1. Clustering Vertices of 3D Animated Meshes
Abdullah Bulbul

2. Introduction Progress Indicator 3D meshes are made of vertices
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3D meshes are made of vertices
Complex 3D meshes
Huge number of vertices
Cluster the vertices
Data reduction
Developments in IR
Adapt IR findings to Computer Graphics
Progress
Indicator
Stanford Bunny:
~ vertices
Armadillo:
~ vertices

3. Motivation (1/3) A little history...
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A little history...
Our aim was finding the points that are looked at
Used eye tracker
Accuracy: 0.5 degree, 20 pixels of error
Vertex based calculations: accuracy not sufficient
Which vertex is looked at?
Many candidates
Users look at

4. Motivation (2/3) Solution Cluster vertices to form these regions
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Solution
No per-vertex calculation
Region based calculations
Cluster vertices to form these regions

5. Motivation (3/3) Data reduction: Perceptible regions:
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Data reduction:
Operate only for cluster representatives
Perceptible regions:
A vertex is so small (millions of vertices)
Selecting a vertex does not make sense
Instead, select a cluster

6. Background (1/2) Clustering in IR Incremental Algorithms
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Clustering in IR
Incremental Algorithms
Can (1993) - Incremental clustering for dynamic information processing
Charikar et al. (1997) - Incremental clustering and dynamic information retrieval
Single Pass
Partitioning
Multi Pass
Overlapping
Graph Theoretical
Hierarchical

7. Background (2/2) 3D mesh decomposition
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3D mesh decomposition
Katz et al. (2003) - Hierarchical mesh decomposition using fuzzy clustering and cuts
Berretti et al. (2009) - 3D mesh decomposition using reeb graphs

8. Approach Data to use – properties of vertices No binary term vectors
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Data to use – properties of vertices
Position: x, y, z
Velocity
Color: RGB or HSV
Curvature
No binary term vectors
Properties have continuous values (not 0 - 1)
Velocity map
Curvature map

9. Approach Adapt and try several algorithms
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Adapt and try several algorithms
Seed oriented single-pass algorithms
Randomly select cluster heads
Artificial selection of cluster heads
Homogenous distribution
C3M - Select leading documents
Not simple
Requires binary term-vectors
Heuristic approaches
Incremental approaches
C2ICM

10. Seed oriented approaches
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Random selection of cluster heads
Randomly select several vertices to be cluster heads
Assign each vertex to the most similar cluster head
Similarity: Euclidean distance
Not so good: non-connected components in same cluster
Non-homogeneous cluster sizes

11. Seed oriented approaches
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Artificial selection of cluster heads
Most similar cluster heads are as different as possible
Again: Assign each vertex to the most similar cluster head
Similarity: Euclidean distance
Not so good: non-connected components in same cluster
Nearly homogeneous cluster sizes

12. Seed oriented approaches
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C3M
We need binary term vectors
How to convert continuous values to binary ones
Idea:
Divide space into equal sized intervals each corresponding to a term
The term into which a property falls becomes 1 other become 0
For example, assume x values are in the range: 0 to 99
Divide to 10 intervals: 0-9, 10-19, ... , 90-99
If xi is 29, term vector:
And xj is 30, term vector:
No good

13. A Heuristic Approach Start with a vertex
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Start with a vertex
Look at each neigbor
If number of vertices in the cluster < a threshold
Add the neighbor to this cluster
Otherwise, start a new cluster
Solves the aformentioned problem of connectivity
Non-connected vertices cannot be put into the same cluster
Not implemented yet

14. Incremental Approaches
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Vertex properties change through the animation
Cluster structure needs to be maintained
New clusters may be necessary
C2ICM
Cannot be used as it is
Maintenance related issues can be adapted

15. Conclusion Clustering vertices of 3D animated meshes
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Clustering vertices of 3D animated meshes
Several approaches are implemented
What remains
Implement heuristic approach
Develop the incremental approach
Use all properties
Curvature can be used as a constraint

16. End of Presentation
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Questions?
Thank you 