7.8 Quadtree, Hierarchical and Pyramid Representations

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See also Segmentation by Split and Merge Techniques, Hierarchical.

7.8.1 Quadtree Representations

Chapter Contents (Back)
Representation, Quadtree. Quadtree. Hierarchical. Quad-Tree.

Witten, M.[Matthew],
Compactification of information in R-color 2-dimensional rectangular patterns,
PR(10), No. 5-6, 1978, pp. 323-326.
WWW Link. 0309

Samet, H.,
The Quadtree and Related Hierarchical Data Structures,
Surveys(16), No. 2, June, 1984, pp. 187-260. (UMd) Quadtree, Survey. Survey, Data Structures. Survey, Quadtree. What must be the definitive paper on quadtrees. BibRef 8406

Eastman, C.M.,
Automated Space Planning,
AI(4), No. 1, Spring 1973, pp. 41-64.
WWW Link. BibRef 7300
Representations for Space Planning,
CACM(13), No. 4, April 1970, pp. 242-250. BibRef

Kirsch, R.A.,
Resynthesis of Biological Iamges from Tree-Structured Decomposition Data,
GL72(1-19). BibRef 7200

Finkel, R.A., and Bentley, J.L.,
Quad Trees: A Data Structure for Retrieval on Composite Keys,
Acta Inf.(4), No. 1, 1974, pp. 1-9. BibRef 7400

Bentley, J.L.,
Multidimensional Binary Search Trees Used for Associative Searching,
CACM(18), No. 9, September 1975, pp. 509-511. BibRef 7509

Bentley, J.L., and Friedman, J.H.,
Data Structures for Range Searching,
Surveys(11), No. 4, December 1979, pp. 397-409. Survey, Data Structures. BibRef 7912

Tanimoto, S.L.,
Regular Hierarchical Image and Processing Structures in Machine Vision,
CVS78(165-174). BibRef 7800

Tanimoto, S.L., and Pavlidis, T.,
A Hierarchical Data Structure for Picture Processing,
CGIP(4), No. 2, June 1975, pp. 104-119.
WWW Link. Quadtree. Pyramids. See also Structured Computer Vision: Machine Perception through Hierarchical Computational Structures. BibRef 7506

Tanimoto, S.L.,
A Formalism for Image Processing in Pyramids,
PRAI-78(181-183). BibRef 7800

Klinger, A., and Dyer, C.R.,
Experiments on Picture Representation Using Regular Decomposition,
CGIP(5), No. 1, March 1976, pp. 68-105. Quadtree. BibRef 7603

Klinger, A., and Rhodes, M.L.,
Organization and Access of Image Data by Areas,
PAMI(1), No. 1, January 1979, pp. 50-60. BibRef 7901

Klinger, A.,
Searching Images,
PRAI-78(177-180). BibRef 7800

Alexandridis, N.A., Klinger, A.,
Picture Decomposition, Tree Data-Structures, and identifying Directional Symmetries as Node Combinations,
CGIP(8), 1978, pp. 43-77. BibRef 7800

Klinger, A.,
Data Structures and Pattern Recognition,
ICPR76(497-498). BibRef 7600
Regular Decomposition and Picture Structure,
SMC-C74(xx). BibRef

Gargantini, I.,
An Effective Way to Represent Quadtrees,
CACM(25), No. 12, December 1982, pp. 905-910. For Octtree version: See also Linear Octtrees for Fast Processing of Three-Dimensional Objects. BibRef 8212

Dyer, C.R.,
The Space Efficiency of Quadtrees,
CGIP(19), No. 4, August 1982, pp. 335-348.
WWW Link. BibRef 8208

Bell, S.B.M., Diaz, B.M., Holroyd, F.C., and Jackson, M.J.,
Spatially Referenced Methods of Processing Raster and Vector Data,
IVC(1), No. 4, November 1983, pp. 211-220.
WWW Link. BibRef 8311

