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 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