IFCBGFICBG - - PowerPoint PPT Presentation

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IFCBGFICBG - - PowerPoint PPT Presentation

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:SINGHUANIVERSIT IFCBGFICBG CB-CIGGCFAI 3B ,I4ICEB BIBB3B

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SLIDE 1

:SINGHUANIVERSIT

IFCBGFICBG CB-CIGGCFAI

3B ,I4ICEB BIBB3B 1GBI2BJFGL

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 1

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SLIDE 2

.IB

  • ONCLUSION
  • ESULTSANDOMPARISONS
  • AUSSURFACEECONSTRUCTION
  • 3CFG

2019/8/9 2 Surface Reconstruction Based on Modified Gauss Formula

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SLIDE 3
  • 3CFG

2019/8/9 3

n URFACERECONSTRUCTIONFROMPOINTCLOUDS

  • ELLSTUDIED

n )PPLICATIONS

  • 4ANUFACTURE
  • )NIMATION
  • ISUALIATION
  • TC

Surface Reconstruction Based on Modified Gauss Formula

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SLIDE 4
  • 3CFG

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 4

nOMBINATORIALMETHODS

  • TILIEPARTOF THEINPUTSAMPLEPOINTSASVERTICES
  • SUALLSENSITIVETONOISEANDMAPRODUCEAGGEDSURFACES

[Kolluri et al. 2004] [Xiong et al. 2014] [Amenta et al. 2002] etc…

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SLIDE 5
  • 3CFG

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 5

n1MPLICITMETHODS

  • STIMATEIMPLICITFUNCTIONSFROMTHEINPUTSAMPLESANDEXTRACT

ISOSURFACESTOGENERATETRIANGLEMESHES

<0 F(q) Samples F(q)<0 F(q)>0 F(q) =0

slide-6
SLIDE 6
  • 3CFG

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 6

n1MPLICITMETHODS

  • 0OWTOCHOOSEIMPLICITFUNCTIONANDHOWTOSOLVEIT(

<0 F(q) Samples F(q)<0 F(q)>0 F(q) =0

slide-7
SLIDE 7
  • 3CFG

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 7

[Kazhdan et al. 2006] [Calakli and Taubin 2011] [Kazhdan et al. 2013] [Hoppe et al. 1992] [Curless and Levoy 1996] [Carr et al. 2001] … …

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SLIDE 8

n 1NDICATORFUNCTION! = #

% ∈ '( \ * Σ 1/2 % ∈ /* Σ 1 % ∈ Σ

  • BCFIBCB

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 8

Indicator function Indicator function gradients Samples

0! = 1

slide-9
SLIDE 9
  • BCFIBCBCFAG

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 9

n OISSONSURFACERECONSTRUCTION?2AHDAN ETAL

  • ONVOLUTIONOFTHEINDICATORFUNCTION
  • 6VERSMOOTHED

n CREENEDOISSONSURFACERECONSTRUCTION?2AHDAN ET AL

  • )SCALARFUNCTIONFITTINGTERM
  • 6VERFITTING
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SLIDE 10

BGBIBCB

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 10

nIGNEDDISTANCEFUNCTIONMETHODS

  • )SIGNEDDISTANCEFUNCTIONISSMOOTHNEARTHESURFACE
  • ASTOINTERPOLATE
  • ENSITIVETONOISE
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SLIDE 11
  • LFGCICB

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 11

n6BSERVATION

  • 1NDICATORFUNCTIONROBUSTTONOISE
  • IGNEDDISTANCEFUNCTIONEASTOINTERPOLATENEARTHESURFACE

n6BECTIVE

  • )WAFROMTHESURFACEINDICATORFUNCTION
  • EARTHESURFACESIGNEDDISTANCEFUNCTION
  • ALANCEBETWEENDATAFIDELITANDRESILIENCAGAINSTNOISE
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SLIDE 12
  • LFGCICB

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 12

n6URMETHOD

  • ASEDONAUSS3EMMAINTHEPOTENTIALTHEOR
  • STIMATEDDIRECTLFROMANEXPLICITINTEGRALFORMULAWITHOUT

SOLVINGANLINEARSSTEM

  • ASTOPARALLELIEWITHSMALLOVERHEAD
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SLIDE 13

.IB

  • ONCLUSION
  • ESULTSANDOMPARISONS
  • IGGIFCBGFICB
  • ELATEDORKS

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 13

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SLIDE 14
  • IGG,AA

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 14

n3ET Σ BEANOPENREGIONINℝ( * Σ DENOTESTHECLOSUREOFΣ ONSIDERTHEFOLLOWINGDOUBLELAERPOTENTIAL.ORAN% ∈ ℝ(, 4 ∈ /Σ[

! % = 5

67

/8 /1 4 %, 4 9: 4 .

n8 ISTHEFUNDAMENTALSOLUTIONOFTHE3APLACEEUATIONWHICH CANBESTATEDEXPLICITLAS 8 %, 4 = − 1 4> % − 4 .

