Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- IMPA-CMA2011-20Oct2011 by Gabriel Taubin 3941 views
- Calakli Springer2012 by Fatih Calakli 7409 views
- Calakli pg2011 by Gabriel Taubin 7341 views
- Calakli 3DIMPVT2012 by Fatih Calakli 6942 views
- Andalo icdp2011 by Gabriel Taubin 7265 views
- Build Your Own 3D Scanner: 3D Scann... by Douglas Lanman 35307 views

4,029 views

Published on

Slides used by Fatih Calakli to present his paper at Pacific Graphics 2011

No Downloads

Total views

4,029

On SlideShare

0

From Embeds

0

Number of Embeds

3,082

Shares

0

Downloads

0

Comments

0

Likes

1

No embeds

No notes for slide

- 1. SSD: Smooth Signed Distance Surface Reconstruction Fatih Calakli and Gabriel Taubin School of Engineering, Brown University
- 2. Motivation• Industry – Reverse engineering – Fast metrology – Physical simulations
- 3. Motivation• Industry – Reverse engineering – Fast metrology – Physical simulations• Entertainment – Animating digital clays for movies or games
- 4. Motivation• Industry – Reverse engineering – Fast metrology – Physical simulations• Entertainment – Animating digital clays for movies or games• Archeology and Art – Digitization of cultural heritage and artistic works
- 5. Motivation• Industry – Reverse engineering – Fast metrology – Physical simulations• Entertainment – Animating digital clays for movies or games• Archeology and Art – Digitization of cultural heritage and artistic works• Medical Imaging – Visualization – Segmentation• …
- 6. Data acquisitionLaser range scanning devices Multi-camera systems Structured lighting systems
- 7. [Snavely et. al. 2006][Furukawa and Ponce 2008]
- 8. [Snavely et. al. 2006] MVSsoftware [Furukawa and Ponce 2008]
- 9. [Snavely et. al. 2006][Furukawa and Ponce 2008]
- 10. [Snavely et. al. 2006][Furukawa and Ponce 2008]
- 11. ChallengesUniform sampling
- 12. Challenges Uniform samplingNon-uniform sampling Noisy data Misaligned scans
- 13. Outline• Introduction• Related Work• Approach• Evaluation• Conclusion
- 14. General Approaches• Interpolating polygon meshes -Boissonnat, 1984 -Edelsbrunner, 1984 -Amenta et al., 1998 -Bernardini et al., 1999 -Dey et al., 2003, 2007, …• Implicit function fitting -Hoppe et al., 1992 -Curless et al., 1996 -Whitaker, 1998 -Carr et al., 2001 -Davis et al., 2002 -Ohtake et al., 2004 -Turk et al., 2004 -Shen et al., 2004
- 15. General Approaches• Interpolating polygon meshes -Boissonnat, 1984 -Edelsbrunner, 1984 -Amenta et al., 1998 -Bernardini et al., 1999 -Dey et al., 2003, 2007, …• Implicit function fitting -Hoppe et al., 1992 -Curless et al., 1996 -Whitaker, 1998 -Carr et al., 2001 -Davis et al., 2002 -Ohtake et al., 2004 -Turk et al., 2004 -Shen et al., 2004 Surface from Scattered Points: A Brief Survey of Recent Developments [Schall and Samozino, 2005]
- 16. General Approaches• Interpolating polygon meshes -Boissonnat, 1984 -Edelsbrunner, 1984 -Amenta et al., 1998 -Bernardini et al., 1999 -Dey et al., 2003, 2007, …• Implicit function fitting -Hoppe et al., 1992 -Curless et al., 1996 -Whitaker, 1998 -Carr et al., 2001 -Davis et al., 2002 -Ohtake et al., 2004 -Turk et al., 2004 -Shen et al., 2004 -Kazhdan et al., 2006 -Manson et al., 2008
- 17. Implicit function framework Oriented Points, D(samples from unknown surface S) Find a scalar valued function f : D , whose zero level set Z(f) = S’ is the estimate for true surface S
- 18. Implicit function framework <0 0 f >0 Oriented Points, D(samples from unknown surface S) Find a scalar valued function f : D , whose zero level set Z(f) = S’ is the estimate for true surface S
- 19. Implicit function framework Z( f ) Oriented Points, D Computed Implicit Surface, S’(samples from unknown surface S) Find a scalar valued function f : D , whose zero level set Z(f) = S’ is the estimate for true surface S
- 20. Poisson reconstruction [Kazhdan ‘06] 0 1 0 Indicator Function Smooth Signed Distance Function
- 21. Outline• Introduction• Related Work• Our Approach• Evaluation• Conclusion
- 22. Continuous formulation• Oriented point set: D = { ( pi, ni ) } sampled from a surface S
- 23. Continuous formulation• Oriented point set: D = { ( pi, ni ) } sampled from a surface S• Implicit surface: S = { x | f (x) = 0 } such that
- 24. Continuous formulation• Oriented point set: D = { ( pi, ni ) } sampled from a surface S• Implicit surface: S = { x | f (x) = 0 } such that f (pi) = 0 and ∇f (pi) = ni ∀(pi,ni) ∈ D
- 25. Continuous formulation• Oriented point set: D = { ( pi, ni ) } sampled from a surface S• Implicit surface: S = { x | f (x) = 0 } such that f (pi) = 0 and ∇f (pi) = ni ∀(pi,ni) ∈ D• Least squares energy: N N 2 2 ED ( f ) f (p i ) 1 f (p i ) n i i 1 i 1 2 ER ( f ) 2 Hf (x) dx V
