ibraheem Alhashim
2015 arXiv   pre-print
We focus on methods designed to help generate or process shapes with large number of interconnected components often found in man-made shapes.  ...  Finally, we look at different shape representations and tools that facilitate the modification of shape topology and we focus on those particularly useful in free-form 3D modeling.  ...  The use of Reeb graphs was later extended in [Biasotti et al. 2006 ] for the task of finding sub-part correspondences using graph-matching techniques.  ... 
arXiv:1506.06855v1 fatcat:53sf5r2ey5cu5ckmilrfoo6a3m

A Spline-based Volumetric Data Modeling Framework and Its Applications [article]

Bo Li
2013 arXiv   pre-print
In this dissertation, we concentrate on the challenging research issue of developing a spline-based modeling framework, which converts the conventional data (e.g., surface meshes) to tensor-product trivariate  ...  These properties make our techniques highly preferable in many physically-based applications including mechanical analysis, shape deformation and editing, virtual surgery training, etc.  ...  Contribution Summary In this thesis, we have investigated and presented a spline-based volumetric modeling framework to solve 3D objects modeling problems.  ... 
arXiv:1308.0869v1 fatcat:hiscx3juzzgivfzjdjcahp7une

A Survey of Spline-based Volumetric Data Modeling Framework and Its Applications [article]

Bo Li
2013 arXiv   pre-print
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years.  ...  ., triangle mesh) has many attractive properties, it is incapable of expressing the interior space and materials.  ...  In object-based vectorization [106] , the whole image is segmented into a few objects. The color of each object then is approximated by spline patch.  ... 
arXiv:1308.0867v1 fatcat:pc3sdvzoubfvboqetz3xtrxquy

Structural Descriptors for 3D Shapes

Michela Spagnuolo, Silvia Biasotti, Bianca Falcidieno, Simone Marini, Tim Crawford, Remco C. Veltkamp
2006
The idea is to define a shape description framework based on results of differential topology which deal with the description of shapes by means of the properties of one, or more, real-valued functions  ...  This work is partially supported by the EU Newtwork of Excellence AIM{@}SHAPE.  ...  Acknowledgments This work has been partially supported by the EU Newtwork of Excellence "AIMSHAPE" (Contract n. 506766).  ... 
doi:10.4230/dagsemproc.06171.10 fatcat:x75sro5eyvh4fhs3b3n5jckmjm

Shape google

Alexander M. Bronstein, Michael M. Bronstein, Leonidas J. Guibas, Maks Ovsjanikov
2011 ACM Transactions on Graphics  
Using multiscale diffusion heat kernels as "geometric words", we construct compact and informative shape descriptors by means of the "bag of features" approach.  ...  In this paper, we explore analogous approaches in the 3D world applied to the problem of non-rigid shape retrieval in large databases.  ...  of Laplace-Beltrami eigenvalues and eigenfunctions.  ... 
doi:10.1145/1899404.1899405 fatcat:rwtead35svcmrplfxr3lfmtz6a

Nonplanar 3D Printing of Bifurcating Forms

Ioanna Mitropoulou, Mathias Bernhard, Benjamin Dillenburger
2022
As a result, novel design potential is unlocked by having control over the layered configuration of paths in the object, and 3D printing becomes viable for architectural applications.  ...  The introduction of robotic arms in additive manufacturing enables the scaling up of three-dimensional (3D) printing processes and the realization of nonplanar path geometries.  ...  A plethora of applications in geometry processing is based on Morse Theory and Reeb graphs.  ... 
doi:10.3929/ethz-b-000509867 fatcat:ynpvpoydbjat3k3tjpnulvlhmi
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