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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.
In computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. K-dimensional is that which concerns exactly k orthogonal axes or a space of any number of dimensions. [1] k-d trees are a useful data structure for several applications, such as:
For 2D space and similarity transformation the basis is defined by a pair of points. The point of origin is placed in the middle of the segment connecting the two points (P2, P4 in our example), the x ′ {\displaystyle x'} axis is directed towards one of them, the y ′ {\displaystyle y'} is orthogonal and goes through the origin.
For high-dimensional data, tree-based exact vector search techniques such as the k-d tree and R-tree do not perform well enough because of the curse of dimensionality. To remedy this, approximate k-nearest neighbor searches have been proposed, such as locality-sensitive hashing (LSH) and product quantization (PQ) that trade performance for ...
The PH-tree [1] is a tree data structure used for spatial indexing of multi-dimensional data (keys) such as geographical coordinates, points, feature vectors, rectangles or bounding boxes. The PH-tree is space partitioning index [ 2 ] with a structure similar to that of a quadtree or octree . [ 3 ]
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A hyperbolic tree (often shortened as hypertree) is an information visualization and graph drawing method inspired by hyperbolic geometry. A basic hyperbolic tree. Nodes in focus are placed in the center and given more room, while out-of-focus nodes are compressed near the boundaries.
Simple example of an R-tree for 2D rectangles Visualization of an R*-tree for 3D points using ELKI (the cubes are directory pages). R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons.