*Bentley, J.L.*, and
*Stanat, D.F.*,

**Analysis of Range Searches in Quad Trees**,

*IPL(3)*, No. 6, July 1975, pp. 170-173.
BibRef
**7507**

*Lee, D.T.*, and
*Wong, C.K.*,

**Worst-Case Analysis for Region and Partial Region Searches in
Multidimensional Binary Search Trees and Quad Trees**,

*Acta Inf.(9)*, No. 1, 1977, pp. 23-29.
BibRef
**7700**

*Hunter, G.M.*, and
*Steiglitz, K.*,

**Operations on Images Using Quad Trees**,

*PAMI(1)*, No. 2, April 1979, pp. 145-153.
BibRef
**7904**

Earlier:
*PRAI-78*(184).
BibRef

*Hunter, G.M.*,
*Steiglitz, K.*,

**Linear Transformation of Pictures Represented by Quad Trees**,

*CGIP(10)*, No. 3, July 1979, pp. 289-296.

WWW Link.
BibRef
**7907**

*Samet, H.*,

**An Algorithm for Converting Rasters to Quadtrees**,

*PAMI(3)*, No. 1, January 1981, pp. 93-95.
BibRef
**8101**

*Samet, H.*,

**Algorithms for the Conversion of Quadtrees to Rasters**,

*CVGIP(26)*, No. 1, April 1984, pp. 1-16.

WWW Link.
BibRef
**8404**

*Vaishnavi, V.K.*,
*Wood, D.*,

**Data Structures for the Rectangle Containment and Enclosure Problems**,

*CGIP(13)*, No. 4, August 1980, pp. 372-384.

WWW Link. Segment Tree description for geometric objects.
BibRef
**8008**

*Li, M.*,
*Grosky, W.I.*,
*Jain, R.*,

**Normalized Quadtrees with Respect to Translations**,

*CGIP(20)*, No. 1, September 1982, pp. 72-81.

WWW Link.
BibRef
**8209**

And:
*PRIP81*(60-62).
BibRef

*Grosky, W.I.*,
*Jain, R.*,

**Optimal Quadtrees for Image Segments**,

*PAMI(5)*, No. 1, January 1983, pp. 77-83.
BibRef
**8301**

*Oliver, M.A.*, and
*Wiseman, N.E.*,

**Operations on Quadtree-Encoded Images**,

*Computer Journal(26)*, No. 1, February 1983, pp. 83-91.
BibRef
**8302**

And:

**Operations on Quadtree Leaves and Related Image Areas**,

*Computer Journal(26)*, No. 4, November 1983, pp. 375-380.
BibRef

*Samet, H.*,

**Reconstruction of Quadtrees from Quadtree Medial Axis Transforms**,

*CVGIP(29)*, No. 3, 1985, pp. 311-328.

WWW Link.
BibRef
**8500**

*Shaffer, C.A.*,
*Samet, H.*,

**Optimal Quadtree Construction Algorithms**,

*CVGIP(37)*, No. 3, March 1987, pp. 402-419.

WWW Link.
BibRef
**8703**

And:

**An Optimal Quadtree Construction Algorithm**,

*ICPR86*(317-319).
BibRef

*Shaffer, C.A.*, and
*Samet, H.*,

**Set Operations for Unaligned Linear Quadtrees**,

*CVGIP(50)*, No. 1, April 1990, pp. 29-49.

WWW Link. Minimized the nodes for union and intersection operations.
BibRef
**9004**

*Samet, H.*, and
*Shaffer, C.A.*,

**A Model for the Analysis of Neighbor Finding in Pointer Based Quadtrees**,

*PAMI(7)*, No. 6, November 1985, pp. 717-720.
Refined the model for neighbor finding to show it
was not as bad as the earlier numbers did.
BibRef
**8511**

*Samet, H.*,

**Neighbor Finding Techniques for Images Represented by Quadtrees**,

*CGIP(18)*, No. 1, January 1982, pp. 37-57.

