slides

Report
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 Reconstruction
Input (87K points)
Dynamic Surface Reconstruction
Online L2 Reconstruction
Input (87K points)
Dynamic Surface Reconstruction
Online L2 Reconstruction
Input (87K points)
Weighted LOP
(1.4 FPS)
Dynamic Surface Reconstruction
Online L2 Reconstruction
Input (87K points)
Our Technique
(10.8 FPS)
Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Attraction
Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Attraction
Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Attraction
Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Attraction
Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Repulsion
Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Recap: Locally Optimal Projection
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Performance Issues
Attraction: performance strongly depends on the # of input points
Acceleration Approach
Reduce number of spatial components!
Naïve subsampling  information loss
Our Approach
Model data by Gaussian mixture  fewer spatial entities
Our Approach
Model data by Gaussian mixture  fewer spatial entities
Requires continuous attraction of Gaussians
?
Our Approach
Model data by Gaussian mixture  fewer spatial entities
Requires continuous attraction of Gaussians
 Continuous LOP (CLOP)
CLOP Overview
Input
Compute Gaussian Mixture
Solve Continuous Attraction
CLOP Overview
Input
Compute Gaussian Mixture
Solve Continuous Attraction
Gaussian Mixture Computation
Hierarchical Expectation Maximization:
1. initialize each point
with Gaussian
Gaussian Mixture Computation
Hierarchical Expectation Maximization:
1. initialize each point
with Gaussian
Gaussian Mixture Computation
Hierarchical Expectation Maximization:
1. initialize each point
with Gaussian
Gaussian Mixture Computation
Hierarchical Expectation Maximization:
1. initialize each point
with Gaussian
Gaussian Mixture Computation
Hierarchical Expectation Maximization:
1. initialize each point
with Gaussian
2. pick parent Gaussians
Gaussian Mixture Computation
Hierarchical Expectation Maximization:
1. initialize each point
with Gaussian
2. pick parent Gaussians
3. EM: fit parents based
on maximum likelihood
Gaussian Mixture Computation
Hierarchical Expectation Maximization:
1. initialize each point
with Gaussian
2. pick parent Gaussians
3. EM: fit parents based
on maximum likelihood
4. Iterate over levels
CLOP (8 FPS)
Gaussian Mixture Computation
Conventional HEM: blurring
CLOP (8 FPS)
Gaussian Mixture Computation
Conventional HEM: blurring
Gaussian Mixture Computation
Conventional HEM: blurring
Introduce regularization
Gaussian Mixture Computation
Conventional HEM: blurring
Introduce regularization
CLOP Overview
Input
Compute Gaussian Mixture
Solve Continuous Attraction
Continuous Attraction from Gaussians
Discrete
K
q
p1
p2
p3
Continuous Attraction from Gaussians
Discrete
K
q
Θ1
Continuous
Θ2
Continuous Attraction from Gaussians
Continuous Attraction from Gaussians
Continuous Attraction from Gaussians
Continuous Attraction from Gaussians
Continuous Attraction from Gaussians
Continuous Attraction from Gaussians
Continuous Attraction from Gaussians
Continuous Attraction from Gaussians
Continuous Attraction from Gaussians
Results
Weighted LOP
Continuous LOP
Results
Weighted LOP
Continuous LOP
Results
Weighted LOP
Continuous LOP
Performance
7x Speedup
Weighted LOP
Input (87K points )
Continuous LOP
Performance
Accuracy
WLOP
CLOP
Accuracy
Gargoyle
L1 Normals
L1 Normals
=
Conclusion
LOP on Gaussian mixtures
faster
more accurate
See the paper:
Faster repulsion
L1 normals
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