1. 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

2. 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

3. Overview of Quadtree Recursive decomposition.
Similar to divide and conquer
Geographic Information System, Image processing and so on..

4. 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 Q1 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

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

6. Example of tiling Uniform orientation Easy to implement
Yamaguchi et al. [1984]
Triangular quadtree to generate an
isometric view from octree. (3D)

7. Rope and Net Fast! But.. N H M I O G F B L Q J37 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..

8. Alternates of Quadtree k-d tree
Fewer leaf nodes : 4 sons -> 2 sons
Good at higher dimensional data!

9. Point quadtree vs k-d tree
2^k branching factor for k dimension
k-d tree

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

11. Octree
Structure to store the volume element
Is it possible?

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

13. 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

14. Cont. Special case Closed curve by strip tree.
Extends past its endpoints.
So what?

15. Cont. Intersecting two strip trees. Curve approximation. Null Clear.
Possible

16. 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

17. Cont.
Any questions?