WWW Link.
BibRef
**8201**

Earlier:

**Neighbor Finding in Quadtrees**,

*PRIP81*(68-74).
BibRef

*Samet, H.*,

**Neighbor Finding in Images Represented by Octrees**,

*CVGIP(46)*, No. 3, June 1989, pp. 367-386.

WWW Link.
BibRef
**8906**

*Samet, H.*,
*Shaffer, C.A.*,
*Nelson, R.C.*,
*Huang, Y.G.*,
*Fujimura, K.*,
*Rosenfeld, A.*,

**Recent Developments in Linear Quadtree-Based
Geographic Information Systems**,

*IVC(5)*, No. 3, August 1987, pp. 187-197.

WWW Link.
BibRef
**8708**

*Mark, D.M.*, and
*Abel, D.J.*,

**Linear Quadtrees from Vector Representations of Polygons**,

*PAMI(7)*, No. 3, May 1985, pp. 344-349.
BibRef
**8505**

*Chaudhuri, B.B.*,

**Applications of Quadtree, Octree, and Binary Tree Decomposition Techniques
to Shape Analysis and Pattern Recognition**,

*PAMI(7)*, No. 6, November 1985, pp. 652-661.
BibRef
**8511**

*Bauer, M.A.*,

**Set Operations on Linear Quadtrees**,

*CVGIP(29)*, No. 2, February 1985, pp. 248-258.

WWW Link.
BibRef
**8502**

*Lauzon, J.P.*,
*Mark, D.M.*,
*Kikuchi, L.*,
*Guevara, J.A.*,

**Two-Dimensional Run-Encoding for Quadtree Representation**,

*CVGIP(30)*, No. 1, April 1985, pp. 56-69.

WWW Link.
*Run Length Code*.
BibRef
**8504**

*Peters, F.J.[Frans J.]*,

**An Algorithm for Transformations of Pictures by Quadtrees**,

*CVGIP(32)*, No. 3, December 1985, pp. 397-403.

WWW Link. Translation, scaling, and rotations.
BibRef
**8512**

*Ravindran, S.*,
*Manohar, M.*,

**Algorithm For Converting A Forest Of Quadtrees To A Binary Array**,

*IVC(5)*, No. 4, November 1987, pp. 297-300.

WWW Link.
BibRef
**8711**

*Li, S.X.[Shu-Xiang]*,
*Loew, M.H.[Murray H.]*,

**The Quadcode and Its Arithmetic**,

*CACM(30)*, No. 7, July 1987, pp. 621-626.
The code is a direct representation of the image, not
exactly a quadtree.
BibRef
**8707**

*van Lierop, M.L.P.*,

**Geometrical Transformations on Pictures Represented by Leafcodes**,

*CVGIP(33)*, No. 1, January 1986, pp. 81-98.

WWW Link.
BibRef
**8601**

*Walsh, T.R.*,

**Efficient Axis-Translation of Binary Digital Pictures by
Blocks in Linear Quadtree Representation**,

*CVGIP(41)*, No. 3, March 1988, pp. 282-292.

WWW Link.
BibRef
**8803**

*Bhaskar, S.K.*,
*Rosenfeld, A.*,
*Wu, A.Y.*,

**Parallel Processing of Regions Represented by Linear Quadtrees**,

*CVGIP(42)*, No. 3, June 1988, pp. 371-380.

WWW Link.
BibRef
**8806**

*Wu, A.Y.*,
*Bhaskar, S.K.*,
*Rosenfeld, A.*,

**Parallel Processing of Region Boundaries**,

*PR(22)*, No. 2, 1989, pp. 165-172.

WWW Link.
BibRef
**8900**

*Wu, A.Y.[Angela Y.]*,
*Rosenfeld, A.[Azriel]*,

**Parallel processing of encoded bit strings**,

*PR(21)*, No. 6, 1988, pp. 559-565.

WWW Link.
**0309**

BibRef

*Gao, P.*,
*Smith, T.R.*,

**Space Efficient Hierarchical Structures:
Relatively Addressed Compact Quadtrees for GISs**,

*IVC(7)*, No. 3, August 1989, pp. 173-177.

