Feature-Aware Filtering for Point-Set Surface Denoising

1. Shape Modeling International 2013 (short paper) Feature-Aware Filtering for Point-Set Surface Denoising 2013. 07. 11 Min Ki Park* SeungJoo Lee In Yeop Jang Yong Yi Lee Kwan H. Lee Gwangju Institute of Science and Technology (GIST)

2. Contents • Introduction • Related work • The proposed method • Experimental results • Conclusion

3. Introduction • Point-based surface • No triangulation process • Simple and flexible data structure • Measurement noise • Reflection, sensing error, misalignment of partial scans • Denoising of a raw dataset is required [Alexa01]

4. Noise filtering • Input surface(signal) • Additive noise • Output surface(signal) • Noise free Filtering

5. Feature-preserving noise filtering • Local averaging • Loss of salient features, details Filtering

6. Related work – Point-set surface denoising • Umbrella operator [Pauly02] • Discrete Laplacian of a surface using an umbrella operator • Equal to isotropic diffusion • Bilateral filtering [Fleishman03] • Height above surface is regarded as the grayscale intensity • Feature preservation using bilateral weights

7. Related work – Point-set surface denoising • Normal filtering [Jones04] • Normal improvement for smooth point rendering using spatial deformation • Higher-order filtering [Duguet04] • Extend the bilateral filtering to second-order filtering • Surface curvature approximation using jet estimation

8. Related work – Point-set surface denoising • Robust moving least squares [Fleishman05; Őztireli09] • A novel MLS based surface definition via robust statistics • Outlier removal during surface reconstruction • Non-local means [Guillemot12] • Improve feature preservation by exploiting self-similarities

9. Problems of previous methods • Fail to preserve sharp features during denoising process • Tangent discontinuity • Shallow feature • Highly curved surface • Require a considerable computation time • Moving least squares surface reconstruction • Higher-order filtering via jet estimation

10. Goal • In this paper, we develop a fast and efficient denoising filter while preserving sharp features and small details

11. Key idea • Maintain multiple normals at the tangent discontinuity point after recognizing sharp features • The second-order filter based on the curvature information

12. Algorithm overview Noisy surface Feature detection Normal estimation Second-order filtering

13. Feature detection • Sharp feature detection via tensor voting [Park12] : density : identity matrix : neighborhood : Straight line Eigen-analysis Spatial neighborhood N(p)

14. Adaptive sub-neighborhood(ASN) • Tensor also encodes the local structure similarity ASN

15. Normal estimation Tangent plane • Smooth surface • Classical normal estimation (PCA) • Averaging the local neighborhood • Normal at discontinuities • Maintain multiple normals of surface segments • Distance-based normal clustering Tangent plane Tangent plane Abrupt change : Mahalanobis distance : Covariance matrix of all normals within ASN

16. Vertex position update (previous) • First-order surface approximation • [Fleishman03; Jones03; Sun07; Zheng11] • Projecting a point onto a local first-order predictor (tangent plane) • Accurate prediction for a plane, not for a highly curved surface Tangent plane of q Tangent plane of p [Jones03]’s predictor [Fleishman03]’s predictor Noisy point

17. Second-order prediction • Second-order surface approximation • Curvature of a smooth surface of p and q • Second-order (curvature) predictor Predictor of p Circle of curvature Predictor of p [Jones03]’s predictor [Fleishman03]’s predictor Noisy point

18. Second-order prediction • Second-order surface approximation Center of curvature Our predictor Underlying surface

19. Our prediction • Predictor is determined by angle between two normals Second-order approximation First-order approximation

20. Proposed denoising filter • Feature-aware filtering • Non-feature • Use the smooth surface normal at a point • Feature • Use the normal of a cluster of the largest similarity to that of the neighborhood Spatial kernel Range kernel Predictor

21. Results • CAD-like model 10% Gaussian noise Ground-truth 20% Gaussian noise Noisy model Bilateral filtering RIMLS Our method

22. Results • Free-form surface Ground-truth Noisy model Bilateral filtering RIMLS Our method

23. Results 15% ↑ Bilateral filtering RIMLS 0% Proposed

24. Comparison (6 algorithms) * Results by MeshLab software [Cignoni]

25. Comparison (6 algorithms) * Results by MeshLab software [Cignoni]

26. More results Proposed method Bilateral filtering Raw data RIMLS

27. Computation time • Computation time of our method is comparable to the first-order filtering * Intel i7 2.93 GHz CPU and 4GB RAM, no GPU

28. Conclusion • Novel second-order filtering for point-set denoising • Feature detection • Adaptive sub-neighborhood • Normal clustering • Feature-aware filtering • The first- or second-order surface approximation • Limitation • Dependent on the point normal estimates

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