observer relative data extraction linas bukauskas 3dvdm group aalborg university, denmark 2001
TRANSCRIPT
Observer Relative Data Extraction
Linas Bukauskas
3DVDM group
Aalborg University, Denmark
2001
2001 N/X VMMD Workshop 2001 2
Content• Motivation• Observer Relative Data Extraction
– Visibility Range– Tree Structure– Visibility cases
• Experimental Results• Related Work• Conclusions• Future Work
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Motivation
• Unbounded Universe of objects– CAVE® and Panorama creates fully immersed
environment
• All objects are not visible at once– Catalog of stars 50GB
(donor: Jim Gray @ Microsoft Research)
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Motivation (cont`d)
• Visualization system can not handle all objects in the Universe– Rendering of the world is time consuming
• Observer is moving through the Universe– Arriving objects appear, leaving - disappear
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Example of Moving Observer in 3D
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ORDE Queries
• Objects that are visible• Objects of specific visibility level
• Objects that will become (in) visible• Objects that might be visible soon
• Objects that might be visible moving along the path
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Distance Based Organization
• Create tree structure to access data
• Use distance based organization– Visibility Factor a parameter in a node
The tree will order objects according the visibility factor
– Second storage access structureB-Tree like structure
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Distant Based Organization
• Visibility Factor
• Visible Objects
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Distant Based Organization Fails
• Objects far away can be visible (if large)
• Near objects can be invisible (if small)
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Observer Relative Data Extraction
• Requirements– Static Visibility Factor– Cluster/partition the space– Hierarchical structure– Second storage structure
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Visibility Range (cont´d)
• Definition: Let Oi be an object. The visibility range associated with the object, VRi(Oi) is:
• VR is a Minimal Bounding Square (MBS)
• Brightness and color can be incorporated
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Visibility Range
• Overlapping object visibility ranges.
MBS
VR
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The Tree Structure
• Hierarchical structure of MBRs and MBSs
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7
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1 2 3 4 5 6 7
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The Tree Structure
• Querying: Overlaps
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The Tree Structure (Cont´d)
• Two types of nodes:– MBRs internal– MBSs leaf nodes
• Pack more objects into leaf 1KB nodes2D 3D
Internal 256 170Leafnode 341 256
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Three Cases of Queries
• Perfect– Visibility Ranges are as is
• Conservative– Visibility Ranges are enlarged
• Optimistic– Visibility Ranges are reduced
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Perfect Case
• Point query – Observer position as input
– Extracts only Visible Objects
• Window Query– Region of movement
– Extracts now Visible Objects +Objects visible soon
Scale factor: r = 1
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Conservative Case
• Point query – Observer position as input
– Surplus Visible Objects
– does not extract exactly Visible Objects
• Window Query– More surplus Visible Objects
Scale factor: r > 1
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Optimistic Case
• Point query – Observer position as input
– Very Visible Objects
• Window Query– Region as input
– Ensure Visible Object extraction, surplus invisible.
Scale factor: 0 < r < 1
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Three Cases of Queries
• Perfect – Finds exactly visible objects for the observer
• Conservative– Finds visible objects with a buffer for the
observer to move
• Optimistic– Optimistically extracts visible objects, with a
surplus amount of invisible data.
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Experiments
• R-Tree vs. VR-Tree– Universe 100x100 units– Varying size of data set 250.000 - 1 mio. – Largest VR span 1% and 10% of the Universe– Page size 1 KB– Implemented on GIST
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R vs. VR –Tree
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140
0.25 0.5 0.75 1
# of objects in mln
I/O
per
ob
ject
2.3
2.4
2.5
2.62.7
2.8
2.9
3
0.25 0.5 0.75 1
# of objects in mln
10 % of universe1% of Universe
VR
R
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Supernovas• Supernovas has impact in Optimistic case
– Perfect & Conservative vs. Optimistic
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10000
20000
30000
40000
50000
0.25 0.5 0.75 1
# of objects in mln
IO
01000020000300004000050000600007000080000
0.25 0.5 0.75 1
# of objects in mln
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Related Work
• R-Tree (A. Guttman. R-Trees: A Dynamic Index Structure for Spatial
Searching.1984)
– X-Tree (S. Berchtold, D. A. Keim, and H.-P. Kriegel. The X-tree : An Index Structure for
High-Dimensional data, 1996.)
– SS-Tree (D. A. White and R. Jain. Similarity Indexing with the SS-tree. 1996)
– SR-Tree (N. Katayama and S. Satoh. The SR-tree: An Index Structure for High-Dimensional Nearest Neighbor Queries.1997)
– TPR-Tree (S. Saltenis, C. S. Jensen, S. T. Leutenegger, and M. A. Lopez. Indexing the Positions of Continuously Moving Objects, 2000)
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Related Work (cont’d)
• Space partitioning– Kd-Tree, Quad/Oct-Trees – kdB-Tree (J. T. Robinson. The K-D-B-Tree: A Search Structure For Large
Multidimensional Dynamic Indexes.1981)
– LSDh Tree (A. Henrich. The LSD h -Tree: An Access Structure for Feature Vectors. 1998)
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Conclusions
• Work in progress– Observer position dependant queries– Visibility Ranges– Three special cases of queries
• Perfect, Conservative, Optimistic
– Empirical evaluation
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Future Work
• Evaluate tree in a higher dimensions– Does it make sense in Virtual Reality setting?
• Incremental data extraction when moving– Incoming and leaving objects
• Retrieve data that will be visible along the path– Given a path points optimize data extraction
• Validate results with cases from the real life
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Acknowledgment
• Michael Böhlen
• 3DVDM project members
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Questions?