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**2009. April. 01 Yongsu Song PNU STEM Lab**

The Quadtree and Related Hierarchical Data Structures HANAN SAMET Computer Science Department, University of Maryland, College Park, Maryland 20742 2009. April. 01 Yongsu Song PNU STEM Lab

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**Plan Part 1 : Overview of Quadtree Part 2 : Basic Operation**

Start, Merge, Split, Group Example of tiling Rope and Net Part 3 : Alternates of Quadtree Octree K-d tree Approximation Methods Part 4 : Conclusion

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**Overview of Quadtree Recursive decomposition.**

Similar to divide and conquer Geographic Information System, Image processing and so on..

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**Cont. N H M I O G F B L Q J 37 38 39 40 57 58 59 B F G H I J L M N O Q**

1 N H M I O G F B L Q J 37 38 39 40 57 58 59 60 A B C D E F G H I J K L M 37 38 39 40 N O P Q 57 58 60 59

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**2. Basic Operation Start, Merge, Split, Group**

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**Example of tiling Uniform orientation Easy to implement**

Yamaguchi et al. [1984] Triangular quadtree to generate an isometric view from octree. (3D)

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**Rope and Net Fast! But.. N H M I O G F B L Q J**

37 38 39 40 57 58 59 60 Rope : Link between two adjacent nodes of equal size where at least one of them is a leaf node. Net : Linked list whose elements are all the nodes that are adjacent along a given side of a node. A B C D E F G H I J K L M 37 38 39 40 N O P Q 57 58 60 59 Fast! But..

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**Alternates of Quadtree k-d tree**

Fewer leaf nodes : 4 sons -> 2 sons Good at higher dimensional data!

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**Point quadtree vs k-d tree**

2^k branching factor for k dimension k-d tree

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**Approximation Methods**

Image approximation. Shape approximation. Good : High resolution levels to low resolution. Bad : Comparing similar shapes.

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Octree Structure to store the volume element Is it possible?

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Cont. Stair case 3 7 2 5 1 5 2 7 5

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**Curvilinear Data Boundaries of regions? Strip tree More complex?**

Point to left child node ? Point to right child node X1 Y1 X2 Y2 WL WR

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**Cont. Special case Closed curve by strip tree.**

Extends past its endpoints. So what?

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**Cont. Intersecting two strip trees. Curve approximation. Null Clear.**

Possible

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**Conclusion The main idea Efficient For Region and Point**

Recursive decomposition Efficient For Region and Point Divide and conquer Reduce size range of target data Important of data structure Apply Approximation skills

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Cont. Any questions?

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