Continuous Projection for Fast L1 Reconstruction
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Transcript of Continuous Projection for Fast L1 Reconstruction
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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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Dynamic Surface Reconstruction
Input (87K points)
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Dynamic Surface Reconstruction
Online L2 Reconstruction Input (87K points)
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Dynamic Surface Reconstruction
Online L2 Reconstruction Input (87K points) Weighted LOP (1.4 FPS)
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Dynamic Surface Reconstruction
Online L2 Reconstruction Input (87K points) Our Technique(10.8 FPS)
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Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Attraction
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Recap: Locally Optimal Projection
Attraction
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
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Recap: Locally Optimal Projection
Attraction
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
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Recap: Locally Optimal Projection
Attraction
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
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Recap: Locally Optimal Projection
Repulsion
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
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Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
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Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
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Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
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Performance Issues
Attraction: performance strongly depends on the # of input points
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Acceleration Approach
Reduce number of spatial components!Naïve subsampling information loss
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Our Approach
Model data by Gaussian mixture fewer spatial entities
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Our Approach
Model data by Gaussian mixture fewer spatial entitiesRequires continuous attraction of Gaussians
?
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Our Approach
Model data by Gaussian mixture fewer spatial entities Requires continuous attraction of Gaussians
Continuous LOP (CLOP)
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Solve Continuous Attraction Compute Gaussian Mixture
CLOP Overview
Input
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Solve Continuous Attraction Compute Gaussian Mixture
CLOP Overview
Input
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Gaussian Mixture Computation
Hierarchical Expectation Maximization: 1. initialize each point with Gaussian
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Gaussian Mixture Computation
Hierarchical Expectation Maximization: 1. initialize each point with Gaussian
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Gaussian Mixture Computation
Hierarchical Expectation Maximization: 1. initialize each point with Gaussian
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Gaussian Mixture Computation
Hierarchical Expectation Maximization: 1. initialize each point with Gaussian
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Gaussian Mixture Computation
Hierarchical Expectation Maximization: 1. initialize each point with Gaussian
2. pick parent Gaussians
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Gaussian Mixture Computation
Hierarchical Expectation Maximization: 1. initialize each point with Gaussian
2. pick parent Gaussians3. EM: fit parents based
on maximum likelihood
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Gaussian Mixture Computation
Hierarchical Expectation Maximization:
CLOP (8 FPS)
1. initialize each point with Gaussian
2. pick parent Gaussians3. EM: fit parents based
on maximum likelihood4. Iterate over levels
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Gaussian Mixture Computation
Conventional HEM: blurring
CLOP (8 FPS)
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Gaussian Mixture Computation
Conventional HEM: blurring
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Gaussian Mixture Computation
Conventional HEM: blurringIntroduce regularization
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Gaussian Mixture Computation
Conventional HEM: blurringIntroduce regularization
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Solve Continuous Attraction Compute Gaussian Mixture
CLOP Overview
Input
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K
Continuous Attraction from Gaussians
q
p1 p3p2
Discrete
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K
q
Continuous Attraction from Gaussians
Discrete
ContinuousΘ1Θ2
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Continuous Attraction from Gaussians
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Continuous Attraction from Gaussians
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Continuous Attraction from Gaussians
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Continuous Attraction from Gaussians
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Continuous Attraction from Gaussians
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Continuous Attraction from Gaussians
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Continuous Attraction from Gaussians
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Continuous Attraction from Gaussians
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Continuous Attraction from Gaussians
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Results
Weighted LOP Continuous LOP
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Results
Weighted LOP Continuous LOP
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Results
Weighted LOP Continuous LOP
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Performance
Input (87K points )
7x Speedup
Weighted LOP Continuous LOP
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Performance
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WLOP
Accuracy
CLOP
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Accuracy
Gargoyle
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L1 Normals
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L1 Normals
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LOP on Gaussian mixturesfastermore accurate
See the paper:Faster repulsionL1 normals
Conclusion
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