Vivek Kantariya(09bce020)

Guided by :Prof. Vibha Patel

Short form for K-Dimensional Tree. Space-partitioning data structure. Used for organizing points in a k-

dimensional space. Used in searches involving a multi

dimensional search key. Special case of binary space partitioning

trees.

Every non leaf node is a splitting hyper plane that divides the space into two parts, known as subspaces.

Every node in the tree is associated with one of the k-dimensions, with the hyper plane perpendicular to that dimension's axis.

for example, if for a particular split the "x" axis is chosen,

all points in the sub tree with a smaller "x" value than the node will appear in the left sub tree and ,

all points with larger "x" value will be in the right sub tree.

Start from root node & traverse through left or right node according to partitioned plane , until we reached to leaf node.

This type of adding leads to unbalanced tree , we need to rebalance it by removing & again adding elements to improve performance.

It is class of hierarchical data structures which are based on principle of recursive decomposition of space.

They are differentiated by ◦ Type of data◦ decomposition process◦ The resolution ( number of times that the

decomposition process is applied )

Successive subdivision of the image array into four equal-size quadrants.

Root node corresponds to the entire array. Each son of a node represents a quadrant. The leaf nodes of the tree corresponds to

those blocks for which no further subdivision is necessary.

Useful to represent multidimensional point data.

Used to represent images in 3 dimensions , also called Octree.

Recursively subdivide image into eight congruent disjoint cubes (called octants) until blocks are obtained of a uniform color or a predetermined level of decomposition is reached.

The rectangle data type lies somewhere between the point and region data types.

Rectangles are often used to approximate other objects in an image for which they serve as the minimum rectilinear enclosing object.

More than one rectangle can be associated with a given enclosing block.

1. www.ieeexplore.ieee.org◦ A NEW APPROACH TO CREATING SPATIAL INDEX

WITH R-TREE byZe-Bao Zhang, Jian-Pei Zhang, Jing Yang, Yue Yang

◦ A NEW VARIATION OF R-TREE FOR INDEXING SPACIAL DATA IN GIS byChen Yongkang , Zhou Xintie , Shi Tailai , Feng Xiaoming

◦ HIERARCHICAL SPATIAL DATA STRUCTURES by Hanan Samet

◦ Guidelines for Presentation and Comparison of Indexing Techniques by

Justin Zobel , Alistair Moat , Kotagiri Ramamohanarao.

◦ KD-Tree: A Compact KDB-Tree Structure for Indexing Multidimensional Data

by Byunggu Yu , Thomas Bailey , Ratko Orlandic , Jothi Somavaram.

2. http://wikipedia.org/wiki/R_tree3. http://en.wikipedia.org/wiki/K-d_tree