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Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation

Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation. Jing Yuan Paul Ruhnau Etienne Memin Christoph Schnörr Dept. of Math. & Comp. Sci. University of Mannheim IRISA, Renne. Motivation. Fluid Dynamics Compressible / Incompressible. Aerodynamics/Remote Sensing.

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Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation

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  1. Discrete Orthogonal Decompositionand Variational Fluid Flow Estimation Jing Yuan Paul Ruhnau Etienne Memin Christoph Schnörr Dept. of Math. & Comp. Sci. University of Mannheim IRISA, Renne

  2. Motivation Fluid Dynamics Compressible / Incompressible Aerodynamics/Remote Sensing Jing YUAN, CVGPR Group, Uni Mannheim

  3. Motion Flow Estimation Jing YUAN, CVGPR Group, Uni Mannheim

  4. Related Works & Contributions D. Suter, "Motion Estimation and Vector Splines“, CVPR’94 E. Gupta & J. Prince, “Stochastic Models for DIV-CURL Optical Flow Methods“, 1996 T. Corpetti, E. Memin & P. Perez, “Dense Estimation of Fluid Flows”, PAMI, 2002 T. Kohlberger, E. Memin & C. Schnoerr, “Variational Dense Motion Estimation Using the Helmholtz Decomposition”, ScaleSpace’03 . Discrete orthogonal decomposition & high-order regularization. . Subspace-correction algorithm. . Truly Solenoidal (div-free) flows = laminar flows + vorticities’ part. Jing YUAN, CVGPR Group, Uni Mannheim

  5. Orthogonal Decomposition Jing YUAN, CVGPR Group, Uni Mannheim

  6. Orthogonal Decomposition Jing YUAN, CVGPR Group, Uni Mannheim

  7. Orthogonal Decomposition Jing YUAN, CVGPR Group, Uni Mannheim

  8. Non-rigid Flow Estimation Jing YUAN, CVGPR Group, Uni Mannheim

  9. Discretization: Mimetic Finite-Difference Method M. Hyman and M. Shashkov, Natural Discretizations for the Divergence, Gradient, and Curl on Logically Rectangular Grids, 1997 M. Hyman and M. Shashkov, Adjoint Operators for the Natural Discretizations of the Divergence, Gradient and Curl on Logically Rectangular Grids, 1997 Jing YUAN, CVGPR Group, Uni Mannheim

  10. Discretization: Mimetic Finite-Difference Method M. Hyman and M. Shashkov, the orthogonal decomposition theorems for mimetic finite difference methods, SIAM J. Numer. Anal., 1999 Jing YUAN, CVGPR Group, Uni Mannheim

  11. Discretization: Mimetic Finite-Difference Method Jing YUAN, CVGPR Group, Uni Mannheim

  12. Estimation of Solenoidal Flows Jing YUAN, CVGPR Group, Uni Mannheim

  13. Algorithms & Implementation Ref. Xue-Cheng Tai, Jin-Chao Xu‘ papers on space decomposition. Jing YUAN, CVGPR Group, Uni Mannheim

  14. Algorithms & Implementation Jing YUAN, CVGPR Group, Uni Mannheim

  15. Algorithm & Implementation • A multi-level computation is implemented together with divergence-curl-invariant mesh refinement. Jing YUAN, CVGPR Group, Uni Mannheim

  16. Results • Ground-truth Jing YUAN, CVGPR Group, Uni Mannheim

  17. Results • Divergence-free Flow Estimation Jing YUAN, CVGPR Group, Uni Mannheim

  18. Results • Divergence-free Flow Estimation Jing YUAN, CVGPR Group, Uni Mannheim

  19. Results Jing YUAN, CVGPR Group, Uni Mannheim

  20. Results • General Non-rigid Flow Estimation Jing YUAN, CVGPR Group, Uni Mannheim

  21. Results Jing YUAN, CVGPR Group, Uni Mannheim

  22. Future Work • 3-D non-rigid motion estimation. • The pictures of divergence and curl provide us detail information about the non-rigid motion field. Based on them, motion pattern will be analyzed. Jing YUAN, CVGPR Group, Uni Mannheim

  23. Algorithm & Implementation Jing YUAN, CVGPR Group, Uni Mannheim

  24. Discretization: Mimetic Finite-Difference Method Jing YUAN, CVGPR Group, Uni Mannheim

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