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Polygon Evolution by Vertex Deletion [chapter]

Longin Jan Latecki, Rolf Lakämper
1999 Lecture Notes in Computer Science  
evolution steps which are just the iterations of a basic procedure of vertex deletion.  ...  We propose a simple approach to evolution of polygonal curves that is specially designed to t discrete nature of curves in digital images.  ...  P, then rst all vertices of Q are deleted that are not close to any v ertex of P, and then, whenever a vertex of P is deleted, then a vertex of Q that is close to it is deleted in the corresponding evolution  ... 
doi:10.1007/3-540-48236-9_35 fatcat:l53w7tllfzfz7ivx3szrelcl6u

Continuity of discrete curve evolution

L. J. Latecki
2000 Journal of Electronic Imaging (JEI)  
In this paper we prove t h a t the process of the discrete curve evolution is continuous: if polygon Q is close to polygon P, then the polygons obtained by their evolution remain close.  ...  This intuitively means that rst all vertices of Q are deleted that are not close to any v ertex of P, and then, whenever a vertex of P is deleted, then a vertex of Q that is close to it is deleted in the  ...  1), and then, whenever a vertex of P is deleted, then a vertex of Q that is close to it is deleted in the corresponding evolution step of Q (Theorem 2).  ... 
doi:10.1117/1.482748 fatcat:j4wv33irc5cvlhest35nbkzfvi

Continuity of the discrete curve evolution

Longin J. Latecki, R. R. Ghadially, Rolf Lakaemper, Ulrich Eckhardt, Longin J. Latecki, Robert A. Melter, David M. Mount, Angela Y. Wu
1999 Vision Geometry VIII  
In this paper we prove t h a t the process of the discrete curve evolution is continuous: if polygon Q is close to polygon P, then the polygons obtained by their evolution remain close.  ...  This intuitively means that rst all vertices of Q are deleted that are not close to any v ertex of P, and then, whenever a vertex of P is deleted, then a vertex of Q that is close to it is deleted in the  ...  1), and then, whenever a vertex of P is deleted, then a vertex of Q that is close to it is deleted in the corresponding evolution step of Q (Theorem 2).  ... 
doi:10.1117/12.364095 fatcat:dgcq7cso7ra5njryz25u46dsr4

Evolution of Vertex and Pixel Shaders [chapter]

Marc Ebner, Markus Reinhardt, Jürgen Albert
2005 Lecture Notes in Computer Science  
Initially, the shading computations were carried out by dedicated hardwired algorithms for each vertex and then interpolated by the rasterizer.  ...  Todays graphics hardware contains vertex and pixel shaders which can be reprogrammed by the user. Vertex and pixel shaders allow almost arbitrary computations per vertex respectively per pixel.  ...  Acknowledgments Our system uses the GAlib genetic package version 2.4, written by Matthew Wall at the Massachusetts Institute of Technology [23] .  ... 
doi:10.1007/978-3-540-31989-4_23 fatcat:5zlp7ta6xjf3zkdvfzf2umi2hq

A universal predictor-corrector type incremental algorithm for the construction of weighted straight skeletons based on the notion of deforming polygon [article]

Baris Irhan
2020 arXiv   pre-print
polygon.  ...  In the proposed algorithm, the raw input provided by the polygon itself is enough to resolve edge collapse and edge split events.  ...  To keep track of the evolution of straight skeleton structure, a vertex also stores pointers to the vertex above and the vertex below, which are associated, respectively, with the polygon above and polygon  ... 
arXiv:2011.07107v1 fatcat:2mm7jwf37barrb4wvsmywhuqii

Discrete Curve Evolution on Arbitrary Triangulated 3D Mesh [chapter]

Sergii Poltaretskyi, Jean Chaoui, Chafiaa Hamitouche-Djabou
2014 Lecture Notes in Computer Science  
Discrete Curve Evolution (DCE) algorithm is used to eliminate objects' contour distortions while at the same time preserve the perceptual appearance at a level sufficient for object recognition.  ...  We introduce a new cost function for border vertex which is only based on geodesic distances.  ...  Since in every evolution step, the number of digital line segments in the curve decomposition decreases by one, the evolution converges to a convex polygon, which defines the highest level in the shape  ... 
doi:10.1007/978-3-319-09955-2_34 fatcat:4hajr5zwvrct5dm7ytel77ao2e

An Algorithm for Limited Visibility Graph Searching [article]

Ath. Kehagias, A.C. Papazoglou
2021 arXiv   pre-print
Our LVGS algorithm is a conversion of Guibas and Lavalle's polygonal region search algorithm.  ...  An alternative strategy to handle polygonal regions is to first approximate them by discretization and then study the search problem on a graph equivalent to the discretized region.  ...  The polygonal region search algorithm of [15, 16] is complex to implement and can be computationally impractical for complicated regions.  ... 
arXiv:2105.06150v1 fatcat:jsiileakxfglxc6madruweug2y

Reachability Analysis Using Polygonal Projections [chapter]