WWW Link.
*GIS*.
BibRef
**8908**

*Holroyd, F.C.*,
*Mason, D.C.*,

**Efficient Linear Quadtree Construction Algorithm**,

*IVC(8)*, No. 3, August 1990, pp. 218-224.

WWW Link.
BibRef
**9008**

*Shaffer, C.A.*, and
*Stout, Q.F.*,

**Linear Time Distance Transforms for Quadtrees**,

*CVGIP(54)*, No. 2, September 1991, pp. 215-223.

WWW Link. Compute the chessboard distance for both pointer and linear quadtrees.
BibRef
**9109**

*Schrack, G.[Günther]*,

**Finding Neighbors of Equal Size in Linear Quadtrees
and Octrees in Constant Time**,

*CVGIP(55)*, No. 3, May 1992, pp. 221-230.

WWW Link. Constant time algorithm in linear quadtrees.
BibRef
**9205**

*Kasif, S.*,

**Optimal Parallel Algorithms for Quadtree Problems**,

*CVGIP(59)*, No. 3, May 1994, pp. 281-285.

WWW Link.
BibRef
**9405**

*Dehne, F.*,
*Rauchaplin, A.*,
*Ferreira, A.G.*,

**Hypercube Algorithms for Parallel-Processing of Pointer-Based Quadtrees**,

*CVIU(62)*, No. 1, July 1995, pp. 1-10.
BibRef
**9507**

*Schrack, G.F.*,
*Gargantini, I.*,

**Mirroring and Rotating Images in Linear Quadtree Form with
Few Machine Instructions**,

*IVC(11)*, No. 2, March 1993, pp. 112-118.

WWW Link.
BibRef
**9303**

*Wilke, L.M.*,
*Schrack, G.F.*,

**Improved Mirroring And Rotation Functions For Linear Quadtree Leaves**,

*IVC(13)*, No. 6, August 1995, pp. 491-495.

WWW Link.
BibRef
**9508**

*Shusterman, E.*,
*Feder, M.*,

**Image compression via improved quadtree decomposition algorithms**,

*IP(3)*, No. 2, March 1994, pp. 207-215.

IEEE DOI
**0402**

BibRef

*Vassilakopoulos, M.*,
*Manolopoulos, Y.*,
*Economou, K.*,

**Overlapping Quadtrees for the Representation of Similar Images**,

*IVC(11)*, No. 5, June 1993, pp. 257-262.

WWW Link.
BibRef
**9306**

*Manolopoulos, Y.*,
*Nardelli, E.*,
*Proietti, G.*,
*Vassilakopoulos, M.*,

**On the Creation of Quadtrees by Using a Branching-Process**,

*IVC(14)*, No. 2, March 1996, pp. 159-164.

WWW Link.
**9607**

BibRef

*Lee, S.S.*,
*Horng, S.J.*,
*Tsai, H.R.*,
*Tsai, S.S.*,

**Building a Quadtree and Its Applications on a Reconfigurable Mesh**,

*PR(29)*, No. 9, September 1996, pp. 1571-1579.

WWW Link.
*Parallel Algorithms*.
*Reconfigurable Mesh*.
BibRef
**9609**

*Ziavras, S.G.*,
*Alexandridis, N.A.*,

**Improved Algorithms for Translation of Pictures Represented by
Leaf Codes**,

*IVC(6)*, No. 1, February 1988, pp. 13-20.

