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# Region Quadtrees in Data Structure

The region quadtree is useful to represent a partition of space in two dimensions by breaking the region into four equal quadrants, subquadrants, and so on with each leaf node consisting of data corresponding to a specific subregion. Each node in the tree either is associated with exactly four children or no children (a leaf node). The height of quadtrees that follow this decomposition strategy (i.e. subdividing subquadrants until and unless there is interesting data in the subquadrant for which more refinement is required) is sensitive to and dependent on the spatial distribution of interesting areas in the space being broken. The region quadtree is denoted as a type of trie.

A region quadtree with a depth of n may be implemented to represent an image consisting of 2n × 2n pixels, where each pixel value is either 0 or 1. The root node is useful to represent the entire image region. If the pixels in any region are neither entirely 0s nor 1s, it is subdivided. In this application, each leaf node is useful to represent a block of pixels that are either all 0s or all 1s. Note the potential savings in terms of space when these trees are implemented for storing images; these images often have many regions of considerable size that have the same colour value throughout. Instead of storing a big 2-Dimensional array of every pixel in the image, a quadtree can be able to capture the same information potentially many divisive levels larger than the pixel-resolution sized cells that we would otherwise need. The pixel and image sizes are able to bind the tree resolution and overall size.

A region quadtree may also be implemented as a variable resolution representation of a data field. Such as, the temperatures in an area may be stored as a quadtree, with each leaf node storing the average temperature throughout the subregion it represents.

If a region quadtree is implemented to represent a set of point data (such as the latitude and longitude of a set of cities), regions are subdivided until and unless each leaf contains maximum a single point.

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