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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 L 2 ReconstructionInput (87K points)

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Dynamic Surface Reconstruction Online L 2 ReconstructionInput (87K points) Weighted LOP (1.4 FPS)

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Dynamic Surface Reconstruction Online L 2 ReconstructionInput (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 entities Requires 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 CLOP Overview

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Solve Continuous Attraction CLOP Overview

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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 Gaussians 3.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 Gaussians 3.EM: fit parents based on maximum likelihood 4.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: blurring Introduce regularization

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Gaussian Mixture Computation Conventional HEM: blurring Introduce regularization

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Solve Continuous Attraction CLOP Overview

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Solve Continuous Attraction CLOP Overview

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K Continuous Attraction from Gaussians q p1p1 p3p3 p2p2 Discrete

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K q Continuous Attraction from Gaussians Discrete Continuous Θ1Θ1 Θ2Θ2

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Continuous Attraction from Gaussians K q Θ1Θ1

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Solve Continuous Attraction CLOP Overview

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Results Weighted LOPContinuous LOP

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Results Weighted LOPContinuous LOP

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Results Weighted LOPContinuous LOP

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Performance Input (87K points ) 7x Speedup Weighted LOPContinuous 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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LOP on Gaussian mixtures faster more accurate See the paper: Faster repulsion L 1 normals Conclusion Come to our Birds of a Feather! Harvest4D – Harvesting Dynamic 3D Worlds from Commodity Sensor Clouds Tuesday, 1:00 PM - 2:00 PM, East Building, Room 4 =

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