continuous projection for fast l1 reconstruction
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
Attraction
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Recap: Locally Optimal Projection
Attraction
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Recap: Locally Optimal Projection
Attraction
LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]
Recap: Locally Optimal Projection
Repulsion
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]
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 entitiesRequires continuous attraction of Gaussians
?
Our Approach
Model data by Gaussian mixture fewer spatial entities Requires continuous attraction of Gaussians
Continuous LOP (CLOP)
Solve Continuous Attraction Compute Gaussian Mixture
CLOP Overview
Input
Solve Continuous Attraction Compute Gaussian Mixture
CLOP Overview
Input
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 Gaussians3. EM: fit parents based
on maximum likelihood
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
Gaussian Mixture Computation
Conventional HEM: blurring
CLOP (8 FPS)
Gaussian Mixture Computation
Conventional HEM: blurring
Gaussian Mixture Computation
Conventional HEM: blurringIntroduce regularization
Gaussian Mixture Computation
Conventional HEM: blurringIntroduce regularization
Solve Continuous Attraction Compute Gaussian Mixture
CLOP Overview
Input
K
Continuous Attraction from Gaussians
q
p1 p3p2
Discrete
K
q
Continuous Attraction from Gaussians
Discrete
ContinuousΘ1Θ2
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
Input (87K points )
7x Speedup
Weighted LOP Continuous LOP
Performance
WLOP
Accuracy
CLOP
Accuracy
Gargoyle
L1 Normals
L1 Normals
LOP on Gaussian mixturesfastermore accurate
See the paper:Faster repulsionL1 normals
Conclusion
Come to our Birds of a Feather!Harvest4D – Harvesting Dynamic 3D Worlds from Commodity Sensor CloudsTuesday, 1:00 PM - 2:00 PM, East Building, Room 4
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