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Skeletal Representations and Applications [article]

Andrea Tagliasacchi
2014 arXiv   pre-print
I will discuss, in two dimensions, how symmetry can be used to reduce the dimensionality of the data (from a 2D solid to a 1D curve), and how this relates to the classical definition of skeletons by Medial  ...  I will also present several algorithms for their computation and a variety of scenarios where skeletons are employed, with a special focus on geometry processing and shape analysis.  ...  The Maxwell set interpretation of the medial axis addressed in Definition 2.3 provides us with what we need to formulate the medial axis computation as a Voronoi diagram problem.  ... 
arXiv:1301.6809v2 fatcat:7rajrbs6mzgx5d7lncla7r25tu

Curve-Skeleton Properties, Applications, and Algorithms

Nicu D. Cornea, Deborah Silver, Patrick Min
2007 IEEE Transactions on Visualization and Computer Graphics  
We also give a taxonomy of methods and analyze the advantages and drawbacks of each class of algorithms.  ...  There are many algorithms in the literature describing extraction methodologies for different applications; however, it is unclear how general and robust they are.  ...  We would like to thank Dr. Raman Balasubramanian and Xiaosong Yuan for their initial help. We would also like to thank the reviewers for their useful comments and suggestions.  ... 
doi:10.1109/tvcg.2007.1002 pmid:17356219 fatcat:5fjr5p4jofcwplq2fksu5nb5z4

Musculoskeletal MRI segmentation using multi-resolution simplex meshes with medial representations

Benjamin Gilles, Nadia Magnenat-Thalmann
2010 Medical Image Analysis  
We extend the current framework by introducing a multi-resolution approach and a reversible medial representation, in order to reduce the complexity of geometric and non-penetration constraints computation  ...  Such discrete models have already proven to be efficient and versatile for medical image segmentation.  ...  Acknowledgments This work is supported by CO-ME (Computer Aided and Image Guided Medical Interventions) project funded by Swiss National Research Foundation. We would like to thank Dr.  ... 
doi:10.1016/j.media.2010.01.006 pmid:20303319 fatcat:tw7pidvtvzc6tbidcmotwxmgwe

An automatic coarse and fine surface mesh generation scheme based on medial axis transform: Part II implementation

H. Nebi G�rsoy, Nicholas M. Patrikalakis
1992 Engineering with Computers  
This meshing scheme is based on the medial axis transform (MAT) [2] to interrogate shape and to subdivide it into topologically simple subdomains.  ...  The algorithm can be effectively used to create coarse discretization and fine triangular surface meshes.  ...  Sherbrooke contributed to the computer implementation.  ... 
doi:10.1007/bf01194321 fatcat:bgkwojkjjvhuvjfaz7zwir2mfu

Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers [article]

Abhiram Reddy, Michael S. Dimitriyev, Gregory M. Grason
2021 arXiv   pre-print
Additionally, we find a previously unrecognized non-monotonic dependence of DG stability on the elastic asymmetry, the comparative entropic stiffness of matrix-forming to tubular-network forming blocks  ...  As such, the particular medial-based approach deployed here is readily generalizable to study packing frustration far beyond the case of DG morphologies in neat BCP assemblies.  ...  ACKNOWLEDGMENTS The authors are grateful to E.  ... 
arXiv:2112.06977v1 fatcat:3wfuhejw5bafllv2bsku7sxl5a

Skeleton extraction by mesh contraction

Oscar Kin-Chung Au, Chiew-Lan Tai, Hung-Kuo Chu, Daniel Cohen-Or, Tong-Yee Lee
2008 ACM SIGGRAPH 2008 papers on - SIGGRAPH '08  
Left to right are the original mesh and the results of the contraction after 1, 2 and 3 iterations. Faces with zero area are drawn in red.  ...  Abstract Extraction of curve-skeletons is a fundamental problem with many applications in computer graphics and visualization.  ...  Acknowledgements We would like to thank the anonymous reviewers for their valuable comments, Yu-Shuen Wang for giving a talk at HKUST that inspired this work, Youyi Zheng for his help in implementing the  ... 
doi:10.1145/1399504.1360643 fatcat:kkg2277qyvgivbzl3mr37aqkm4

Skeleton extraction by mesh contraction

Oscar Kin-Chung Au, Chiew-Lan Tai, Hung-Kuo Chu, Daniel Cohen-Or, Tong-Yee Lee
2008 ACM Transactions on Graphics  
Left to right are the original mesh and the results of the contraction after 1, 2 and 3 iterations. Faces with zero area are drawn in red.  ...  Abstract Extraction of curve-skeletons is a fundamental problem with many applications in computer graphics and visualization.  ...  Acknowledgements We would like to thank the anonymous reviewers for their valuable comments, Yu-Shuen Wang for giving a talk at HKUST that inspired this work, Youyi Zheng for his help in implementing the  ... 
doi:10.1145/1360612.1360643 fatcat:eywszfarojhkvlb5pe6zji7k7m

Realtime Informed Path Sampling for Motion Planning Search [chapter]

Ross A. Knepper, Matthew T. Mason
2016 Springer Tracts in Advanced Robotics  
We present CALM, the combined adaptive locality model, along with an algorithm to bias path sampling based on the model's predictions.  ...  We demonstrate an alternative approach to path sampling that closes the loop on the expensive collision-testing process.  ...  Wilmarth et al. (1999) sampled on the Voronoi diagram by first sampling uniformly in the space-including within obstacles-then projecting points onto the Voronoi diagram (also called the medial axis).  ... 
doi:10.1007/978-3-319-29363-9_23 fatcat:6wsdaeft7jhirhisdctvcsgb4e

