Presentation is loading. Please wait.

Presentation is loading. Please wait.

Field Trees and Loose Quadtrees Kenny Weiss CMSC828S Spring 2005.

Published by Modified over 9 years ago

Similar presentations

Presentation on theme: "Field Trees and Loose Quadtrees Kenny Weiss CMSC828S Spring 2005."— Presentation transcript:

1 Field Trees and Loose Quadtrees Kenny Weiss CMSC828S Spring 2005

2 Images vs. Objects Image Based –Given a cell (location) find the object(s) of which it is a member –What features are at a location? Object Based –Given an object, find its constituent cells (locations) –Where is an object located?

3 Loosen Quadtree Restrictions Up until now… –Each cell only contained one object and objects cannot overlap Loosen this restriction –Cell need not be entirely covered by and object –Several objects may occupy a single cell may also overlap –Arbitrary shapes allowed

4 Limits to decomposition Arbitrary shape may be decomposed infinitely If placed in certain locations –Use Min Bounding Box to simplify representation Coverage based –Restrict number of blocks that can cover an object Density based –Restrict number of objects that can be covered by a block We will focus on Coverage based limits on image based representation

5 Quadtree Space Partition Motivation Store the bounding box of objects in hierarchy –Must check every match (at all levels) to see if point is in object Goal: try to put objects in block at lowest possible level to minimize unnecessary computation –Prune as much as possible

6 MX-CIF Quadtree Object must be covered by at most ONE block –Minimum enclosing quadtree block –Resolve collisions Use two 1-dim MX-CIF structures F A E G B D C {A,E} {B,C,D} {G} {F} Key:

7 Problems Large blocks “Orphan” nodes –Small nodes covering several blocks –Artifacts of (arbitrary) choice of origin –Every query will include x in its results {A,E,X} {B,C,D} {G} {F} F A E G B D C X Key:

8 Loose Quadtree/Cover Fieldtree Frank and Barrera, Ulrich Problem: For object o, the min bounding box is not related to size of o Uniformly expand size of space spanned by each block, b, of width, w, by a positive factor, p –Object associated with the min. enclosing expanded block –Expanded width of block, b = (1+p)*w Each object still covered by only one block –Similar to QMAT (quadtree medial axis transform) Key result  radius of min bounding box of object in b is larger than p*w/4

9 MX-CIF vs. Loose Quadtree F A E G B D C {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

10 MX-CIF vs. Loose Quadtree F A E G B D C {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key: B is completely enclosed by this block

11 MX-CIF vs. Loose Quadtree F A E G B D C {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

12 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

13 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

14 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key: C and D are contained at this level

15 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

16 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

17 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF {A} {C,D} {G} {E} {B} Key: ? 20 10 30 35 15 F = {(31,15), (35,19)} Window = {(27.5, 12.5), (37.5,22.5)} {F}

18 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

19 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

20 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

21 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

22 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

23 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key: A fits into the top hierarchy

24 F A E G B D C MX-CIF vs. Loose Quadtree {A,E} {B,C,D} {G} {F} MX-CIF Loose Quadtree p=1, width = (1+p)w = 2w {A} {C,D} {G} {F} {E} {B} Key:

25 Partition Fieldtree Hierarchy of grids whose registration are shifted –Each cell is called a field –Each level forms a non-overlapping partitioning of the space –For each block, b, of width, w, that is being subdivided origins are shifted by w/2 A new node is stored in the smallest field in which it completely fits –Object never has to be stored more than three levels above its proper size

26 Partition Fieldtree Properties Source: www.gdmc.nl/oosterom/slc.ps Boundaries of blocks at different levels will never coincide Grids at different levels have a different origin Blocks at different levels do not form a refinement of those at a previous level

27 Bound on size of enclosure Partition –Always bounded by three levels 8x object size Cover –Radius must be larger than p*w/4 As p decreases, the minimum radius decreases –p = 1/2, ratio is at most 4 –p = 1/4, ratio is at most 8 –P = 1/8, ratio is at most 16  tighter than partition

28 Comparison Goal of both –Expand the area spanned by the subblocks to reduce size of minimum enclosing quadtree block When an object overlaps the axes that pass through the center of the block Cover –Area spanned by four subblocks is expanded Partition –Number of subblocks is enlarged by offsetting their position while retaining their size

29 Comparison (2) Subblocks span an area that overlaps the partition lines –Always for partition fieldtree –Not always for Cover fieldtree some values of p will have partition lines coincide –i.e. p =1, powers of 2 –Differs from regular quadtree, where successive levels are collinear

30 References Foundations of Multidimensional and Metric Data Structures Samet, Hanan to appear in 2005. A Survey Of Hierarchical Partitioning Methods For Vector Images, Noronha, Valerian T dgrc.ca/publicns/syd8808/syd8808.pdf The Spatial Location Code van Oosterom, Peter www.gdmc.nl/oosterom/slc.ps

Download ppt "Field Trees and Loose Quadtrees Kenny Weiss CMSC828S Spring 2005."