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SLIDE 15
  • IGG,AA

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 15

n3ET Σ BEANOPENREGIONINℝ( * Σ DENOTESTHECLOSUREOFΣ ONSIDERTHEFOLLOWINGDOUBLELAERPOTENTIAL.ORAN% ∈ ℝ(, 4 ∈ /Σ[

! % = 5

67

/8 /1 4 %, 4 9: 4 .

nOTETHAT

6? 6@ A

%, 4 = −

B CD EFA G@ A EFA

H

  • WHICHWECALLTHEKERNELFUNCTIONANDDENOTEBI(%, 4)
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SLIDE 16
  • IGG,AA

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 16

n:HEN[THEINDICATORFUNCTIONCANBEFORMALIEDAS χ % ≈ − 1 4π O

P∈Q

x − y G N y x − y

(

  • y. A.
  • nHEREy. A ISASMALLREGIONNEARTHESAMPLEy[THESET y. A P∈Q

COVERTHESURFACE /Σ

1NDICATORFUNCTION!(%) = #

% ∈ '( \ * Σ 1/2 % ∈ /* Σ 1 % ∈ Σ

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SLIDE 17

2,1

  • LOBALNESS

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 17

  • INGULARIT
  • GCBBIL

Indicator Function Value

1

Distance to the Surface

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SLIDE 18

GCBBIL

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 18

n 6RIGINALKERNELI %, 4 = EFA G@(A)

CDG EFA

H

V

n W I %, 4 = I %, 4 , % − 4 ≥ V % −Y % − 4 G 1 4 4> G V((%) % − 4 < V % , Y ∈ 0,1

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SLIDE 19

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 19

Distance to the surface 1

1 2 + 9 % 4V % + 9( % 4V( % Y = 1 \ ! % = 1 2 + 1 2 − Y 4 9 % V % + Y9((%) 4V((%) +O(|V % |) \ ! % = 5

_ E,` E ∩67

W I %, 4 d:(4) + 5

67\ _ E,` E

I %, 4 d: 4 \ ! % ≈ 1 2 + 9 % 2V % Y = 0

GCBBIL

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SLIDE 20

2,1

  • LOBALNESS

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 20

  • INGULARIT
  • GCBBIL
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SLIDE 21

c

  • LOBALNESS

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 21

  • BIFL
  • ,ISCONTINUIT

Indicator functiond %, 4 = −

B CD EFA G@ A EFA H 4. e

surface Indicator Function Value 1 Distance to the Surface f

% − 4

(

2,1

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SLIDE 22

%′

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 22

GBFCB

hiFB hi ji

4 k

hiFB hi %′ ji

4 %

Sample Point 4

%’ k

slide-23
SLIDE 23
  • CBGG

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 23

  • INGULARIT
  • ,ISCONTINUIT

2,1

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SLIDE 24

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 24

CBGG

Complexitym(no)

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SLIDE 25

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 25

G-IDC-C

n,ATATRUCTURE)DAPTIVE6CTREE n6BECTIVE-STIMATEFUNCTIONVALUEFOREACHCELL

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SLIDE 26

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 26

G-IDC-C

npqrs > uℎhwrℎxy9

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SLIDE 27

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 27

G-IDC-C

npqrs < uℎhwrℎxy9

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SLIDE 28

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 28

G-IDC-C

Complexitym(nyzn)

{B {o

slide-29
SLIDE 29

.IB

  • ONCLUSION
  • GIGBCADFGCBG
  • AUSSURFACEECONSTRUCTION
  • ELATEDORKS

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 29

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SLIDE 30
  • CFAGCFCADFGCBG

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 30

nOISSON2AHDAN ETAL nCREENEDOISSON 2AHDAN ETAL:6 n,ALAKLI ETAL. n,ICTIONARLEARNINGIONG ETAL:6

slide-31
SLIDE 31
  • IFL

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 31

n,ATAAMPLESONUNITSPHERE SAMPLES

slide-32
SLIDE 32
  • IFL

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 32

n,ATA)IMHAPE

slide-33
SLIDE 33
  • IFL

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 33

n,ATABerger et al. A benchmark for surface reconstruction ?:6

slide-34
SLIDE 34
  • LBBCG

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 34

n,ATAAUSSIANDISTRIBUTIONNOISES

slide-35
SLIDE 35
  • CFBB

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 35

slide-36
SLIDE 36
  • CFBB

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 36

slide-37
SLIDE 37
  • FCB AC

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 37

n,ATAXiong et al. Robust surface reconstruction via dictionary [TOG 2014]

slide-38
SLIDE 38
  • GGB

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 38

n,ATA-.3http://lgg.epfl.ch/code.php)

slide-39
SLIDE 39
  • FDIFG

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 39

n,ATA6CT.LOWER)IMSHAPE

slide-40
SLIDE 40

BL

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 40

slide-41
SLIDE 41
  • CCCB

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 41

slide-42
SLIDE 42

.IB

  • CBIGCB
  • ESULTSANDOMPARISONS
  • AUSSURFACEECONSTRUCTION
  • ELATEDORKS

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 42

slide-43
SLIDE 43
  • CBIGCB

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 43

n)HBRIDIMPLICITFUNCTION] n)NEXPLICITINTEGRALFORMULABASEDONAUSS3EMMA]

  • WITHOUTSOLVINGANLINEARSSTEM]
  • HASANATURALPARALLELIMPLEMENTATION]

n,ISKINTEGRATION] n)CONCISEANDEFFICIENTVERSIONOF.44

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SLIDE 44
  • IIFCF

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 44

n0ASH6CTREE n-NHANCEDIMPLEMENTATIONOFTHE.44 n)CLOSEDFORMFORMULAFORDISKINTEGRATION nOMPLETELERSION

slide-45
SLIDE 45
  • Thanks!

2019/8/9 Surface Reconstruction Based on Modified Gauss Formula 45