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Multiscale Planar Graph Generation [article]

Varsha Chauhan, Alexander Gutfraind, Ilya Safro
2019 arXiv   pre-print
The method follows a multi-scale randomized editing approach generating a hierarchy of coarsened networks of a given planar graph and introducing edits at various levels in the hierarchy.  ...  While the currently-available synthetic network generators can model networks that exhibit realism, they do not guarantee or achieve planarity.  ...  Multiscale Planar Graph Generation Multiscale network generation (MNG) introduced in [2] is an editing model that generates realistic networks.  ... 
arXiv:1802.09617v2 fatcat:euyxreozynglflkmi2y64j27fu

Multiscale planar graph generation

Varsha Chauhan, Alexander Gutfraind, Ilya Safro
2019 Applied Network Science  
The method follows a multi-scale randomized editing approach generating a hierarchy of coarsened networks of a given planar graph and introducing edits at various levels in the hierarchy.  ...  While the currently-available synthetic network generators can model networks that exhibit realism, they do not guarantee or achieve planarity.  ...  The proposed multiscale planar graph generator follows the main ideas of MNG and makes them applicable on planar graphs.  ... 
doi:10.1007/s41109-019-0142-3 fatcat:yvc2vao4crhoza3l57j5rmne6i

Studying Geometric Graph Properties of Road Networks Through an Algorithmic Lens [article]

David Eppstein, Michael T. Goodrich
2009 arXiv   pre-print
In particular, we study road networks as multiscale-dispersed graphs, which is a concept we formalize in terms of disk neighborhood systems.  ...  Unlike previous approaches, our study is not based on the assumption that road networks are planar graphs.  ...  Moreover, since G is a multiscale-dispersed graph, we have the following useful combinatorial lemma. Suppose we are given the planarization G of G.  ... 
arXiv:0808.3694v2 fatcat:ymgolnnwovgepak7upbgd565n4

Multiscale TILT Feature Detection with Application to Geometric Image Segmentation

Chi-Pang Lam, Allen Y. Yang, Ehsan Elhamifar, S. Shankar Sastry
2013 2013 IEEE International Conference on Computer Vision Workshops  
Finally, we present an application of the multiscale TILT detection algorithm to the classical problem of building facade segmentation.  ...  Second, we apply a Markov random field model to a multiscale low-rank representation of the image geometric layer, and obtain an effective algorithm to detect TILT features.  ...  Without loss of generality, we assume A and E are square matrices.  ... 
doi:10.1109/iccvw.2013.79 dblp:conf/iccvw/LamYES13 fatcat:2dasdefhvffm5olnif263sjzlm

Page 5705 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
Classical results on differential invariants associated to planar curves are relevant to planar object recognition under par- tial occlusion, and recent results concerning the evolution of closed planar  ...  A problem-solving scheme for generation of plausible interpretations is presented.  ... 

Going Off-road: Transversal Complexity in Road Networks [article]

David Eppstein, Michael T. Goodrich, Lowell Trott
2009 arXiv   pre-print
By viewing road networks as multiscale-dispersed graphs, we show that a random line will cross the edges of such a graph O(sqrt(n)) times on average.  ...  The average transversal complexity of a geometric graph is the number of edges of that graph that are crossed by random line or line segment.  ...  Thus, we get a planar embedding.  ... 
arXiv:0909.2891v1 fatcat:aw2gxq5tyndknka4vkt7svma3i

Adaptive multiscale detection of filamentary structures in a background of uniform random points

Ery Arias-Castro, David L. Donoho, Xiaoming Huo
2006 Annals of Statistics  
Each anisotropy graph is reduced to a subgraph that consist of strips with significant counts.  ...  At the heart of our approach is an analysis of the data by counting membership in multiscale multianisotropic strips.  ...  Extends naturally to detecting general planar curves which are not graphs.  ... 
doi:10.1214/009053605000000787 fatcat:xsbu4y7fw5gxpdn5hh52xhonva

Segment and Label Indoor Scene Based on RGB-D for the Visually Impaired [chapter]

Zhe Wang, Hong Liu, Xiangdong Wang, Yueliang Qian
2014 Lecture Notes in Computer Science  
This work propose a multiscale-voxel strategy to reduce the effects of noise and improve plane segmentation.  ...  Then the segmentation result is combined with depth data and color data to apply graph-based image segmentation algorithm.  ...  This proves the proposed multiscale strategy is suitable for the depth data generated by the Kinect sensors and have better plane extracting results.  ... 
doi:10.1007/978-3-319-04114-8_38 fatcat:ygxyndeh4jbunkvr62ucfvbne4

