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Continuous Projection for Fast L1 Reconstruction Reinhold Preiner*Oliver MattauschMurat Arikan* Renato PajarolaMichael Wimmer* * Institute of Computer Graphics and Algorithms, Vienna University of Technology Visualization and Multimedia Lab, University of Zurich Slide 2 Dynamic Surface Reconstruction Input (87K points) Slide 3 Dynamic Surface Reconstruction Online L 2 ReconstructionInput (87K points) Slide 4 Dynamic Surface Reconstruction Online L 2 ReconstructionInput (87K points) Weighted LOP (1.4 FPS) Slide 5 Dynamic Surface Reconstruction Online L 2 ReconstructionInput (87K points) Our Technique (10.8 FPS) Slide 6 Recap: Locally Optimal Projection LOP [Lipman et al. 2007], WLOP [Huang et al. 2009] Attraction Slide 7 Recap: Locally Optimal Projection Attraction LOP [Lipman et al. 2007], WLOP [Huang et al. 2009] Slide 8 Recap: Locally Optimal Projection Attraction LOP [Lipman et al. 2007], WLOP [Huang et al. 2009] Slide 9 Recap: Locally Optimal Projection Attraction LOP [Lipman et al. 2007], WLOP [Huang et al. 2009] Slide 10 Recap: Locally Optimal Projection Repulsion LOP [Lipman et al. 2007], WLOP [Huang et al. 2009] Slide 11 Recap: Locally Optimal Projection LOP [Lipman et al. 2007], WLOP [Huang et al. 2009] Slide 12 Recap: Locally Optimal Projection LOP [Lipman et al. 2007], WLOP [Huang et al. 2009] Slide 13 Recap: Locally Optimal Projection LOP [Lipman et al. 2007], WLOP [Huang et al. 2009] Slide 14 Performance Issues Attraction: performance strongly depends on the # of input points Slide 15 Acceleration Approach Reduce number of spatial components! Nave subsampling information loss Slide 16 Our Approach Model data by Gaussian mixture fewer spatial entities Slide 17 Our Approach Model data by Gaussian mixture fewer spatial entities Requires continuous attraction of Gaussians ? Slide 18 Our Approach Model data by Gaussian mixture fewer spatial entities Requires continuous attraction of Gaussians Continuous LOP (CLOP) Slide 19 Solve Continuous Attraction CLOP Overview Slide 20 Solve Continuous Attraction CLOP Overview Slide 21 Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian Slide 22 Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian Slide 23 Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian Slide 24 Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian Slide 25 Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian 2.pick parent Gaussians Slide 26 Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian 2.pick parent Gaussians 3.EM: fit parents based on maximum likelihood Slide 27 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 Slide 28 Gaussian Mixture Computation Conventional HEM: blurring CLOP (8 FPS) Slide 29 Gaussian Mixture Computation Conventional HEM: blurring Slide 30 Gaussian Mixture Computation Conventional HEM: blurring Introduce regularization Slide 31 Gaussian Mixture Computation Conventional HEM: blurring Introduce regularization Slide 32 Solve Continuous Attraction CLOP Overview Slide 33 Solve Continuous Attraction CLOP Overview Slide 34 K Continuous Attraction from Gaussians q p1p1 p3p3 p2p2 Discrete Slide 35 K q Continuous Attraction from Gaussians Discrete Continuous 11 22 Slide 36 Continuous Attraction from Gaussians K q 11 Slide 37 Slide 38 Slide 39 Slide 40 Slide 41 Slide 42 Slide 43 Slide 44 Slide 45 Slide 46 Solve Continuous Attraction CLOP Overview Slide 47 Results Weighted LOPContinuous LOP Slide 48 Results Weighted LOPContinuous LOP Slide 49 Results Weighted LOPContinuous LOP Slide 50 Performance Input (87K points ) 7x Speedup Weighted LOPContinuous LOP Slide 51 Performance Slide 52 WLOP Accuracy CLOP Slide 53 Accuracy Gargoyle Slide 54 L1 Normals Slide 55 Slide 56 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 =