Bell, S.B.M., Holroyd, F.C.,
Tesseral Amalgamators And Hierarchical Tessellations,
IVC(9), No. 5, October 1991, pp. 313-328.
WWW Link. BibRef 9110

Matsuyama, T., Hao, L.V., and Nagao, M.,
A File Organization for Geographic Information Systems Based on Spatial Proximity,
CVGIP(26), No. 3, June 1984, pp. 303-318.
WWW Link. BibRef 8406

Milford, D.J., and Willis, P.C.,
Quad Encoded Display,
IEE-P(E: 131), No. 3, May 1984, pp. 70-75. BibRef 8405

Samet, H.,
Hierarchical Representations of Collections of Small Rectangles,
Surveys(20), No. 4, December, 1988, pp. 271-309. Survey, Data Structures. Extension of the quadtree idea to general rectangles. BibRef 8812

Nelson, R.C., and Samet, H.,
A Consistent Hierarchical Representation for Vector Data,
Computer Graphics(20), No. 4, August 1986, pp. 197-206. BibRef 8608

Samet, H.,
Applications of Spatial Data Structures,
Reading, MA: Addison-Wesley1990. BibRef 9000 Book BibRef

Samet, H.,
Design and Analysis of Spatial Data Structures,
Reading, MA: Addison-Wesley1990. (or 1989??) BibRef 9000 Book BibRef

Shaffer, C.A., Juvvadi, R., and Heath, L.S.,
Generalized Comparison of Quadtree and Bintree Storage Requirements,
IVC(11), No. 7, September 1993, pp. 402-412.
WWW Link. BibRef 9309

Kim, Y.M., and Park, S.B.,
Complementary Quadtree,
IVC(11), No. 7, September 1993, pp. 413-418.
WWW Link. BibRef 9309

Samet, H.,
Deletion in Two-Dimensional Quad Trees,
CACM(23), No. 12, December 1980, pp. 703-710. BibRef 8012

Ahuja, N., Davis, L.S., Milgram, D.L., and Rosenfeld, A.,
Piecewise Approximation of Pictures Using Maximal Neighborhoods,
TC(27), No. 4, April 1978, pp. 375-379. BibRef 7804

Jones, L.P., and Iyengar, S.S.,
Space and Time Efficient Virtual Quadtrees,
PAMI(6), No. 2, March 1984, pp. 244-247. BibRef 8403
Virtual Quadtrees,
CVPR83(133-136). BibRef
Representation of a Region as a Forest of Quad-Trees,
PRIP81(57-59). More on the quadtree problem. BibRef

Cohen, Y., Landy, M.S., and Pavel, M.,
Hierarchical Coding of Binary Images,
PAMI(7), No. 3, May 1985, pp. 284-298. BibRef 8505

Mazumder, P.,
Planar Decomposition for Quadtree Data Structure,
CVGIP(38), No. 3, June 1987, pp. 258-274.
WWW Link. BibRef 8706

Manohar, M., Rao, P.S.[P. Sudarsana], and Iyengar, S.S.,
Template Quadtrees for Representing Region and Line Data Present in Binary Images,
CVGIP(51), No. 3, September 1990, pp. 338-354.
WWW Link. The leaf nodes are represented as templates other than pure black or white. BibRef 9009

Gautier, N.K., Iyengar, S.S., Lakhani, N.B., Manohar, M.,
Space and Time Efficiency of the Forest-of-Quadtrees Representation,
IVC(3), No. 2, May 1985, pp. 63-70.
WWW Link. BibRef 8505

Samet, H., and Webber, R.E.,
On Encoding Boundaries with Quadtrees,
PAMI(6), No. 3, May, 1984, pp. 365-369. BibRef 8405
Storing Collections of Polygons Using Quadtrees,
TOG(4), 1985, pp. 182-222. BibRef
Using Quadtrees to Represent Polygonal Maps,
CVPR83(127-132). More on the quad-tree problem for lines. BibRef

Samet, H., Webber, R.E.,
A Comparison of the Space Requirements of Multi-Dimensional Quadtree-Based File Structures,
VC(5), 1989, pp. 349-359. BibRef 8900

