1. Gwangju Institute of Science and Technology Intelligent Design and Graphics Laboratory Multi-scale tensor voting for feature extraction from unstructured point clouds Min Ki Park* Seung Joo Lee Kwan H. Lee Gwangju Institute of Science and Technology (GIST) Geometric Modeling and Processing 2012 2012. 06. 22

2. Geometric Modeling and Processing 2012 Contents Introduction Previous work Method – Tensor voting of 3D point cloud – Multi-scale tensor voting Experimental results Limitation and Future work 2/34

3. Geometric Modeling and Processing 2012 Point-based Surface Scanning technology – A huge amount of dense point data – Laser scanner, structured-light and Time-of-Flight sensor No need to generate triangular meshes Difficulties – No connectivity and normal information – Random noise, outliers and non-uniform distributions 3/34

4. Geometric Modeling and Processing 2012 Why feature extraction? Better understanding of underlying surfaces – Insight about crucial characteristics of geometry – A priori knowledge for various geometry processing applications e.g.) Adaptive sampling, feature-preserving simplification, geometry segmentation, etc. 4/34 [Demarsin et al. 07]

5. Geometric Modeling and Processing 2012 Previous work - PCA-based Approach Differential properties of a surface – Principal component analysis (PCA) of covariance matrix – Approximation of normal or curvature over local neighborhood Multi-scale feature classification – Differential properties at multiple scales – Enhancement of feature recognition in noisy data Drawbacks – First- or second-derivative approximation – Wide band of feature points in the vicinity of a sharp edge 5/34 [Pauly et al. 02]

6. Geometric Modeling and Processing 2012 Previous work - Surface reconstruction Moving least squares (MLS) – Local surface approximation fit to neighborhood – Point projection to the approximated surface Robust Moving least squares (RMLS) – Feature-preserving noise removal during MLS reconstruction – More accurate approximations of features Drawbacks – Considerable computational cost 6/34 [Daniels et al. 07]

7. Geometric Modeling and Processing 2012 In this paper, 7/34

8. Geometric Modeling and Processing 2012 Contributions Extend the tensor voting theory to feature extraction of point set with any intrinsic dimensionality Propose the multi-scale tensor voting scheme for robust shape analysis Provide a very high computational efficiency 8/34

9. Geometric Modeling and Processing 2012 Key Idea Tensor voting for shape analysis In voting process, 9/34 [P. Mordohai2005] Input image Edge detection By human observer Scale parameter control how many neighboring points vote!! How to determine an optimal scale?

10. Geometric Modeling and Processing 2012 Overview of the algorithm 10/34

11. Geometric Modeling and Processing 2012 Tensor voting in 3D - Neighborhood selection 11/34 K-nearest neighbor Our neighborhood selection suggested by [Ma et al. 2011] Non-uniformly distributed Unbalanced neighborhood!

12. Geometric Modeling and Processing 2012 Tensor voting in 3D - Normal voting from neighborhood Normal space voting for two points 12/34

13. Geometric Modeling and Processing 2012 Tensor voting in 3D - Normal voting tensor 13/34 The size of the vote is attenuated by the Gaussian function For every neighbor, integrate the votes

14. Geometric Modeling and Processing 2012 Tensor voting in 3D - Voting analysis 14/34

15. Geometric Modeling and Processing 2012 Tensor voting in 3D - Voting analysis 15/34 On a faceOn a curve Randomly scattered

16. Geometric Modeling and Processing 2012 Tensor voting in 3D - Feature weight 16/34 Feature weight

17. Geometric Modeling and Processing 2012 In the presence of noise, Can you distinguish a feature point from noise? – A face needs to be smoothed out – An edge needs to be preserved 17/34

18. Geometric Modeling and Processing 2012 Revisit - Scale parameter It depends on noise level and sampling qualities How to adjust it? – Control voting neighborhood – Modify attenuation degree 18/34

19. Geometric Modeling and Processing 2012 Multi-scale tensor voting Adaptive scale in tensor computation – Small scale for the fine point data – Large scale for the noisy point data 19/34 Feature weight Scale

20. Geometric Modeling and Processing 2012 Optimal scale of a point Fine model 20/34 Large variation Keep large values Keep small values

21. Geometric Modeling and Processing 2012 Optimal scale of a point Noisy model 21/34 Large variation Gradual Increase Gradual decrease

22. Geometric Modeling and Processing 2012 How to determine an optimal scale? 22/34

23. Geometric Modeling and Processing 2012 Discussion - our multi-scale TV It allows the tensor voting framework to deal with both a noisy region and a sharp edge – Feature preserving Similar to [Pauly et al. 2003], but, no evaluation of the measure over the entire scale space Efficient implementation – Update points newly included in the voting at the current scale 23/34

24. Geometric Modeling and Processing 2012 24/34

25. Geometric Modeling and Processing 2012 Feature classification Adaptive thresholding for unclassified points. If the feature weight is local maximum (30%), add to a feature set 25/34 missing If largest 30% points in local neighborhood

26. Geometric Modeling and Processing 2012 Feature completion 26/34 Outliers In the presence of severe noise, many outliers exist Outlier removal – Make feature clusters – Remove clusters of small size (under 10) Misclassified feature set is successfully removed

27. Geometric Modeling and Processing 2012 Results 27/34 Input model Color-coded The result The result by polylines feature weight

28. Geometric Modeling and Processing 2012 Result - poorly sampled point models 28/34 jagged sparse 5k 10k 5k

29. Geometric Modeling and Processing 2012 Result - Robustness to noise 29/34 PCA-based method Our method

30. Geometric Modeling and Processing 2012 Results - Computational time 30/34 Only tensor addition and eigen analysis Multi-scale? – Asymptotically identical to the single scale

31. Geometric Modeling and Processing 2012 Dimensionality advantage 31/34 PCA-based method Gauss map Clustering Our method Non-manifold Space curve Different intrinsic dimension PCA Gauss map clustering Our tensor voting Plane with one normal Space curve with two normals

32. Geometric Modeling and Processing 2012 Real scanned data 32/34 Processing time: 15 secs for 173k vertices

33. Geometric Modeling and Processing 2012 Limitation and future work Limitations – Sampling quality is very poor – Signal-to-Noise ratio is too low Fail to distinguish between a sharp edge and a planar region in the vicinity of a real edge In future work, – Improve the reliability for many uncertainties (e.g., poor sampling quality, extreme noise) – Fit a continuous feature-line to the feature points 33/34

34. Geometric Modeling and Processing 2012 Thank you for your attention Q&A Intelligent Design and Graphics Laboratory Gwangju Institute of Science and Technology (GIST) http://ideg.gist.ac.kr Contact info. minkp@gist.ac.kr 34/34