Similar presentations

1 DATA STRUCTURES USED IN SPATIAL DATA MINING. 2 What is Spatial data ? broadly be defined as data which covers multidimensional points, lines, rectangles,

1 DATA STRUCTURES USED IN SPATIAL DATA MINING. 2 What is Spatial data ? broadly be defined as data which covers multidimensional points, lines, rectangles,
Hierarchical Cellular Tree: An Efficient Indexing Scheme for Content-Based Retrieval on Multimedia Databases Serkan Kiranyaz and Moncef Gabbouj.

Hierarchical Cellular Tree: An Efficient Indexing Scheme for Content-Based Retrieval on Multimedia Databases Serkan Kiranyaz and Moncef Gabbouj.
Clustering.

Clustering.
Spatial Indexing SAMs. Spatial Indexing Point Access Methods can index only points. What about regions? Z-ordering and quadtrees Use the transformation.

Spatial Indexing SAMs. Spatial Indexing Point Access Methods can index only points. What about regions? Z-ordering and quadtrees Use the transformation.
Spatial Data Structures Hanan Samet Computer Science Department

Spatial Data Structures Hanan Samet Computer Science Department
Informed Search Methods How can we improve searching strategy by using intelligence? Map example: Heuristic: Expand those nodes closest in “as the crow.

Informed Search Methods How can we improve searching strategy by using intelligence? Map example: Heuristic: Expand those nodes closest in “as the crow.
Chapter 4: Trees Part II - AVL Tree

Chapter 4: Trees Part II - AVL Tree
CSE 681 Bounding Volumes. CSE 681 Bounding Volumes Use simple volume enclose object(s) tradeoff for rays where there is extra intersection test for object.

CSE 681 Bounding Volumes. CSE 681 Bounding Volumes Use simple volume enclose object(s) tradeoff for rays where there is extra intersection test for object.
Collision Detection and Resolution Zhi Yuan Course: Introduction to Game Development 11/28/2011 1.

Collision Detection and Resolution Zhi Yuan Course: Introduction to Game Development 11/28/
Computer graphics & visualization Collisions. computer graphics & visualization Simulation and Animation – SS07 Jens Krüger – Computer Graphics and Visualization.

Computer graphics & visualization Collisions. computer graphics & visualization Simulation and Animation – SS07 Jens Krüger – Computer Graphics and Visualization.
Ray Tracing CMSC 635. Basic idea How many intersections?  Pixels  ~10 3 to ~10 7  Rays per Pixel  1 to ~10  Primitives  ~10 to ~10 7  Every ray.

Ray Tracing CMSC 635. Basic idea How many intersections?  Pixels  ~10 3 to ~10 7  Rays per Pixel  1 to ~10  Primitives  ~10 to ~10 7  Every ray.
Data Mining Cluster Analysis: Advanced Concepts and Algorithms

Data Mining Cluster Analysis: Advanced Concepts and Algorithms
Searching on Multi-Dimensional Data

Searching on Multi-Dimensional Data
CSE 381 – Advanced Game Programming Scene Management

CSE 381 – Advanced Game Programming Scene Management
Generated Waypoint Efficiency: The efficiency considered here is defined as follows: As can be seen from the graph, for the obstruction radius values (200,

Generated Waypoint Efficiency: The efficiency considered here is defined as follows: As can be seen from the graph, for the obstruction radius values (200,
Computer Graphics1 Quadtrees & Octrees. Computer Graphics2 Quadtrees n A hierarchical data structure often used for image representation. n Quadtrees.

Computer Graphics1 Quadtrees & Octrees. Computer Graphics2 Quadtrees n A hierarchical data structure often used for image representation. n Quadtrees.
Spatial Mining.

Spatial Mining.
Mining for High Complexity Regions Using Entropy and Box Counting Dimension Quad-Trees Rosanne Vetro, Wei Ding, Dan A. Simovici Computer Science Department.

Mining for High Complexity Regions Using Entropy and Box Counting Dimension Quad-Trees Rosanne Vetro, Wei Ding, Dan A. Simovici Computer Science Department.
CS447/547 10- 1 Realistic Rendering -- Solids Modeling -- Introduction to 2D and 3D Computer Graphics.

CS447/ Realistic Rendering -- Solids Modeling -- Introduction to 2D and 3D Computer Graphics.
1 CSIS 7101: CSIS 7101: Spatial Data (Part 2) Efficient Processing of Spatial Joins Using R-trees Rollo Chan Chu Chung Man Mak Wai Yip Vivian Lee Eric.

1 CSIS 7101: CSIS 7101: Spatial Data (Part 2) Efficient Processing of Spatial Joins Using R-trees Rollo Chan Chu Chung Man Mak Wai Yip Vivian Lee Eric.

Similar presentations

Ads by Google