Samet, H., Rosenfeld, A., Shaffer, C.A., and Webber, R.E.,
Quadtree Region Representation in Cartography: Experimental Results,
SMC(13), 1983, pp. 1148-1154. BibRef 8300
A Geographic Information System Using Quadtrees,
PR(17), No. 6, 1984, pp. 647-656.
WWW Link. BibRef
Processing Geographic Data with Quadtrees,
ICPR84(212-215). Storage of special data structures. BibRef

Samet, H., Shaffer, C.A.[Clifford A.], and Webber, R.E.[Robert E.],
The Segment Quadtree: A Linear Quadtree-Based Representation for Linear Features,
CVPR85(385-389). (Univ. of Maryland and Rutgers Univ.), Good for graphics and lines. One of many applications of quadtrees. BibRef 8503

Samet, H.,
A Top-Down Quadtree Traversal Algorithm,
PAMI(7), No. 1, January 1985, pp. 94-98. BibRef 8501

Samet, H.,
Data Structures for Quadtree Approximation and Compression,
CACM(28), No. 9, September 1985, pp. 973-993. Datastructures without using pointers. Locational coding of leaf nodes. BibRef 8509

Chien, C.H., Aggarwal, J.K.,
A Normalized Quadtree Representation,
CVGIP(26), No. 3, June 1984, pp. 331-346.
WWW Link. BibRef 8406
Earlier: CVPR83(121-126). For Octrees: See also Volume/Surface Octrees for the Representation of Three-Dimensional Objects. BibRef

Aoki, M.,
Rectangular Region Coding for Image Data Compression,
PR(11), No. 5-6, 1979, pp. 297-312.
WWW Link. BibRef 7900

Aoki, M.,
Local Image Continuity Measure and its Application,
ICPR80(1320-1322). BibRef 8000

Abel, D.J.,
A B(+) Tree Structure for Large Quadtrees,
CVGIP(27), No. 1, July 1984, pp. 19-31.
WWW Link. BibRef 8407

Abel, D.J., and Smith, J.L.,
A Data Structure and Algorithm Based on a Linear Key for a Rectangle Retrieval Problem,
CVGIP(24), No. 1, October 1983, pp. 1-13.
WWW Link. BibRef 8310

Tamminen, M.,
Comment on Quad- and Octtrees,
CACM(27), No. 3, March 1984, pp. 248-249. Improves on the efficencies of two recent algorithms: For Octtrees: See also Linear Octtrees for Fast Processing of Three-Dimensional Objects. and Quadtrees: See also Effective Way to Represent Quadtrees, An. BibRef 8403

Tamminen, M.,
Encoding Pixel Trees,
CVGIP(28), No. 1, October 1984, pp. 44-57.
WWW Link. BibRef 8410

Tamminen, M.,
Performance Analysis of Cell Based Geometric File Organizations,
CVGIP(24), No. 2, November 1983, pp. 160-181.
WWW Link. BibRef 8311

Kawaguchi, E., Endo, T.,
On a Method of Binary Picture Representation and its Application to Data Compression,
PAMI(2), No. 1, January 1980, pp. 27-35. Linear encoding requires less than 2 bits per node. BibRef 8001

Kawaguchi, E., Endo, T., and Matsunaga, J.I.,
Depth-First Picture Expression Viewed from Digital Picture Processing,
PAMI(5), No. 4, July 1983, pp. 373-384. BibRef 8307

Ahuja, N.,
Efficient Planar Embedding of Trees for VLSI Layouts,
CVGIP(34), No. 2, May 1986, pp. 189-203.
WWW Link. BibRef 8605

Kunii, T.L., Fujishiro, I., Mao, X.,
G-Quadtree: A Hierarchical Representation of Gray-Scale Digital Images,
VC(2), 1986, pp. 219-226. BibRef 8600

