Surface Reconstruction S. Ohrhallinger, S. Mudur and M. Wimmer 2 - PowerPoint PPT Presentation

Minimizing Edge Length to Connect Sparsely Sampled Unstructured Point Sets in 3D S. Ohrhallinger 1,2 , S. Mudur 2 and M. Wimmer 1 1 Vienna University of Technology, 2 Concordia University, Montréal

Surface Reconstruction S. Ohrhallinger, S. Mudur and M. Wimmer 2

Surface Reconstruction Dense is easy Sparse is hard Dense is easy Sparse is hard S. Ohrhallinger, S. Mudur and M. Wimmer 3

State of the Art Tight Wrap Wrap Tight Cocone Cocone Shrink Ours Shrink Ours S. Ohrhallinger, S. Mudur and M. Wimmer 4

Problem Domain Interpolating Fitting Interpolating S. Ohrhallinger, S. Mudur and M. Wimmer 5

Problem Domain Interpolating Fitting Interpolating Too smooth S. Ohrhallinger, S. Mudur and M. Wimmer 6

Problem Domain Interpolating Fitting Interpolating Too smooth Closed Mesh Bound Holes Closed Mesh S. Ohrhallinger, S. Mudur and M. Wimmer 7

Problem Domain Interpolating Fitting Interpolating Too smooth Closed Mesh Bound Holes Closed Mesh Parameter Parameter S. Ohrhallinger, S. Mudur and M. Wimmer 8

Problem Domain Interpolating Fitting Interpolating Too smooth Closed Mesh Bound Holes Closed Mesh Parameter Parameter Connect points with polyhedron B in DT , close to smooth surface S Connect points with polyhedron B in DT , close to smooth surface S S. Ohrhallinger, S. Mudur and M. Wimmer 9

Related Work α-Shapes [4,5] S. Ohrhallinger, S. Mudur and M. Wimmer 10

Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] S. Ohrhallinger, S. Mudur and M. Wimmer 11

Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] S. Ohrhallinger, S. Mudur and M. Wimmer 12

Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Sculpturing Sculpturing [8,14,15,18] [8,14,15,18] S. Ohrhallinger, S. Mudur and M. Wimmer 13

Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Voronoi Filtering Sculpturing Sculpturing [3,16,17] [8,14,15,18] [8,14,15,18] S. Ohrhallinger, S. Mudur and M. Wimmer 14

Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Voronoi Filtering Sculpturing Sculpturing [3,16,17] [8,14,15,18] [8,14,15,18] Optimization Optimization [26,27,28] [26,27,28] S. Ohrhallinger, S. Mudur and M. Wimmer 15

Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Voronoi Filtering Sculpturing Sculpturing [3,16,17] [8,14,15,18] [8,14,15,18] Optimization Optimization Flow [26,27,28] [26,27,28] [20,21,22,23,24,25] S. Ohrhallinger, S. Mudur and M. Wimmer 16

Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Voronoi Filtering Sculpturing Sculpturing [3,16,17] [8,14,15,18] [8,14,15,18] Ours Ours Optimization Optimization Flow [26,27,28] [26,27,28] [20,21,22,23,24,25] S. Ohrhallinger, S. Mudur and M. Wimmer 17

We extend our 2D Method create inflate sculpture create inflate sculpture [OM13] [OM13] S. Ohrhallinger, S. Mudur and M. Wimmer 18

We extend our 2D Method create inflate sculpture create inflate sculpture [OM13] [OM13] S. Ohrhallinger, S. Mudur and M. Wimmer 19

Minimization Objective S. Ohrhallinger, S. Mudur and M. Wimmer 20

Minimization Objective Circumradius Circumradius S. Ohrhallinger, S. Mudur and M. Wimmer 21

Minimization Objective Circumradius Aspect ratio Circumradius Aspect ratio S. Ohrhallinger, S. Mudur and M. Wimmer 22

Minimization Objective Circumradius Aspect ratio Area Circumradius Aspect ratio Area S. Ohrhallinger, S. Mudur and M. Wimmer 23

Minimization Objective Longest edge Circumradius Aspect ratio Area Longest edge Circumradius Aspect ratio Area in triangle in triangle S. Ohrhallinger, S. Mudur and M. Wimmer 24

Minimization Objective Longest edge Circumradius Aspect ratio Area Longest edge Circumradius Aspect ratio Area in triangle in triangle S. Ohrhallinger, S. Mudur and M. Wimmer 25

A fast Approximation S. Ohrhallinger, S. Mudur and M. Wimmer 26

A fast Approximation NP-hard NP-hard S. Ohrhallinger, S. Mudur and M. Wimmer 27

A fast Approximation NP-hard NP-hard S. Ohrhallinger, S. Mudur and M. Wimmer 28

A fast Approximation NP-hard NP-hard S. Ohrhallinger, S. Mudur and M. Wimmer 29

A fast Approximation NP-hard NP-hard Still NP-hard? Still NP-hard? Still NP-hard? S. Ohrhallinger, S. Mudur and M. Wimmer 30

