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Multi-scale tensor voting for feature extraction from unstructured point clouds

Geometric Modeling and Processing 2012. Multi-scale tensor voting for feature extraction from unstructured point clouds. 2012. 06. 22. Min Ki Park* Seung Joo Lee Kwan H. Lee Gwangju Institute of Science and Technology (GIST). Contents. Introduction Previous work Method

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Multi-scale tensor voting for feature extraction from unstructured point clouds

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

  2. Contents • Introduction • Previous work • Method • Tensor voting of 3D point cloud • Multi-scale tensor voting • Experimental results • Limitation and Future work

  3. 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

  4. Why feature extraction? [Demarsin et al. 07] • 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.

  5. Previous work -PCA-based Approach [Pauly et al. 02] • 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

  6. Previous work -Surface reconstruction [Daniels et al. 07] • 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

  7. In this paper, • Given An unstructured point set 1) no connectivity and normal information 2) random noise contained 3) Unknown intrinsic dimensionality • Goal Extract a set of feature points

  8. 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

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

  10. Overview of the algorithm

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

  12. Tensor voting in 3D -Normal voting from neighborhood Normal space voting for two points

  13. Tensor voting in 3D -Normal voting tensor For every neighbor, integrate the votes The size of the vote is attenuated by the Gaussian function

  14. Tensor voting in 3D -Voting analysis where

  15. Tensor voting in 3D -Voting analysis Randomly scattered On a face On a curve

  16. Tensor voting in 3D -Feature weight Feature weight • A point with larger is most likely on a feature • Feature confidence value (feature weight) e.g.,), is on a plane , is on an edge or corner

  17. 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

  18. Revisit - Scale parameter • It depends on noise level and sampling qualities • How to adjust it? • Control voting neighborhood • Modify attenuation degree

  19. Multi-scale tensor voting Scale Feature weight • Adaptive scale in tensor computation • Small scale for the fine point data • Large scale for the noisy point data

  20. Optimal scale of a point Large variation Keep large values Keep small values • Fine model

  21. Optimal scale of a point Large variation Gradual Increase Gradual decrease • Noisy model

  22. How to determine an optimal scale? • Adaptive scale selection algorithm • Initial scale • Compute of point at scale • Classify using pre-defined threshold • Observe the feature weight variation over scale domain 4.1. The large increase tells the optimal scale 4.2. Otherwise, larger scale is likely to be optimal • Update the current scale and repeat [2-4] until the every point is classified or maxIter is reached.

  23. 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

  24. Each point has own optimal scale and feature weight • If , is a feature point • If , is a non-feature point • How to classify the remaining points ?

  25. Feature classification If largest 30% points in local neighborhood missing • Adaptive thresholding for unclassified points. If the feature weight is local maximum (30%), add to a feature set

  26. Feature completion 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. Results Inputmodel Color-coded The result The result by polylines feature weight

  28. Result - poorly sampled point models 5k 5k 10k jagged sparse

  29. Result -Robustness to noise PCA-based method Our method

  30. Results -Computational time • Only tensor addition and eigen analysis • Multi-scale? • Asymptotically identical to the single scale

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

  32. Real scanned data Processing time: 15 secs for 173k vertices

  33. 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

  34. 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

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