Fuhrmann, D.R.,
Quadtree Traversal Algorithms for Pointer-Based and Depth-First Representations,
PAMI(10), No. 6, November 1988, pp. 955-960.
IEEE DOI BibRef 8811

Radha, H., Leonardi, R., Vetterli, M., Naylor, B.F.,
Binary Space Partitioning Tree Representation of Images,
JVCIR(2), 1991, pp. 201-221. See also Image Compression Using Binary Space Partitioning Trees. BibRef 9100

Subramanian, K.R., Naylor, B.F.,
Converting Discrete Images to Partitioning Trees,
VCG(3), No. 3, Jul-Sep 1997, pp. 273-288. 9710

Shankar, R.V., Ranka, S.,
Hypercube Algorithms for Operations on Quadtrees,
PR(25), No. 7, July 1992, pp. 741-747.
WWW Link. BibRef 9207

Sullivan, G.J., Baker, R.L.,
Efficient Quadtree Coding of Images and Video,
IP(3), No. 3, May 1994, pp. 327-331.
IEEE DOI BibRef 9405

Samet, H.[Hanan],
Object-Based and Image-Based Representations of Objects by Their Interiors,
AIU96(316-332). BibRef 9600

Samet, H.[Hanan],
Quadtree Representation of Binary Images,
ICPR80(815-818). BibRef 8000

Mobasseri, B.G.,
A Generalized Solution to the Quadtree Expected Complexity Problem,
PRL(16), 1995, pp. 443-456. BibRef 9500
A new quadtree complexity theorem,

Mobasseri, B.G.,
Soft-Linked Quadtree: A Cascaded Ring Structure Using Flexible Linkage Concept,
IEEE DOI BibRef 8800

Vassilakopoulos, M., and Manolopoulos, Y.,
A Random Model for Analyzing Region Quadtrees,
PRL(16), 1995, pp. 1137-1145. BibRef 9500

Unnikrishnan, A., Venkatesh, Y.V., Shankar, P.,
Distribution of Black Nodes at Various Levels in a Linear Quadtree,
PRL(6), 1987, pp. 341-342. BibRef 8700

Burton, F.W., Kollias, V.J., Kollias, J.G.,
Expected and Worst-Case Storage Requirements for Quadtrees,
PRL(3), 1985, pp. 131-135. BibRef 8500

Chang, H.K.C., Liu, S.H., Tso, C.K.,
Two-Dimensional Template Based Encoding for Linear Quadtree Representation,
PhEngRS(63), No. 11, November 1997, pp. 1275-1282. 9711

Lin, T.W.,
Compressed Quadtree Representations for Storing Similar Images,
IVC(15), No. 11, November 1997, pp. 833-843.
WWW Link. 9712

Lightstone, M., Mitra, S.K.,
Quadtree Optimization for Image and Video Coding,
VLSIVideo(17), No. 2-3, November 1997, pp. 215-224. 9712

Bourbakis, N.G., Barlos, F., Mertoguno, J.S.,
Hermes Autonomous Vision System: The Flat Quadtree Model,
PRAI(12), No. 3, May 1998, pp. 265-291. 9807

Aref, W.G.[Walid G.], Samet, H.[Hanan],
Efficient Window Block Retrieval in Quadtree-Based Spatial Databases,
GeoInfo(1), No. 1, April 1997, pp. 59-91.
DOI Link BibRef 9704

Nardelli, E.[Enrico], Proietti, G.[Guido],
Probabilistic models for images and quadtrees: Differences and equivalences,
IVC(17), No. 9, July 1999, pp. 659-665.
WWW Link. BibRef 9907
An accurate model for quadtrees representing noiseless images of spatial data,
ICIP94(II: 610-614).