WWW Link.
BibRef
**8802**

*Faloutsos, C.*,

**Analytical Results on the Quadtree Decomposition of
Arbitrary Rectangles**,

*PRL(13)*, 1992, pp. 31-40.
BibRef
**9200**

*Webber, R.E.*,
*Dillencourt, M.B.*,

**Compressing Quadtrees Via Common Subtree Merging**,

*PRL(9)*, 1989, pp. 193-200.
BibRef
**8900**

*Shaffer, C.A.*,

**A Formula for Computing the Number of Quadtree Node Fragments
Created by a Shift**,

*PRL(7)*, 1988, pp. 45-49.
BibRef
**8800**

*Menon, S.*,
*Gao, P.*,
*Smith, T.R.*,

**Multi-Colored Quadtrees for GIS:
Exploiting Bit-Parallelism for Rapid Boolean Overlay**,

*PRL(8)*, 1988, pp. 171-179.
BibRef
**8800**

*Schreiber, F.A.*,
*Wolfler, R.C.*,

**Use of Neural Networks to Estimate the Number of Nodes of an
Edge Quadtree**,

*GMIP(59)*, No. 2, March 1997, pp. 61-72.
**9704**

BibRef

*Lin, T.W.*,

**Set Operations on Constant Bit-Length Linear Quadtrees**,

*PR(30)*, No. 7, July 1997, pp. 1239-1249.

WWW Link.
**9707**

BibRef

*Chen, P.M.*,

**A Quadtree Normalization Scheme Based on Cyclic Translations**,

*PR(30)*, No. 12, December 1997, pp. 2053-2064.

WWW Link.
**9805**

BibRef

*Sarkar, D.[Debranjan]*,
*Gupta, N.[Nishit]*,

**Operations on binary images represented by interpolation based bintrees**,

*PRL(20)*, No. 4, April 1999, pp. 395-403.
BibRef
**9904**

*Tsai, Y.H.[Yao-Hong]*,
*Chung, K.L.[Kuo-Liang]*,

**Some image operations on S-tree-related spatial data structures**,

*IVC(17)*, No. 12, October 1999, pp. 897-904.

WWW Link.
BibRef
**9910**

*Laferte, J.M.*,
*Perez, P.*,
*Heitz, F.*,

**Discrete Markov Image Modeling and Inference on the Quadtree**,

*IP(9)*, No. 3, March 2000, pp. 390-404.

IEEE DOI
**0003**

BibRef

*Laferte, J.M.*,
*Heitz, F.*,
*Perez, P.*,

**A Multiresolution EM Algorithm for Unsupervised Image Classification
Using a Quadtree Model**,

*ICPR96*(II: 849-853).

IEEE DOI
**9608**

(IRISA/INRIA, F)
BibRef

*Ito, A.*,
*Inoue, K.*,
*Wang, Y.*,

**Decomposition Principle for Analyzing Region Quadtrees**,

*PRAI(13)*, No. 4, June 1999, pp. 555.
**0005**

BibRef

*Aizawa, K.*,
*Nakamura, A.*,

**Quadtree Adjoining Grammar**,

*PRAI(13)*, No. 4, June 1999, pp. 573.
**0005**

BibRef

*Ewert, S.*,
*van der Walt, A.*,

**A Hierarchy Result for Random Forbidding Context Picture Grammars**,

*PRAI(13)*, No. 7, November 1999, pp. 997.
**0005**

BibRef

*Racherla, G.[Gopal]*,
*Radhakrishnan, S.[Sridhar]*,
*Oommen, B.J.[B. John]*,

**Enhanced layered segment trees: a pragmatic data structure for
real-time processing of geometric objects**,

*PR(35)*, No. 10, October 2002, pp. 2303-2309.

WWW Link.
**0206**

Extension to allow for real time implementations.
I.e. no sorting to insert/delete.
BibRef

*Chan, Y.K.[Yung-Kuan]*,

**Block image retrieval based on a compressed linear quadtree**,

*IVC(22)*, No. 5, 1 May 2004, pp. 391-397.

WWW Link.
**0403**

BibRef

*Leelapatra, W.[Watis]*,
*Kanchanasut, K.[Kanchana]*,
*Lursinsap, C.[Chidchanok]*,

**Displacement BDD and geometric transformations of binary decision
diagram encoded images**,

*PRL(29)*, No. 4, 1 March 2008, pp. 438-456.

WWW Link.
**0711**

Binary decision diagram; Transition branch; Translation; Rotation
BibRef

*Kumar, B.P.[B. Praveen]*,
*Gupta, P.[Phalguni]*,
*Hwang, C.J.*,

**An Efficient Quadtree Datastructure For Neighbor Finding Algorithm**,

*IJIG(1)*, No. 4, October 2001, pp. 619-633.
**0110**

BibRef

*Aizawa, K.[Kunio]*,
*Tanaka, S.[Shojiro]*,

**A Constant-Time Algorithm for Finding Neighbors in Quadtrees**,

*PAMI(31)*, No. 7, July 2009, pp. 1178-1183.

