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

2. Shape Modeling International 2013 /29 Contents  Introduction  Related work  The proposed method  Experimental results  Conclusion 2

3. Shape Modeling International 2013 /29 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 3 [Alexa01]

4. Shape Modeling International 2013 /29 Noise filtering Input surface(signal) – Additive noise Output surface(signal) – Noise free 4 Filtering

5. Shape Modeling International 2013 /29 Feature-preserving noise filtering Local averaging – Loss of salient features, details 5 Filtering

6. Shape Modeling International 2013 /29 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 6

7. Shape Modeling International 2013 /29 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 7

8. Shape Modeling International 2013 /29 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 8

9. Shape Modeling International 2013 /29 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 9

10. Shape Modeling International 2013 /29 Goal In this paper, we develop a fast and efficient denoising filter while preserving sharp features and small details 10

11. Shape Modeling International 2013 /29 Key idea Maintain multiple normals at the tangent discontinuity point after recognizing sharp features The second-order filter based on the curvature information 11

12. Shape Modeling International 2013 /29 Algorithm overview 12 Noisy surface Feature detectionNormal estimation Second-order filtering

13. Shape Modeling International 2013 /29 Feature detection Sharp feature detection via tensor voting [Park12] 13 : density : identity matrix : neighborhood : Straight line Spatial neighborhood N(p) Eigen-analysis

14. Shape Modeling International 2013 /29 Adaptive sub-neighborhood(ASN) 14 Tensor also encodes the local structure similarity ASN

15. Shape Modeling International 2013 /29 Normal estimation Smooth surface – Classical normal estimation (PCA) – Averaging the local neighborhood Normal at discontinuities – Maintain multiple normals of surface segments – Distance-based normal clustering 15 : Mahalanobis distance : Covariance matrix of all normals within ASN Tangent plane Abrupt change Tangent plane

16. Shape Modeling International 2013 /29 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 16 [Jones03]’s predictor [Fleishman03]’s predictor Noisy point Tangent plane of q Tangent plane of p

17. Shape Modeling International 2013 /29 Second-order prediction 17 Circle of curvature Predictor of p Predictor of p [Jones03]’s predictor [Fleishman03]’s predictor Noisy point

18. Shape Modeling International 2013 /29 Second-order prediction Second-order surface approximation 18 Our predictor Underlying surface Center of curvature

19. Shape Modeling International 2013 /29 Our prediction 19 Second-order approximationFirst-order approximation

20. Shape Modeling International 2013 /29 Proposed denoising filter 20 Spatial kernel Range kernel Predictor

21. Shape Modeling International 2013 /29 Results CAD-like model 21 Ground-truth Noisy modelBilateral filteringRIMLSOur method 10% Gaussian noise 20% Gaussian noise

22. Shape Modeling International 2013 /29 Results Free-form surface 22 Ground-truthNoisy modelBilateral filteringRIMLSOur method

23. Shape Modeling International 2013 /29 Results 23 ModelFandiskBunnyArmadillo Bilateral filtering0.0810.0910.098 RIMLS0.0830.0480.060 Proposed0.0540.0510.052 Bilateral filtering RIMLS Proposed 0% 15% ↑

24. Shape Modeling International 2013 /29 Comparison (6 algorithms) 24 * Results by MeshLab software [Cignoni]

25. Shape Modeling International 2013 /29 Comparison (6 algorithms) 25 * Results by MeshLab software [Cignoni]

26. Shape Modeling International 2013 /29 More results 26 Raw dataBilateral filteringRIMLS Proposed method

27. Shape Modeling International 2013 /29 Computation time Computation time of our method is comparable to the first-order filtering 27 * Intel i7 2.93 GHz CPU and 4GB RAM, no GPU

28. Shape Modeling International 2013 /29 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 28

29. Shape Modeling International 2013 /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.krminkp@gist.ac.kr 29