-smooth branching surface construction from cross sections

N.C. Gabrielides, A.I. Ginnis, P.D. Kaklis, M.I. Karavelas
2007 Computer-Aided Design  
The solution of the "one-to-many" branching problem, where one contour on the i-plane is to be connected to M contours on the (i + 1)plane, is based on combining skinning with trimming and hole filling  ...  The "many-to-many" problem is handled by combining the "one-to-many" methodology with a zone-separation technique, that achieves splitting the "many-to-many" problem into two "one-to-many" problems.  ...  In fact, the Voronoi region V k of S k fully contains S k in its interior, and, moreover, V k is star-shaped with respect to the medial axis of S k (see [26] for more details).  ... 
doi:10.1016/j.cad.2007.05.004 fatcat:evz2uuzg2rd7rbst5umph4aj7y

Geometric Modeling Based on Polygonal Meshesv [article]

Leif P. Kobbelt, Stephan Bischoff, Mario Botsch, Kolja Kähler, Christian Rössl, Robert Schneider, Jens Vorsatz
2000 Eurographics State of the Art Reports  
of a given 3D-model to the current application or to the available hardware resources; advanced mesh optimization techniques that are based on the numerical simulation of physical material (e.g. membranes  ...  While traditional computer aided design (CAD) is mainly based on piecewise polynomial surface representations, the recent advances in the efficient handling of polygonal meshes have made available a set  ...  (p, S) ≤ r • dist(p, ME(F)) The medial axis of F is the closure of all points having more than one closest point on F and can be thought of as the continuous extension of the Voronoi diagram 30 .  ... 
doi:10.2312/egt.20001033 fatcat:ys2bwbqzzbg2zm4jb45d2cbvfi

Feature Preserving Mesh Generation from 3D Point Clouds

Nader Salman, Mariette Yvinec, Quentin Merigot
2010 Computer graphics forum (Print)  
Using a feature detection process based on the covariance matrices of Voronoi cells, we first extract from the point cloud a set of sharp features.  ...  We demonstrate the effectiveness of our method on a variety of models including laser scanned datasets ranging from indoor to outdoor scenes.  ...  data-sets.  ... 
doi:10.1111/j.1467-8659.2010.01771.x fatcat:55ozdjutobbntcc6mqbnbbqcga

Process planning for robotic wire and arc additive manufacturing

Donghong Ding, Zengxi Pan, Dominic Cuiuri, Huijun Li
2015 2015 IEEE 10th Conference on Industrial Electronics and Applications (ICIEA)  
Over the past half century, a significant amount of work has been done to develop the capability to produce I take this opportunity to express my sincere appreciation to my principal supervisor Dr.  ...  The excellent research atmosphere that provided in our group was very helpful for the successful completion of this work. Many thanks to Prof. Weihua Li, and A/Prof.  ...  Srinivasan et al. [107] extends Lee's algorithm to computing a generalized Voronoi diagram for polygons with holes.  ... 
doi:10.1109/iciea.2015.7334441 fatcat:xdisv2wkxfdzdijqltmuoc3bn4

Piecewise affine registration of biological images for volume reconstruction

Alain Pitiot, Eric Bardinet, Paul M. Thompson, Grégoire Malandain
2006 Medical Image Analysis  
We investigate the behavior of our approach on several batches of histological data and discuss its sensitivity to parameters and noise.  ...  Given a pair of input images, we first compute a dense similarity field between them with a block matching algorithm.  ...  Imaging and Bioengineering (EB001561) and by a Human Brain Project The authors would like to thank J.  ... 
doi:10.1016/j.media.2005.03.008 pmid:15963755 fatcat:qwss2qjzifasnaegdk3gycgece

Hex-Mesh Generation and Processing: a Survey [article]

Nico Pietroni, Marcel Campen, Alla Sheffer, Gianmarco Cherchi, David Bommes, Xifeng Gao, Riccardo Scateni, Franck Ledoux, Jean-Francois Remacle, Marco Livesu
2022 arXiv   pre-print
The required background, pertaining to geometrical as well as combinatorial aspects, is introduced along the way.  ...  We cover the whole spectrum of alternative approaches to mesh generation, as well as post processing algorithms for connectivity editing and mesh optimization.  ...  Lévy and Liu [2010] generalized Centroidal Voronoi Tessellation [Faber and Gunzburger 1999] for hex-dominant meshing, introducing Lp-Centroidal Voronoi Tessellation.  ... 
arXiv:2202.12670v1 fatcat:ze2zfkgxhrgjnp2jm77wvgwvim

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  
In this sense, Morse theory allows one to construct a general framework for shape characterization, parametrized with respect to the mapping function used, and possibly the space associated with the shape  ...  The approaches surveyed will be discussed in detail, with respect to theory, computation and application. Several properties of the shape descriptors will be analyzed and compared.  ...  ACKNOWLEDGMENT The authors would like to thank Prof. Massimo Ferri and the Vision Mathematics Group at the University of Bologna, Italy, for fruitful discussions on the survey topics.  ... 
doi:10.1145/1391729.1391731 fatcat:yg6k2lwerfd63nuhhxxypcnzju
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