A fast Approximation NP-hard NP-hard Still NP-hard? Still NP-hard? Still NP-hard? S. Ohrhallinger, S. Mudur and M. Wimmer 31

A fast Approximation NP-hard NP-hard ? Still NP-hard? Still NP-hard? Still NP-hard? S. Ohrhallinger, S. Mudur and M. Wimmer 32

Artifact Removal Bound artifacts Bound artifacts S. Ohrhallinger, S. Mudur and M. Wimmer 33

Artifact Removal Bound artifacts Cover hull holes Bound artifacts Cover hull holes S. Ohrhallinger, S. Mudur and M. Wimmer 34

Artifact Removal Bound artifacts Cover hull holes Sculpture slivers Bound artifacts Cover hull holes Sculpture slivers S. Ohrhallinger, S. Mudur and M. Wimmer 35

Our Method: Overview Slivers @holes Sliver sets manifold S. Ohrhallinger, S. Mudur and M. Wimmer 36

Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes S. Ohrhallinger, S. Mudur and M. Wimmer 37

Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Inflate S. Ohrhallinger, S. Mudur and M. Wimmer 38

Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Inflate S. Ohrhallinger, S. Mudur and M. Wimmer 39

Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Sculpture Inflate S. Ohrhallinger, S. Mudur and M. Wimmer 40

Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Sculpture Inflate S. Ohrhallinger, S. Mudur and M. Wimmer 41

Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Sculpture Inflate Dual Dual S. Ohrhallinger, S. Mudur and M. Wimmer 42

Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Sculpture Inflate Dual Dual Inflating exploits Closure to reconstruct very sparse sampling Inflating exploits Closure to reconstruct very sparse sampling S. Ohrhallinger, S. Mudur and M. Wimmer 43

Results (1): Very Sparse Sampling Results (1): Improves sparse sampling Wrap Shrink TCocone Ours Input Input S. Ohrhallinger, S. Mudur and M. Wimmer 44

Results (1): Very Sparse Sampling Results (1): Improves sparse sampling Empty Set Empty Set Wrap Shrink TCocone Ours Input Input S. Ohrhallinger, S. Mudur and M. Wimmer 45

Results (1): Very Sparse Sampling Results (1): Improves sparse sampling Empty Set Empty Set Wrap Shrink TCocone Ours Input Input S. Ohrhallinger, S. Mudur and M. Wimmer 46

Results (1): Very Sparse Sampling Results (1): Improves sparse sampling Empty Set Empty Set Wrap Shrink TCocone Ours Input Input S. Ohrhallinger, S. Mudur and M. Wimmer 47

Results (2): Robust to sub-sampling 35k vertices 35k vertices 33 vertices 33 vertices S. Ohrhallinger, S. Mudur and M. Wimmer 48

Results (3): Noise tolerant RCocone RCocone Ours Ours 0% 1% Perturbation of z-extent Perturbation of z-extent S. Ohrhallinger, S. Mudur and M. Wimmer 49

Results (4): Runtime Ours TCocone Shrink seconds x1000 vertices Our unoptimized algorithm is competitive for global approach Our unoptimized algorithm is competitive for global approach S. Ohrhallinger, S. Mudur and M. Wimmer 50

Results(5): Guarantees of B out Watertight Manifold Watertight Manifold S. Ohrhallinger, S. Mudur and M. Wimmer 51

Results(5): Guarantees of B out Watertight Manifold Watertight Manifold 1 Connected Component 1 Connected Component S. Ohrhallinger, S. Mudur and M. Wimmer 52

Results(5): Guarantees of B out Watertight Manifold contains P (or in interior) Watertight Manifold contains P (or in interior) 1 Connected Component 1 Connected Component S. Ohrhallinger, S. Mudur and M. Wimmer 53

Results(5): Guarantees of B out Watertight Manifold contains P (or in interior) Watertight Manifold contains P (or in interior) 1 Connected Component Conjecture: ε<0.5 1 Connected Component Conjecture: ε<0.5 S. Ohrhallinger, S. Mudur and M. Wimmer 54

Limitation Bottom hole Bottom hole S. Ohrhallinger, S. Mudur and M. Wimmer 55

Limitation Bottom hole Convoluted boundary Bottom hole Convoluted boundary S. Ohrhallinger, S. Mudur and M. Wimmer 56

Limitation inflate Bottom hole Convoluted boundary Bottom hole Convoluted boundary S. Ohrhallinger, S. Mudur and M. Wimmer 57

Limitation inflate Far from B min Bottom hole Convoluted boundary Far from B min Bottom hole Convoluted boundary S. Ohrhallinger, S. Mudur and M. Wimmer 58

Future work Close Convoluted Holes Close Convoluted Holes S. Ohrhallinger, S. Mudur and M. Wimmer 59