Mark R. Greenstreet, Ian Mitchell
1999 Lecture Notes in Computer Science  
Coho is a reachability analysis tool for systems modeled by non-linear, ordinary di erential equations.  ...  This paper addresses reachability for systems modeled by ordinary di erential equations (ODEs).  ...  Originally, we only used the area of the polygon in computing the cost of deleting a vertex.  ... 
doi:10.1007/3-540-48983-5_12 fatcat:2uw3tlopnfg5jmivc3psbviq3q

Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution

Xiang Bai, Longin Latecki, Wen-yu Liu
2007 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Any contour partition can be used, but the partitions obtained by Discrete Curve Evolution (DCE) yield excellent results.  ...  ACKNOWLEDGMENTS This work received support from the National Natural Science Foundation of China (grant No. 60273099) and was in part supported by the US National Science Foundation under Grant No.  ...  As stated above, if a partition point that is also a polygon vertex u i is deleted in a DCE evolution step, (i.e., u i 2 P nÀk À P nÀðkþ1Þ ), or becomes concave (due to the deletion of one of its neighbors  ... 
doi:10.1109/tpami.2007.59 pmid:17224615 fatcat:wkwlb23cezbkhga6xyqnkfo2uy

Pool segmentation for predicting water traps

Yusuke Yasui, Sara McMains, Thomas Glau
2015 Journal of manufacturing systems  
We can quickly find the water trap regions by analyzing the directed graph.  ...  We propose a new method to detect water trap regions in voids of oriented polygonal models that approximate the geometry of mechanical parts.  ...  We determine all of these values of z by tracking the evolution of the boundary of slice polygons.  ... 
doi:10.1016/j.jmsy.2014.07.006 fatcat:d44e4u3vuzgzfestpqteufepcy

Staggered quantum walks on graphs

Renato Portugal
2016 Physical Review A  
Since a polygon is a clique, the particle can move only to neighboring vertices because α j j = 0 if j is not a vertex of the polygon induced by α j and, if j is a vertex in α j , U 0 j belongs to the  ...  U 0 is the coin operator of a QW on a new graph Γ (V , E ) obtained from Γ(V, E) by shrinking the blue polygons into single vertices so that a blue polygon that is a dclique becomes a d-degree vertex in  ... 
doi:10.1103/physreva.93.062335 fatcat:jvshvn4c4za7bn624n6pct7bo4

Optimization approaches to mpi and area merging-based parallel buffer algorithm

Junfu Fan, Min Ji, Guomin Gu, Yong Sun
2014 Boletim de Ciências Geodésicas  
Corresponding optimization approaches involving tree-like area merging strategy, the vertex number oriented parallel task partition method and the inter-process results merging strategy were suggested  ...  ACKNOWLEDGEMENTS This study was supported by National Key Technology R&D Program (No. 2011BAH06B03 and No. 2011BAH24B10, and No. 2012BAH27B04)  ...  In each merging step, only the processes with the same evolution coefficient are merged, unless the number of processes marked by a certain evolution coefficient is only 1.  ... 
doi:10.1590/s1982-21702014000200015 fatcat:sfvflzphofbinekgzoyh6axsdu

Untangling knots by stochastic energy optimization

Milana Huang, R.P. Grzeszczuk, L.H. Kauffman
1996 Proceedings of Seventh Annual IEEE Visualization '96  
By allowing the rope to evolve in this field in search of an energy minimizing configuration we can determine the knot type of the initial configuration.  ...  Nodes arc shifted by first selecting vertex positions to delete. A a. b. C. position can be deleted if the new knot configuration K' is ambient isotopic to the original knot K.  ...  Figure 5 : 5 Shifting vertices: remove vertex by triangle move, add vertex.The list of original vertices and lists of delete and add vertices are properly merged to create a new knot configuration.  ... 
doi:10.1109/visual.1996.568120 dblp:conf/visualization/HuangGK96 fatcat:ineybhpzebd4fc4ye6vey6azly

Morphing methods in evolutionary design optimization

Michael Nashvili, Markus Olhofer, Bernhard Sendhoff
2005 Proceedings of the 2005 conference on Genetic and evolutionary computation - GECCO '05  
We introduce three different morphing methods and employ them as recombination operators in a standard evolution strategy (es).  ...  We compare their performance with an evolution strategy without any recombination operators on two target shape approximation problem.  ...  The sample points are the vertexes of the polygon morphing algorithms.  ... 
doi:10.1145/1068009.1068159 dblp:conf/gecco/NashviliOS05 fatcat:ymffzve45vdnjbkdbkyi344kfm

Fast incorporation of optical flow into active polygons

G. Unal, H. Krim, A. Yezzi
2005 IEEE Transactions on Image Processing  
It also provides an inherent regularization effect resulting from integrating measurements along polygon edges.  ...  We subsequently detail our contribution of computing an optical flow-based prediction step directly from the parameters of an active polygon, and of exploiting it in object tracking.  ...  Both curve evolution and polygon evolution models are utilized to carry out the tracking.  ... 
doi:10.1109/tip.2005.847286 pmid:15971774 fatcat:3ztlp5ivrndmpnltc5r7fl6z6i
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