A Translation-Invariant Renormalizable Non-Commutative Scalar Model

R. Gurau, J. Magnen, V. Rivasseau, A. Tanasa
2008 Communications in Mathematical Physics  
The non-planar graphs remain convergent and the main difference concerns the planar irregular graphs.  ...  However some ultraviolet convergent two point graphs, such as the "non-planar tadpole" generate infrared divergences which are not of the renormalizable type 1 .  ...  Planar irregular four-points graphs. Take now the graph of Fig. 3 . This graph has vanishing genus (g = 0) and two faces broken by external lines (B = 2).  ... 
doi:10.1007/s00220-008-0658-3 fatcat:pvj7q6x6enfcxly4rxurppnaqe

OBJECT CLASSIFICATION VIA PLANAR ABSTRACTION

Sven Oesau, Florent Lafarge, Pierre Alliez
2016 ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
The main idea consists in first abstracting the input object into planar parts at several scales, then discriminate between the different classes of objects solely through features derived from these planar  ...  Abstracting into planar shapes provides a means to both reduce the computational complexity and improve robustness to defects inherent to the acquisition process.  ...  Figure 1 : 1 Multiscale Planar Abstraction. Left: Input point cloud of a goblet with outliers and noise.  ... 
doi:10.5194/isprs-annals-iii-3-225-2016 fatcat:74xlipircfhuhoesxsrfxrurz4

OBJECT CLASSIFICATION VIA PLANAR ABSTRACTION

Sven Oesau, Florent Lafarge, Pierre Alliez
2016 ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
The main idea consists in first abstracting the input object into planar parts at several scales, then discriminate between the different classes of objects solely through features derived from these planar  ...  Abstracting into planar shapes provides a means to both reduce the computational complexity and improve robustness to defects inherent to the acquisition process.  ...  Figure 1 : 1 Multiscale Planar Abstraction. Left: Input point cloud of a goblet with outliers and noise.  ... 
doi:10.5194/isprsannals-iii-3-225-2016 fatcat:56otbm3kjrhmph4dms2fix5ueq

Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing

Allen Tannenbaum, Guillermo Sapiro, Peter J. Olver
1997 SIAM Journal on Applied Mathematics  
Then, given a transformation group G acting on Rn, we write down a general expression for any G-invariant hypersurface geometric evolution in R n .  ...  The study of geometric flows for smoothing, multiscale representation, and analysis of two and three dimensional objects has received much attention in the past few years.  ...  The smoothing and multiscale representation of planar objects was originally performed by filtering their boundary with a Gaussian filter [9, 37, 68] .  ... 
doi:10.1137/s0036139994266311 fatcat:uzeosnct5bbrbkaitiootdnk3e

Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions

Arthur D. Szlam, Mauro Maggioni, Ronald R. Coifman, James C. BremerJr., Manos Papadakis, Andrew F. Laine, Michael A. Unser
2005 Wavelets XI  
Classically, analysis on manifolds and graphs has been based on the study of the eigenfunctions of the Laplacian and its generalizations.  ...  Recently a framework for building natural multiresolution structures on manifolds and graphs was introduced, that greatly generalizes, among other things, the construction of wavelets and wavelet packets  ...  It is desirable to extend the multiscale tools of signal processing from the Euclidean setting to more general situations, in particular the case of manifolds and graphs.  ... 
doi:10.1117/12.616931 fatcat:hcuxkfkwhne7xnmnjh7rxej46u

Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours [chapter]

Petros Maragos, Kimon Drakopoulos
2012 Mathematics and Visualization  
To this goal we extend existing work on graph morphology to multiscale dilation and erosion and implement them recursively using level sets of functions defined on the graph's nodes.  ...  In this chapter we focus on formulating and implementing on abstract domains such as arbitrary graphs popular methods and techniques developed for image analysis, in particular multiscale morphology and  ...  Background on Lattice and Multiscale Morphology A general formalization [37, 19] of morphological operators views them as operators on complete lattices.  ... 
doi:10.1007/978-3-642-34141-0_3 fatcat:pgaq7qrpnzaupjqpftbkji5tmy

Quantum corrections for translation-invariant renormalizable non-commutative ϕ4theory

Daniel N Blaschke, François Gieres, Erwin Kronberger, Thomas Reis, Manfred Schweda, René I.P Sedmik
2008 Journal of High Energy Physics  
The obtained results show that the IR divergences are also suppressed in the massless case, which is of importance for the gauge field theoretic generalization of the scalar field model.  ...  By explicitly performing Feynman graph calculations at one loop and higher orders we illustrate the mechanism which overcomes the UV/IR mixing problem and ultimately leads to a renormalizable model.  ...  In this respect we recall that its renormalizability has been proved quite generally in reference [6] using multiscale analysis.  ... 
doi:10.1088/1126-6708/2008/11/074 fatcat:sslriyoa4fbobmgn353nzxvdpi
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