Feature aware filtering for point set surface denoising
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Shape Modeling International 2013 (short paper). Feature-Aware Filtering for Point-Set Surface Denoising. 2013. 07. 11. Min Ki Park* Seung Joo Lee In Yeop Jang Yong Yi Lee Kwan H. Lee Gwangju Institute of Science and Technology (GIST). Contents. Introduction Related work

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Feature aware filtering for point set surface denoising

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)


Contents
Contents

  • Introduction

  • Related work

  • The proposed method

  • Experimental results

  • Conclusion


Introduction
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]


Noise filtering
Noise filtering

  • Input surface(signal)

    • Additive noise

  • Output surface(signal)

    • Noise free

Filtering


Feature preserving noise filtering
Feature-preserving noise filtering

  • Local averaging

    • Loss of salient features, details

Filtering


Related work point set surface denoising
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


Related work point set surface denoising1
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


Related work point set surface denoising2
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


Problems of previous methods
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


Feature aware filtering for point set surface denoising
Goal

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


Key idea
Key idea

  • Maintain multiple normals at the tangent discontinuity point after recognizing sharp features

  • The second-order filter based on the curvature information


Algorithm overview
Algorithm overview

Noisy

surface

Feature detection

Normal estimation

Second-order filtering


Feature detection
Feature detection

  • Sharp feature detection via tensor voting [Park12]

: density

: identity matrix

: neighborhood

: Straight line

Eigen-analysis

Spatial neighborhood N(p)


Adaptive sub neighborhood asn
Adaptive sub-neighborhood(ASN)

  • Tensor also encodes the local structure similarity

ASN


Normal estimation
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


Vertex position update previous
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


Second order prediction
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


Second order prediction1
Second-order prediction

  • Second-order surface approximation

Center of curvature

Our predictor

Underlying surface


Our prediction
Our prediction

  • Predictor is determined by angle between two normals

Second-order approximation

First-order approximation


Proposed denoising filter
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


Results
Results

  • CAD-like model

10% Gaussian noise

Ground-truth

20% Gaussian noise

Noisy model

Bilateral filtering

RIMLS

Our method


Results1
Results

  • Free-form surface

Ground-truth

Noisy model

Bilateral filtering

RIMLS

Our method


Results2
Results

15% ↑

Bilateral filtering

RIMLS

0%

Proposed


Comparison 6 algorithms
Comparison (6 algorithms)

* Results by MeshLab software [Cignoni]


Comparison 6 algorithms1
Comparison (6 algorithms)

* Results by MeshLab software [Cignoni]


More results
More results

Proposed method

Bilateral filtering

Raw data

RIMLS


Computation time
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


Conclusion
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


Feature aware filtering for point set surface denoising

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