IEEE DOI
**0905**

Find neighbors in quadtree.
BibRef

*Mathew, R.[Reji]*,
*Taubman, D.S.[David S.]*,

**Quad-Tree Motion Modeling With Leaf Merging**,

*CirSysVideo(20)*, No. 10, October 2010, pp. 1331-1345.

IEEE DOI
**1011**

BibRef

And:

**Joint motion and geometry modeling with quad-tree leaf merging**,

*ICIP08*(2872-2875).

IEEE DOI
**0810**

BibRef

Earlier:

**Motion Modeling with Geometry and Quad-tree Leaf Merging**,

*ICIP07*(II: 297-300).

IEEE DOI
**0709**

BibRef

Earlier:

**Hierarchical and Polynomial Motion Modeling with Quad-Tree Leaf Merging**,

*ICIP06*(1881-1884).

IEEE DOI
**0610**

BibRef

*Mathew, R.[Reji]*,
*Taubman, D.S.[David S.]*,

**Scalable Modeling of Motion and Boundary Geometry With Quad-Tree Node
Merging**,

*CirSysVideo(21)*, No. 2, February 2011, pp. 178-192.

IEEE DOI
**1103**

BibRef

Earlier:

**Joint scalable modeling of motion and boundary geometry with quad-tree
node merging**,

*ICIP09*(3745-3748).

IEEE DOI
**0911**

BibRef

*Mathew, R.[Reji]*,
*Taubman, D.S.[David S.]*,
*Zanuttigh, P.*,

**Scalable Coding of Depth Maps With R-D Optimized Embedding**,

*IP(22)*, No. 5, May 2013, pp. 1982-1995.

IEEE DOI
**1304**

BibRef

*Kim, H.[Hongyeon]*,
*Kang, S.[Sungmin]*,
*Lee, S.[Seokjoo]*,
*Min, J.K.[Jun-Ki]*,

**The Efficient Algorithms for Constructing Enhanced Quadtrees Using
MapReduce**,

*IEICE(E99-D)*, No. 4, April 2016, pp. 918-926.

WWW Link.
**1604**

BibRef

IEEE DOI

BibRef

*Holt, K.M.*,
*Neuhoff, D.L.*,

**Strategies for quadtree predictive image coding**,

*ICIP03*(II: 247-250).

IEEE DOI
**0312**

BibRef

*Teng, C.Y.[Chia-Yuan]*,
*Neuhoff, D.L.*,

**A new quadtree predictive image coder**,

*ICIP95*(II: 73-76).

IEEE DOI
**9510**

BibRef

*Lee, M.[Michael]*, and
*Samet, H.[Hanan]*,

**Navigating through Triangle Meshes Implemented as Linear Quadtrees**,

*UMD*--TR3900, April 1998

WWW Link.
BibRef
**9804**

*Ogniewicz, R.L.*,

**Sekeleton-Space: a Multiscale Shape Description
Combining Region and Boundary Information**,

*CVPR94*(746-751).

IEEE DOI
BibRef
**9400**

*Kummert, Á.[Ágnes]*,
*Kabos, S.[Sándor]*,

**Calculation and estimation of sample statistics of binary images using
quadtree data representations**,

*CAIP93*(58-64).

Springer DOI
**9309**

BibRef

*Fan, N.P.*,
*Li, C.C.*,

**Computing Quadtree Medial Axis Transform by a
Multi-Layered Pyramid of Lisp-Processor Arrays**,

*CVPR88*(628-634).

IEEE DOI
BibRef
**8800**

*Punys, J.*,

**Hierarchical 2D shape representation and compression by rectangles**,

*ICPR88*(II: 675-677).

IEEE DOI
**8811**

BibRef

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

Quadtree Boundary Operations .

Last update:Apr 26, 2017 at 10:20:07