Tree data structure in which each internal node has exactly four children, to partition a 2D area
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Quadtree
Type
Tree
Invented
1974
Invented by
Raphael Finkel and J.L. Bentley
Time complexity in big O notation
Operation
Average
Worst case
Space complexity
A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are the two-dimensional analog of octrees and are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The data associated with a leaf cell varies by application, but the leaf cell represents a "unit of interesting spatial information".
The subdivided regions may be square or rectangular, or may have arbitrary shapes. This data structure was named a quadtree by Raphael Finkel and J.L. Bentley in 1974.[1] A similar partitioning is also known as a Q-tree.
All forms of quadtrees share some common features:
They decompose space into adaptable cells.
Each cell (or bucket) has a maximum capacity. When maximum capacity is reached, the bucket splits.
The tree directory follows the spatial decomposition of the quadtree.
A tree-pyramid (T-pyramid) is a "complete" tree; every node of the T-pyramid has four child nodes except leaf nodes; all leaves are on the same level, the level that corresponds to individual pixels in the image. The data in a tree-pyramid can be stored compactly in an array as an implicit data structure similar to the way a complete binary tree can be stored compactly in an array.[2]
^Finkel, R. A.; Bentley, J. L. (1974). "Quad trees a data structure for retrieval on composite keys". Acta Informatica. 4 (1): 1–9. doi:10.1007/BF00288933. S2CID 33019699. Retrieved 6 November 2019.
^
Milan Sonka, Vaclav Hlavac, Roger Boyle.
"Image Processing, Analysis, and Machine Vision".
2014.
p. 108-109.
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