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.
Elsevier DOI 0309

Samet, H.,
The Quadtree and Related Hierarchical Data Structures,
Surveys(16), No. 2, June, 1984, pp. 187-260. Quadtree, Survey. Survey, Data Structures. Survey, Quadtree. (UMd) The paper to define and explor quadtrees. BibRef 8406

Eastman, C.M.[Charles M.],
Automated Space Planning,
AI(4), No. 1, Spring 1973, pp. 41-64.
Elsevier DOI 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., 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., Friedman, J.H.,
Data Structures for Range Searching,
Surveys(11), No. 4, December 1979, pp. 397-409. Survey, Data Structures. BibRef 7912

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

Klinger, A., 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.[Charles R.],
The Space Efficiency of Quadtrees,
CGIP(19), No. 4, August 1982, pp. 335-348.
Elsevier DOI 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.
Elsevier DOI BibRef 8311

Bell, S.B.M.[Sarah B.M.], Holroyd, F.C.[Fred C.],
Tesseral Amalgamators And Hierarchical Tessellations,
IVC(9), No. 5, October 1991, pp. 313-328.
Elsevier DOI BibRef 9110

Matsuyama, T.[Takashi], Hao, L.V.[Le Viet], Nagao, M.[Makoto],
A File Organization for Geographic Information Systems Based on Spatial Proximity,
CVGIP(26), No. 3, June 1984, pp. 303-318.
Elsevier DOI k-d tree implementations. Disk optimization. BibRef 8406

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

Samet, H.[Hanan],
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., Samet, H.[Hanan],
A Consistent Hierarchical Representation for Vector Data,
Computer Graphics(20), No. 4, August 1986, pp. 197-206. BibRef 8608

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

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

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

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

Samet, H.[Hanan], Rosenfeld, A.[Azriel], Shaffer, C.A.[Clifford A.], Webber, R.E.[Robert 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.
Elsevier DOI BibRef
Processing Geographic Data with Quadtrees,
ICPR84(212-215). Storage of special data structures. BibRef

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

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

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

Samet, H.[Hanan],
Data Structures for Quadtree Approximation and Compression,
CACM(28), No. 9, September 1985, pp. 973-993. BibRef 8509
Quadtree Representation of Binary Images,
ICPR80(815-818). Datastructures without using pointers. Locational coding of leaf nodes. BibRef

Shaffer, C.A.[Clifford A.], Juvvadi, R.[Ramana], Heath, L.S.[Lenwood S.],
Generalized Comparison of Quadtree and Bintree Storage Requirements,
IVC(11), No. 7, September 1993, pp. 402-412.
Elsevier DOI probabilistic analysis of storage. BibRef 9309

Kim, Y.M.[Young-Mo], Par, S.B.[Song-Bai],
Complementary Quadtree,
IVC(11), No. 7, September 1993, pp. 413-418.
Elsevier DOI Coding of tree issues. BibRef 9309

Ahuja, N., Davis, L.S.[Larry 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., 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., Pavel, M.,
Hierarchical Coding of Binary Images,
PAMI(7), No. 3, May 1985, pp. 284-298. BibRef 8505

Mazumder, P.[Pinaki],
Planar Decomposition for Quadtree Data Structure,
CVGIP(38), No. 3, June 1987, pp. 258-274.
Elsevier DOI BibRef 8706

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

Gautier, N.K.[Nancy K.], Iyengar, S.S.[S. Sitharama], Lakhani, N.B.[Narinder B.], Manohar, M.,
Space and Time Efficiency of the Forest-of-Quadtrees Representation,
IVC(3), No. 2, May 1985, pp. 63-70.
Elsevier DOI BibRef 8505

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

Aoki, M.[Masayoshi],
Rectangular Region Coding for Image Data Compression,
PR(11), No. 5-6, 1979, pp. 297-312.
Elsevier DOI BibRef 7900
Local Image Continuity Measure and its Application,
ICPR80(1320-1322). BibRef

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

Abel, D.J., 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.
Elsevier DOI BibRef 8310

Tamminen, M.[Markku],
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.[Markku],
Encoding Pixel Trees,
CVGIP(28), No. 1, October 1984, pp. 44-57.
Elsevier DOI BibRef 8410

Tamminen, M.[Markku],
Performance Analysis of Cell Based Geometric File Organizations,
CVGIP(24), No. 2, November 1983, pp. 160-181.
Elsevier DOI 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., 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.[Narendra],
Efficient Planar Embedding of Trees for VLSI Layouts,
CVGIP(34), No. 2, May 1986, pp. 189-203.
Elsevier DOI 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.[Ravi V.], Ranka, S.[Sanjay],
Hypercube Algorithms for Operations on Quadtrees,
PR(25), No. 7, July 1992, pp. 741-747.
Elsevier DOI 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

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., 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.[Tsong-Wuu],
Compressed Quadtree Representations for Storing Similar Images,
IVC(15), No. 11, November 1997, pp. 833-843.
Elsevier DOI 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.
Elsevier DOI 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.
Elsevier DOI 0001

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.
Elsevier DOI 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

Liu, H.[Hui], Huang, K.K.[Ke-Kun], Ren, C.X.[Chuan-Xian], Yu, Y.F.[Yu-Feng], Lai, Z.R.[Zhao-Rong],
Quadtree coding with adaptive scanning order for space-borne image compression,
SP:IC(55), No. 1, 2017, pp. 1-9.
Elsevier DOI 1705
Remote sensing image compression BibRef

Wu, K.[Kejun], Yang, Y.[You], Liu, Q.[Qiong], Zhang, X.P.[Xiao-Ping],
Focal Stack Image Compression Based on Basis-Quadtree Representation,
MultMed(25), 2023, pp. 3975-3988.

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., 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:Apr 18, 2024 at 11:38:49