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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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Iowa State University Department of Computer Science Artificial Intelligence Research Laboratory Research supported in part by grants from the National.

Iowa State University Department of Computer Science Artificial Intelligence Research Laboratory Research supported in part by grants from the National.

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