1. CENG 789 – Digital Geometry Processing 10- Data-Driven Shape Analysis
Follow in slide show (F5) mode for the explanatory animations.
Asst. Prof. Yusuf Sahillioğlu
Computer Eng. Dept, , Turkey

2. Shape Analysis Tasks Already covered some important tasks.
Shape descriptors.
Shape registration; rigid and non-rigid.
Talk about other tasks today.
Shape segmentation.
Shape representation/approximation.
Shape correspondence.
Shape retrieval.
Human-centric shape analysis.
Shape synthesis.
Scene synthesis and labeling.

3. Shape Segmentation Data-driven shape segmentation.
User-guided shape segmentation.
Live-wire interaction (well-known in image processing).

4. Shape Segmentation Data-driven shape segmentation.
Shape representation: MDS.
Followed by k-means clustering algorithm.

5. Shape Segmentation Data-driven shape segmentation.
Shape representation: MDS (bending-invariant).

6. Shape Segmentation Data-driven shape segmentation.
Shape representation: MDS (bending-invariant).

7. Shape Segmentation
Data-driven shape segmentation.
K-means clustering.

8. Shape Segmentation Data-driven shape segmentation.
User-driven shape segmentation.
Watch the user interaction that guides the segmentation.
Inspired from: 3-sweep for shape reconstruction.

9. Shape Segmentation Data-driven shape segmentation.
More sophisticated data-driven segmentation methods exist.
Hierarchical decomposition.
Randomized cuts.
Core extraction.
Fitting primitives.
Shape diameter function.

10. Shape Segmentation Data-driven shape segmentation.
Why segment? Once you have the parts, you can go wild.

11. Shape Approximation
Computing simple geometric descriptions for dense surfaces.
Mesh decimation (minimal elements; already covered).
Mesh decimation based on context.

12. Shape Approximation
Computing simple geometric descriptions for dense surfaces.
Mesh decimation (minimal elements; already covered).
Mesh decimation based on volume.
At extreme simplification levels, model the volumetric extent of the original shape.

13. Shape Approximation
Computing simple geometric descriptions for dense surfaces.
Mesh decimation (minimal elements; already covered).
Mesh decimation based on volume.
Sphere interpolation replacing classic point interpolation.

14. Shape Representation
Computing simple geometric descriptions for dense surfaces.
Bag-of-words (bag-of-features) shape representation.

15. Shape Representation
Computing simple geometric descriptions for dense surfaces.
Bag-of-words (bag-of-features) shape representation.
Need a visual vocabulary for shape (not text) processing.

16. Shape Representation
Computing simple geometric descriptions for dense surfaces.
Bag-of-words (bag-of-features) shape representation.

17. Shape Correspondence
Define a map-distortion function that quantifies how good a given map is.
Combinatorial search on space of maps.
Use the map minimizing the distortion function.

18. Shape Correspondence Well-studied for isolated pair of X shapes. X =
Isometric or non-rigid
Rigid
Non-isometric
At its infancy for collection analysis.
Use context info to improve results.

19. Shape Correspondence Well-studied for isolated pair of X shapes. X =
Isometric or non-rigid
Rigid
Non-isometric
At its infancy for collection analysis.

20. Shape Correspondence At its infancy for collection analysis.
Replace a (bad) map w/ a composition of (better) maps.
= w/ a composition of maps on the shortest/best path b/w 2 shapes.

21. Shape Correspondence At its infancy for collection analysis.
Consistent (left) vs inconsistent (right) maps.

22. Shape Retrieval Query-by-text. Google search.
Shape adaptation: DB needs to be manually tagged 
Query-by-example.
Shape adaptation: User provides a 3D model; popular but hard to come up with a 3D model .
Query-by-sketch.
Shape adaptation: User simply draws; easy for user but not so accurate due to view and drawing differences .

23. Shape Retrieval Index database models with Features.
Bending-invariant representations.
Bag-of-words. ..
Convert to query model into that index.
Retrieve the most compatible model according to the indexing.

24. Shape Retrieval Evaluation of shape retrieval performance.
Precision-recall plots.

25. Shape Retrieval Evaluation of shape retrieval performance.
Precision-recall plots.
Ideally this curve should be a horizontal line at unit precision.

26. Human-centric Shape Analysis
Recognize/classify/segment objects based on their interaction with human agents.
Human body.
Human hand. ..

27. Shape Synthesis Synthesize new shapes based on the existing ones.
No fancy devices/scanners to build a new 3D model; just meaningful measurement, e.g., weight, height, etc. of a human.
PCA-based synthesis.
Part-based synthesis.

28. Shape Synthesis Synthesize new shapes based on the existing ones.
Ergonomics: 3D printers now build cloths & helmets.
Create your own 3D model with your measurements (weight, height, etc.) and test/reshape the helmet on it before 3D printing.

29. Shape Synthesis Synthesize new shapes based on the existing ones.
Show patient how she would look like before aesthetic or epithesis surgery.

30. Shape Synthesis
Idea: Represent the shapes in a low-dimensional space.

31. Shape Synthesis
Correlation between the input data pi = [kg, cm, ..] for shape si and the shape si represented by aij needed.
Training: pi = is defined/precomputed for each shape si
ai = B pi //Learn correlation matrix B (ai = [ai0, ai1, .., aiD])
Create a new shape w/ the desired meaningful measures pnew
anew = B pnew
Transform anew into coordinate representation in PCA space
snew = s + \sum_{j=0}{D} aij dj
a0 = B0 p0 a1 = B1 p1 a2 = B2 p2 .. ak = Bk pk
B = average of {Bk}

32. Shape Synthesis
Coming up with measurements specific to the collection is a challenge
Weight, height, silhouette for human collection.
???? for airplane collection.
???? for ???? collection.
Learn correlation with more sophisticated methods than linear mapping ai= B pi.
Computational tools for organizing 3D model collections.
Algorithms for understanding collections’ semantic and geometric properties and relations (correspondence, segmentation, retrieval, etc.).

33. Scene Synthesis
Most intuitive approach is to keep the user in the loop via sketches.

34. Scene Labeling
Need to issue this command to a robot: Fetch me the mug on coffee table.
Need labels on scene point cloud (acquired by, e.g., Kinect).
Pairwise analysis might work well.