1 / 39

Random Walks for Vector Field Denoising

Random Walks for Vector Field Denoising. João Paixão , Marcos Lage , Fabiano Petronetto , Alex Laier , Sinésio Pesco , Geovan Tavares, Thomas Lewiner , Hélio Lopes Matmidia Laboratory – Department of Mathematics PUC–Rio – Rio de Janeiro, Brazil. Motivation. Vector Fields in

kareem-carter
Download Presentation

Random Walks for Vector Field Denoising

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Random Walks for Vector Field Denoising JoãoPaixão, Marcos Lage, FabianoPetronetto, Alex Laier, SinésioPesco, Geovan Tavares, Thomas Lewiner, Hélio Lopes Matmidia Laboratory – Department of Mathematics PUC–Rio – Rio de Janeiro, Brazil

  2. Motivation • Vector Fields in • Science and Engineering Flow in an artificial heart Flow patterns in a tube Universityof Cambridge (2009)

  3. Motivation • Noise in vector data-acquisition Flow around a live swimming fish (Yoshida et al 2004)

  4. Problem

  5. Problem:Noise Denoising

  6. Gaussian Filtering E.g. 5x5 Gaussian Filter

  7. Limitations • Feature Destruction Gaussian Filtering Original Original + Noise

  8. Limitations • Feature Destruction

  9. Random Walks on the Graph Feature

  10. Previous Work • Smolka et al. 2001 Random Walk for Image Enhancement

  11. Previous Work • Sun et al. 2007 Mesh Denoising

  12. Random Walks for Vector Fields • What we want • -Meshless • -Feature-preserving • What do we need • Graph • Probabilities that avoid crossing features

  13. How to build the graph

  14. Feature Functions Direction Magnitude

  15. Feature Functions Direction Magnitude Other feature functions in the paper!

  16. Probabilities Probability from vector i to vector j is the neighborhoodof vector i. 2 4 1 3

  17. Time to walk B A

  18. Time to walk B A

  19. Time to walk B A

  20. Time to walk B A

  21. Time to walk B A

  22. Time to walk B A - the probability of going from node Ato node Bafter n steps

  23. Random Walk Filtering Weighted Average of Random Walk Probabilities

  24. Feature-preserving Discontinuity

  25. Simple Example Original Original + Noise

  26. Simple Example Gaussian Random Walk

  27. Granular Flow

  28. Granular Flow GaussianFiltering RandomWalkFiltering

  29. Particle Image Velocimetry

  30. Particle Image Velocimetry Gaussian Random Walk

  31. Landslide

  32. Landslide

  33. Landslide

  34. Landslide

  35. Landslide

  36. Summary • -Feature Preserving • -Meshless • -Interpretative • -Flexible • -Easy to implement

  37. Limitations • -Number of parameters • -Dependency in them

  38. Future Works • - 3D vector field denoising algorithm

  39. Thank you for your attention

More Related