Yang, Y.H.[Yuh-Horng], Chung, K.L.[Kuo-Liang], Tsai, Y.H.[Yao-Hong],
A compact improved quadtree representation with image manipulations,
IVC(18), No. 3, February 2000, pp. 223-231.
WWW Link. 0001

Samet, H.,
Object Representations,
FIU01(Chapter 7). BibRef 0100

Chen, P.M.[Pei-Min],
Variant code transformations for linear quadtrees,
PRL(23), No. 11, September 2002, pp. 1253-1262.
Elsevier DOI 0206

Vörös, J.[Jozef],
Quadtree-based representations of grid-oriented data,
IVC(24), No. 3, 1 March 2006, pp. 263-270.
WWW Link. 0604
Image representation; Robotics; Potentials; Voronoi diagram; Rapid prototyping BibRef

Caselles, V.[Vicent], Monasse, P.[Pascal],
Geometric Description of Images as Topographic Maps,
Springer2010. Lecture Notes in Mathematics, Vol. 1984 ISBN: 978-3-642-04610-0
WWW Link. Geometric contents of an image and tree structure to represent it. Buy this book: Geometric Description of Images as Topographic Maps (Lecture Notes in Mathematics) 1002

Wang, Y., Guo, M.,
An Integrated Spatial Indexing of Huge Point Image Model,
DOI Link 1209
2D Quadtree, 3D-R Tree. BibRef

Ageenko, E.[Eugene], Franti, P.[Pasi],
Forward Adaptive Modeling for Context-based Compression of Large Binary Images in Applications Requiring Spatial Access,
IEEE DOI BibRef 9900

Franti, P.[Pasi], Ageenko, E.[Eugene],
On the Use of Context Tree for Binary Image Compression,
IEEE DOI BibRef 9900

Balmelli, L.[Laurent], Kovacevic, J.[Jelena], Vetterli, M.[Martin],
Quadtrees for Embedded Surface Visualization: Constraints and Efficient Data Structures,
HTML Version. Code for this work is also available:
HTML Version. BibRef 9900

Benoit-Cattin, H., Planat, A.C., Joachimsmann, P.R., Baskurt, A., Clarysse, P., Magnin, I.E.,
On the coding of active quadtree mesh,
ICIP98(II: 895-898).

Yang, D.K.[De-Kun],
Compressed quadtree with content-addressable memory,
ICIP94(II: 395-399).

Vassilakopoulos, M.[Michael], Manolopoulos, Y.[Yannis],
Analytical results on the Quadtree storage-requirements,
Springer DOI 9309

Kertész, M.[Miklós], Kummert, Á.[Ágnes], Csillag, F.[Ferenc],
From pyramids to quadtrees: Approximation of heterogeneous surfaces by fixing complexity,
Springer DOI 9309

Lindenbaum, M., and Samet, H.,
A Probabilistic Analysis of Hierarchical Geometric Data Structures,
ICPR90(II: 91-96).
IEEE DOI Quadtree, Evaluation. BibRef 9000

Nakamura, Y., Abe, S., Ohsawa, Y., Sakauchi, M.,
An Efficient Data Management Method for Spatial Objects Using MD-tree-Experimental Evaluation and Comparisons,
IEEE DOI BibRef 9200
Data structures for multilayer N-dimensional data using hierarchical structure,
ICPR90(II: 97-102).

Nakamura, Y., Abe, S., Ohsawa, Y., Sakauchi, M.,
MD-Tree: A Balanced Hierarchical Data Structure for Multi-Dimensional Data with Highly Efficient Dynamic Characteristics,
ICPR88(I: 375-378).

Chen, C., Zou, H.,
Linear Binary Tree,
ICPR88(I: 576-578).
IEEE DOI BibRef 8800

Kawaguchi, E., Taniguchi, R.I.,
Coded DF-Expression for Binary and Multi-Valued Picture,
ICPR88(II: 1159-1163).
IEEE DOI BibRef 8800

Liang, Z.H.[Ze-Huan],
A Picture Decomposition Algorithm Using a Pictoral Information Measure,
CVWS82(127-134). BibRef 8200

Chapter on 2-D Feature Analysis, Extraction and Representations, Shape, Skeletons, Texture continues in
Quadtree Generation and Computations .

Last update:Mar 13, 2017 at 16:25:24