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An adaptive algorithm for conversion from quadtree to chain codes

Frank Y Shih, Wai-Tak Wong
2001 Pattern Recognition  
An adaptive algorithm is presented for converting the quadtree representation of a binary image to its chain code representation.  ...  Our algorithm has the advantage of constructing the chain codes of the resulting quadtree of the Boolean operation of two quadtrees by re-using the original chain codes.  ...  Otherwise, go back to step 2. Our adaptive conversion algorithm from quadtree to chain code is based on the 8-neighbor traversal algorithm [13] .  ... 
doi:10.1016/s0031-3203(00)00008-x fatcat:sxvax54cgrewbp7e4tdgcwixo4

Using topological sweep to extract the boundaries of regions in maps represented by region quadtrees

M. B. Dillencourt, H. Samet
1996 Algorithmica  
The algorithm works for maps that contain multiple regions as well as holes. The algorithm makes use of active objects (in the form of regions) and an active border.  ...  The algorithm works for many different quadtree representations including those where the quadtree is stored in external storage.  ...  Of course, other representations of the boundary (e.g., chain codes [12] ) are also possible, and the algorithms of this paper can be readily adapted to produce them.  ... 
doi:10.1007/bf01942608 fatcat:52ejo35uprabrhvxxeus2ojfkm

An Overview of Quadtrees, Octrees, and Related Hierarchical Data Structures [chapter]

Hanan Samet
1988 Theoretical Foundations of Computer Graphics and CAD  
An overview of hierarchical data structures for representing images, such as the quadtree and octree, is presented. They are based on the principle of recursive decomposition.  ...  There is a greater emphasis on region data (i.e., 2-dimensional shapes) and to a lesser extent on point, lin.e, and 3-dimension-al data.  ...  The ability to perform set operations quickly is one of the primary reasons for the popularity of quadtrees over alternative representations such as the chain code or vectors.  ... 
doi:10.1007/978-3-642-83539-1_2 fatcat:woensntuqnhmxplj5f626mscsm

Block-run run-length coding of handwriting and bilevel graphics based on quadtree segmentation

H. Yuen, L. Hanzo
1997 Pattern Recognition Letters  
An efficient off-line coding scheme for handwriting and bilevel graphics based on quadtree segmentation and block-run run-length coding (RLC) is presented.  ...  higher coding efficiency than the conventional one-dimensional RLC and its bit rate is close to that of on-line dynamographical chain coding. © 1997 Elsevier Science B.V.  ...  In order to apply the off-line coding scheme to the on-line handwriting data, a transcoding algorithm was used to convert the on-line handwriting data into the off-line raster scanning bit pattern.  ... 
doi:10.1016/s0167-8655(96)00133-x fatcat:aqoszr7lhfgtdlmtw3hep5pa2y

Spatial Indexing for Location-Aware Systems

Robert K. Harle
2007 2007 Fourth Annual International Conference on Mobile and Ubiquitous Systems: Networking & Services (MobiQuitous)  
It establishes the principles and requirements of a wide-area spatial indexer, reviews the R-tree, Quadtree and RQ-tree methods proposed before for indoor location-awareness, and significantly adapts the  ...  The proposed indexing method uses a combination of R-trees (for high level spatial information, down to structural level) and Quadtrees (for lower level representation of objects).  ...  Conversely, in an indoor environment, it has proven more useful for a location-aware service to avoid user query initiation.  ... 
doi:10.1109/mobiq.2007.4451027 dblp:conf/mobiquitous/Harle07 fatcat:xpsx5g2wznbj7dznhmukdkimsy

On the size of quadtrees generalized to d-dimensional binary pictures

T.R. Walsh
1985 Computers and Mathematics with Applications  
Among these results are a comparison of the space-efficiency of linear vs regular trees, in terms of both the number of nodes of the tree and the number of bits needed to store each node, and an upper  ...  S~meresu~tsaboutthesize~fquadtreesand~inearq~dtrees'usedt~r~pres~ntbinary2 ~ x 2" digital pictures, are generalized to d-dimensional 2" x . . . x 2" pictures.  ...  Acknowledgement--The author wishes to thank Prof. I. Gargantini for posing these problems and giving valuable assistance in the preparation of the Introduction and Section I of this article.  ... 
doi:10.1016/0898-1221(85)90187-7 fatcat:vkmjwi6ry5dzbc3unjhlfdmboa

Hierarchical data structures and algorithms for computer graphics. I. Fundamentals

H. Samet, R.E. Webber
1988 IEEE Computer Graphics and Applications  
While such data structures are not necessary for the processing of simple scenes, they are central to the efficient processing of large-scale realistic scenes.  ...  Object-space hierarchies are discussed briefly, but the main emphasis is on hierarchies constructed in the image space, such as quadtrees and oc t rees.  ...  Average-case analysis for the execution time of the chain-code-to-raster-quadtree algorithm is linear in the length of the chain code, as shown by analysis" in conjunction with the quadtree complexity  ... 
doi:10.1109/38.513 fatcat:aoqboxnwx5gnzoenouseefauby

