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Continuous Projection for Fast L1 Reconstruction. Reinhold Preiner* Oliver Mattausch† Murat Arikan* Renato Pajarola† Michael Wimmer*. * Institute of Computer Graphics and Algorithms, Vienna University of Technology † Visualization and Multimedia Lab, University of Zurich.

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Continuous Projection for Fast L1 Reconstruction


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continuous projection for fast l1 reconstruction

Continuous Projection for Fast L1 Reconstruction

Reinhold Preiner* Oliver Mattausch† Murat Arikan*

Renato Pajarola† Michael Wimmer*

* Institute of Computer Graphics and Algorithms, Vienna University of Technology

† Visualization and Multimedia Lab, University of Zurich

dynamic surface reconstruction1
Dynamic Surface Reconstruction

Online L2 Reconstruction

Input (87K points)

dynamic surface reconstruction2
Dynamic Surface Reconstruction

Weighted LOP (1.4 FPS)

Online L2 Reconstruction

Input (87K points)

dynamic surface reconstruction3
Dynamic Surface Reconstruction

Our Technique

(10.8 FPS)

Online L2 Reconstruction

Input (87K points)

recap locally optimal projection
Recap: Locally Optimal Projection
  • LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

Attraction

recap locally optimal projection1
Recap: Locally Optimal Projection
  • LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

Attraction

recap locally optimal projection2
Recap: Locally Optimal Projection
  • LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

Attraction

recap locally optimal projection3
Recap: Locally Optimal Projection
  • LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

Attraction

recap locally optimal projection4
Recap: Locally Optimal Projection
  • LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

Repulsion

recap locally optimal projection5
Recap: Locally Optimal Projection
  • LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
recap locally optimal projection6
Recap: Locally Optimal Projection
  • LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
recap locally optimal projection7
Recap: Locally Optimal Projection
  • LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
performance issues
Performance Issues
  • Attraction: performance strongly depends on the # of input points
acceleration approach
Acceleration Approach
  • Reduce number of spatial components!
  • Naïve subsampling  information loss
our approach
Our Approach
  • Model data by Gaussian mixture  fewer spatial entities
our approach1
Our Approach
  • Model data by Gaussian mixture fewer spatial entities
  • Requires continuous attraction of Gaussians

?

our approach2
Our Approach
  • Model data by Gaussian mixture  fewer spatial entities
  • Requires continuous attraction of Gaussians

 Continuous LOP (CLOP)

clop overview
CLOP Overview

Compute Gaussian Mixture

Input

Solve Continuous Attraction

clop overview1
CLOP Overview

Compute Gaussian Mixture

Input

Solve Continuous Attraction

gaussian mixture computation
Gaussian Mixture Computation

initialize each point with Gaussian

  • Hierarchical Expectation Maximization:
gaussian mixture computation1
Gaussian Mixture Computation

initialize each point with Gaussian

  • Hierarchical Expectation Maximization:
gaussian mixture computation2
Gaussian Mixture Computation

initialize each point with Gaussian

  • Hierarchical Expectation Maximization:
gaussian mixture computation3
Gaussian Mixture Computation

initialize each point with Gaussian

  • Hierarchical Expectation Maximization:
gaussian mixture computation4
Gaussian Mixture Computation

initialize each point with Gaussian

pick parent Gaussians

  • Hierarchical Expectation Maximization:
gaussian mixture computation5
Gaussian Mixture Computation

initialize each point with Gaussian

pick parentGaussians

EM: fit parents based on maximum likelihood

  • Hierarchical Expectation Maximization:
gaussian mixture computation6
Gaussian Mixture Computation

initialize each point with Gaussian

pick parentGaussians

EM: fit parents based on maximum likelihood

Iterate over levels

  • Hierarchical Expectation Maximization:

CLOP (8 FPS)

gaussian mixture computation7
Gaussian Mixture Computation
  • Conventional HEM: blurring

CLOP (8 FPS)

gaussian mixture computation8
Gaussian Mixture Computation
  • Conventional HEM: blurring
gaussian mixture computation9
Gaussian Mixture Computation
  • Conventional HEM: blurring
  • Introduce regularization
gaussian mixture computation10
Gaussian Mixture Computation
  • Conventional HEM: blurring
  • Introduce regularization
clop overview2
CLOP Overview

Compute Gaussian Mixture

Input

Solve Continuous Attraction

continuous attraction from gaussians1
Continuous Attraction from Gaussians

Discrete

K

q

Continuous

Θ1

Θ2

results
Results

Weighted LOP

Continuous LOP

results1
Results

Weighted LOP

Continuous LOP

results2
Results

Weighted LOP

Continuous LOP

performance
Performance

7x Speedup

Weighted LOP

Continuous LOP

Input (87K points )

accuracy
Accuracy

WLOP

CLOP

accuracy1
Accuracy

Gargoyle

conclusion

=

Conclusion

LOP on Gaussian mixtures

  • faster
  • more accurate

See the paper:

  • Faster repulsion
  • L1 normals

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