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

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STEMPNU 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

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

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STEMPNU Cont A B CDE FGHIJ K LM NO P Q N H M I O GF B LQ J

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

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STEMPNU Example of tiling 6 1.Uniform orientation 2.Easy to implement Yamaguchi et al. [1984] Triangular quadtree to generate an isometric view from octree. (3D)

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STEMPNU Fast! But.. Rope and Net 7 A B CDE FGHIJ K LM NO P Q N H M I O GF B LQ J 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.

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

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

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

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

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STEMPNU Stair case Cont

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STEMPNU Curvilinear Data Boundaries of regions? Strip tree 13 Point to left child node? Point to right child node? X1? Y1? X2? Y2? WL? WR? More complex?

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

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STEMPNU Intersecting two strip trees. Curve approximation. Cont. 15 NullClear.Possible

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STEMPNU 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 16

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STEMPNU Cont. Any questions? 17

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