The Quadtree and Related Hierarchical Data Structures

Hanan Samet
1984 ACM Computing Surveys  
A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition.  ...  There is a greater emphasis on region data (i.e., two-dimensional shapes) and to a lesser extent on point, curvilinear, and threedimensional data.  ...  Thus it is useful to be able to construct a quadtree from a chain code representation of a binary image. Such an algorithm described by Samet [1980a] is briefly outlined below.  ... 
doi:10.1145/356924.356930 fatcat:3q363g3xondbjivox43umdusjm

Algebraic Topological Analysis of Time-Sequence of Digital Images [chapter]

Rocio Gonzalez–Diaz, Belen Medrano, Pedro Real, Javier Sánchez–Peláez
2005 Lecture Notes in Computer Science  
Our answer is based on an algebraictopological coding, called AT-model, for a nD (n = 2, 3) digital binaryvalued image I consisting simply in taking I together with an algebraic object depending on it.  ...  Considering AT-models for all the 2D digital images in a time sequence, it is possible to get an AT-model for the 3D digital image consisting in concatenating the successive 2D digital images in the sequence  ...  There is an algorithm calculating an AT-model for I.  ... 
doi:10.1007/11555964_18 fatcat:yl4cteadzjfdlph4tzfe6m2wza

Multiresolution rendering by sewing trimmed NURBS surfaces

Ferenc Kahlesz, Ákos Balázs, Reinhard Klein
2002 Proceedings of the seventh ACM symposium on Solid modeling and applications - SMA '02  
and this way they do not provide an automatic solution to create large connected models just from a set of surfaces.  ...  For their efficient rendering multiresolution models are needed. To create such models without artifacts at the trimming curves, one needs to sew parts together along the common boundaries.  ...  If we want to guarantee a κ error on the boundaries, we can achieve this by choosing a general ε = κ 3 for the quadtree algorithm and an appropriate δ = κ−2 bl for a linear approximation (e.g. using midpoint  ... 
doi:10.1145/566282.566323 dblp:conf/sma/KahleszBK02 fatcat:47jp6vwdzvax7ezopeciakwgkm

Multiresolution rendering by sewing trimmed NURBS surfaces

Ferenc Kahlesz, Ákos Balázs, Reinhard Klein
2002 Proceedings of the seventh ACM symposium on Solid modeling and applications - SMA '02  
and this way they do not provide an automatic solution to create large connected models just from a set of surfaces.  ...  For their efficient rendering multiresolution models are needed. To create such models without artifacts at the trimming curves, one needs to sew parts together along the common boundaries.  ...  If we want to guarantee a κ error on the boundaries, we can achieve this by choosing a general ε = κ 3 for the quadtree algorithm and an appropriate δ = κ−2 bl for a linear approximation (e.g. using midpoint  ... 
doi:10.1145/566313.566323 fatcat:bhurktxbczhfrjrv2lpb33kydi

ForestClaw: A parallel algorithm for patch-based adaptive mesh refinement on a forest of quadtrees [article]

Donna Calhoun, Carsten Burstedde
2017 arXiv   pre-print
We have implemented this algorithm in the ForestClaw code using single-grid solvers from ClawPack, a software package for solving hyperbolic PDEs using finite volumes methods.  ...  We describe a parallel, adaptive, multi-block algorithm for explicit integration of time dependent partial differential equations on two-dimensional Cartesian grids.  ...  The authors gratefully acknowledge the Gauß Centre for Supercomputing (GCS) for providing computing time through the John von Neumann Institute for Com-  ... 
arXiv:1703.03116v1 fatcat:oqrjj3l42rby3c6pmbdptczvqi

The chordlet transform with an application to shape compression

Z. He, M. Bystrom
2012 Signal processing. Image communication  
A data structure, the fat quadtree and an algorithm for determining an optimal chordlet representation of an image are proposed.  ...  We propose to extend the line-based dictionary of the beamlet framework to one that includes sets of arcs that are quantized in height.  ...  Due to the introduction and adoption of the new fat quadtree structure, this algorithm must be adapted.  ... 
doi:10.1016/j.image.2011.09.001 fatcat:fa6q3237tvgabikijebmh2e3lq

Triangulating the Square and Squaring the Triangle: Quadtrees and Delaunay Triangulations are Equivalent

Maarten Löffler, Wolfgang Mulzer
2012 SIAM journal on computing (Print)  
Our main tool for the second algorithm is the well-separated pair decomposition(WSPD), a structure that has been used previously to find Euclidean minimum spanning trees in higher dimensions (Eppstein)  ...  More precisely, we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay triangulation; the second finds the Delaunay triangulation, given a compressed  ...  We would like to thank the group at Carleton and especially our hosts Jit Bose and Pat Morin for their wonderful hospitality and for creating a great research environment.  ... 
doi:10.1137/110825698 fatcat:bokamjbnyvetpko26ulgv3laza

A quadtree-adaptive spectral wave model

Stéphane Popinet, Richard M. Gorman, Graham J. Rickard, Hendrik L. Tolman
2010 Ocean Modelling  
For the case of a cyclone-generated wave field, the cost of the adaptive method increases linearly with spatial resolution compared to quadratically for constant-resolution methods.  ...  This equivalence facilitates the generalisation of GSE alleviation techniques to quadtree grids.  ...  This development was made possible by the availability of source codes for both Gerris (Popinet, 2009c; Popinet, 2009d) and WAVEWATCH III.  ... 
doi:10.1016/j.ocemod.2010.04.003 fatcat:temov6s5vvfp5hs45anjirjy4y
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