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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. Plan. Part 1 : Overview of Quadtree Part 2 : Basic Operation Start, Merge, Split, Group

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2009. April. 01 Yongsu Song PNU STEM Lab

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  1. The Quadtree and Related Hierarchical Data StructuresHANAN 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. B F G H I 37 38 J N O 39 40 57 58 L Q M 59 60 A C D E B F G H I J K L M N O P Q 37 38 39 40 57 58 59 60

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

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

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

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

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

  12. Cont. 3 7 2 5 1 5 0 2 7 5 Stair case

  13. Curvilinear Data More complex? Boundaries of regions? Strip tree

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

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

  16. Conclusion • The main idea • 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?

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