Feature-Aware Filtering for Point-Set

hesitantdoubtfulΤεχνίτη Νοημοσύνη και Ρομποτική

29 Οκτ 2013 (πριν από 3 χρόνια και 8 μήνες)

54 εμφανίσεις

Gwangju Institute of Science and Technology

Intelligent Design and Graphics Laboratory

Feature
-
Aware Filtering for Point
-
Set
Surface Denoising

Min Ki Park*


Seung

Joo

Lee

In
Yeop

Jang


Yong Yi Lee



Kwan H. Lee


Gwangju Institute of Science and Technology (GIST)


Shape Modeling International 2013 (short paper)

2013. 07. 11

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Contents


Introduction


Related work


The proposed method


Experimental results


Conclusion

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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]

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Noise filtering


Input surface(signal)


Additive noise


Output surface(signal)


Noise free





4

Filtering

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Feature
-
preserving noise filtering


Local averaging


Loss of salient features, details





5

Filtering

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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

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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









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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









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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

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Goal


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


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Key idea


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




The second
-
order filter based on the
curvature information

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Algorithm overview

12

Noisy


surface

Feature detection

Normal estimation

Second
-
order
filtering

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Feature detection


Sharp feature detection via tensor voting [Park12]

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: density

: identity matrix

: neighborhood

: Straight line

𝜌

(

)

𝐼

𝑁

𝐯





v

Spatial neighborhood N(p)

Eigen
-
analysis

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Adaptive sub
-
neighborhood(ASN)

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Tensor
also
encodes the local structure
similarity













ASN

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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


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:
Mahalanobis

distance

: Covariance matrix of all



normals within ASN

𝐧


Tangent plane

𝐧


Tangent plane

Abrupt
change

𝐧

Tangent plane

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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

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[Jones03]’s predictor

[Fleishman03]’s predictor

Noisy point

Tangent plane of
q

Tangent plane of
p

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Second
-
order prediction


Second
-
order surface approximation


Curvature of a smooth surface
𝛾

of p and q





Second
-
order (curvature) predictor

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𝜑





n
p

p

q

Circle of
curvature

Predictor


of p

𝜸

Predictor of p

[Jones03]’s predictor

[Fleishman03]’s predictor

Noisy point

𝜸

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Second
-
order prediction


Second
-
order surface approximation

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Our predictor

Underlying surface

n
q

n
p

p

𝛾

𝜑

Center of
curvature



𝜃

p

Π
𝛾
p

Π
𝛾
p

𝜃
=
𝜑
2

n

H
q

H

q

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Our prediction


Predictor is determined by angle
𝜃

between two normals

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Second
-
order approximation

Π
𝛾

=

+
(



)

𝐧

+
𝐧

𝐧

+
𝐧

cos
𝜃
𝐧


First
-
order approximation

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Proposed denoising filter


Feature
-
aware filtering










Non
-
feature


Use the smooth surface normal
𝐧


at a point



Feature


Use the normal
𝐧

(
𝒊
)

of a cluster
𝑖

of the largest similarity to that
of the neighborhood


20



=

1
𝐾
(

)

𝑊
𝑐



𝑊
𝑠
(
Π
𝛾



)
Π
𝛾



𝐴𝑆𝑁
(

)

Spatial
kernel

Range
kernel

Predictor

Π
𝛾

=

+
(



)

𝐧

+
𝐧

𝐧

+
𝐧

cos
𝜃
𝐧


𝐧

(

)

𝐧

(

)

𝐧


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Results


CAD
-
like model

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Ground
-
truth

Noisy model

Bilateral filtering

RIMLS

Our method

10% Gaussian noise

20% Gaussian noise

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Results


Free
-
form surface

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Ground
-
truth

Noisy model

Bilateral filtering

RIMLS

Our method

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Results

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Model


Fandisk

Bunny

Armadillo

Bilateral filtering

0.081

0.091

0.098

RIMLS

0.083

0.048

0.060

Proposed

0.054

0.051

0.052

Accuracy
(
%
)
=
1
|
𝑃
|




2
𝑎𝑣𝑔
(
𝑑𝑖
)

Bilateral filtering

RIMLS

Proposed

0%

15%


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Comparison (6 algorithms)

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* Results by
MeshLab

software [
Cignoni
]

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Comparison (6 algorithms)

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* Results by
MeshLab

software [
Cignoni
]

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More results

26

Raw data

Bilateral filtering

RIMLS

Proposed
method

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Computation time










Computation time of
o
ur method is comparable to the
first
-
order filtering

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* Intel i7 2.93 GHz CPU and 4GB RAM, no GPU

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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

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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


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