- 26. Continuous formulation• Oriented point set: D = { ( pi, ni ) } sampled from a surface S• Implicit surface: S = { x | f (x) = 0 } such that f (pi) = 0 and ∇f (pi) = ni ∀(pi,ni) ∈ D• Least squares energy: N N 2 2 ED ( f ) f (p i ) 1 f (p i ) n i i 1 i 1 2 ER ( f ) 2 Hf (x) dx V E( f ) ED ( f ) ER ( f )
- 27. Role of each energy term N N 2 2E( f ) f (p i ) 1 f (p i ) n i 2 || Hf (x) || 2 dx V i 1 i 1• In the vicinity of the data points, – the data terms dominate the total energy – make the function to approximate the “signed Euclidean distance function”.
- 28. Role of each energy term N N 2 2E( f ) f (p i ) 1 f (p i ) n i 2 || Hf (x) || 2 dx V i 1 i 1• In the vicinity of the data points, – the data terms dominate the total energy – make the function to approximate the “signed Euclidean distance function”. N 2 Q (v ) 1 v(p i ) n i 2 || Dv(x) || 2 dx, V i 1 where Dv denotes the Jacobian of the vector field v. If ∇f = v, then Hf = Dv.
- 29. Role of each energy term N N 2 2E( f ) f (p i ) 1 f (p i ) n i 2 || Hf (x) || 2 dx V i 1 i 1• In the vicinity of the data points, – the data terms dominate the total energy – make the function to approximate the “signed Euclidean distance function”.
- 30. Role of each energy term N N 2 2E( f ) f (p i ) 1 f (p i ) n i 2 || Hf (x) || 2 dx V i 1 i 1• In the vicinity of the data points, – the data terms dominate the total energy – make the function to approximate the “signed Euclidean distance function”.• Away from the data points, – the regularization term dominates the total energy – tends to make the gradient vector field ∇f(x) constant.
- 31. Linear families of functions
- 32. Linear families of functions• Popular Smooth Basis Functions – Radial basis functions [Carr et al., ‘01], – Compactly supported basis functions [Othake et al. ‘04], – Trigonometric polynomials [Kazhdan et al. ‘05], – B-splines [Kazhdan et al., 06], – Wavelets [Manson et al. ‘08],
- 33. Linear families of functions• Popular Smooth Basis Functions – Radial basis functions [Carr et al., ‘01], – Compactly supported basis functions [Othake et al. ‘04], – Trigonometric polynomials [Kazhdan et al. ‘05], – B-splines [Kazhdan et al., 06], – Wavelets [Manson et al. ‘08], Non-homogenous, t t Quadratic energy E(F ) F AF 2b F c
- 34. Linear families of functions• Popular Smooth Basis Functions – Radial basis functions [Carr et al., ‘01], – Compactly supported basis functions [Othake et al. ‘04], – Trigonometric polynomials [Kazhdan et al. ‘05], – B-splines [Kazhdan et al., 06], – Wavelets [Manson et al. ‘08], Non-homogenous, t t Quadratic energy E(F ) F AF 2b F c Global minimum AF b
- 35. Independent Discretization• Hybrid FE/FD discretization – Trilinear interplant for the function f(x) – Finite differences for the gradient ∇f(x) – Finite differences for the Hessian Hf(x)
- 36. Independent Discretization• Hybrid FE/FD discretization – Trilinear interplant for the function f(x) – Finite differences for the gradient ∇f(x) – Finite differences for the Hessian Hf(x)• As long as f(x), ∇f(x), and Hf(x) are written as a linear combination of parameter vector F, Non-homogenous, t t Quadratic energy E(F ) F AF 2b F c Global minimum AF b
- 37. Implementation• Iterative solver (conjugate gradient) with cascading multi-grid approach – Solve the problem on a much coarser level – Use the solution at that level to initialize the solution at the next level – Refine with the iterative solver• Iso-surface extraction (crack-free) – Dual marching cubes [Schaefer 2005]
- 38. Outline• Introduction• Related Work• Our Approach• Evaluation• Conclusion
- 39. Input point MPU Poisson D4 Waveletscloud [Othake ‘03 ] [Kazhdan ‘06 ] [Manson ‘08 ] Our SSD
- 40. Input point MPU Poisson D4 Waveletscloud [Othake ‘03 ] [Kazhdan ‘06 ] [Manson ‘08 ] Our SSD
- 41. Input point MPU Poisson D4 Waveletscloud [Othake ‘03 ] [Kazhdan ‘06 ] [Manson ‘08 ] Our SSD
- 42. Input point MPU Poisson D4 Waveletscloud [Othake ‘03 ] [Kazhdan ‘06 ] [Manson ‘08 ] Our SSD
- 43. Accuracy• Hausdorff distance between real surfaces and reconstructed surfaces using Metro tool [Cignoni ’96]. (Lower is better!)
- 44. Performance characteristicsMPU Poisson D4 Wavelets Our SSD[Othake ‘03 ] [Kazhdan ‘06 ] [Manson ‘08 ]
- 45. Outline• Introduction• Related Work• Our Approach• Evaluation• Conclusion
- 46. Conclusion• Theoretical contributions: – Oriented point samples samples of signed Euclidean distance function – Reconstruction as global minimization problem – Yet sparse system• Empirical advantages: – Robustness to noise – Adaptive to sampling density• Future work: – Streaming out-of-core implementations – Parallel GPU implementations
- 47. Ongoing work
- 48. mesh.brown.edu/ssd Thank you! Any questions? This material is based upon work supported bythe National Science Foundation under Grant No. IIS-0808718, CCF-0729126, and CCF-0915661.

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment