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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 - PowerPoint PPT Presentation
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Random Walks for Vector Field Denoising
João Paixão, Marcos Lage, Fabiano Petronetto, Alex Laier, Sinésio Pesco, Geovan Tavares,
Thomas Lewiner, Hélio LopesMatmidia Laboratory – Department of Mathematics
PUC–Rio – Rio de Janeiro, Brazil
MotivationVector Fields inScience and Engineering
Flow in an artificial heart
Flow patterns in a tubeUniversity of Cambridge (2009)
MotivationNoise in vector data-acquisition
Flow around a live swimming fish (Yoshida et al 2004)
Problem
Problem:Noise
Denoising
Gaussian Filtering
E.g. 5x5 Gaussian Filter
LimitationsFeature Destruction
Gaussian FilteringOriginal Original + Noise
LimitationsFeature Destruction
Random Walks on the Graph
Feature
Previous WorkSmolka et al. 2001 Random Walk for Image
Enhancement
Previous Work Sun et al. 2007 Mesh Denoising
Random Walks for Vector FieldsWhat we want-Meshless-Feature-preserving
What do we need- Graph- Probabilities that avoid crossing features
How to build the graph
Feature Functions
||||)(
)(
i
i
viF
iF
Direction
Magnitude
i
Feature Functions
||||)(
)(
i
i
viF
iF
Direction
Magnitude
Other feature functions in the paper!
i
Probabilities
is the neighborhood of vector i.
otherwise0
)( if22
2
21
2
2
)||()(||(2
)||()(||(
,iNjeCep V
jFiFjXiX
ji
)(iNV
3
4
2
14,1p
3,1p
2,1p
Probability from vector i to vector j
Time to walk
A
B
Time to walk
A
B
Time to walk
A
B
Time to walk
A
B
Time to walk
A
B
Time to walk
- the probability of going from node A to node B after n stepsnBAp ,
A
B
Random Walk Filtering
Weighted Average of Random Walk Probabilities
Fjj
njii vpv ,
Feature-preserving
Discontinuity
Simple Example
Original Original + Noise
Simple Example
Gaussian Random Walk
Granular Flow
Granular Flow
Gaussian Filtering Random Walk Filtering
Particle Image Velocimetry
Gaussian Random Walk
Particle Image Velocimetry
Landslide
Landslide
Landslide
Landslide
Landslide
Summary-Feature Preserving-Meshless-Interpretative-Flexible-Easy to implement
Limitations-Number of parameters-Dependency in them
Future Works- 3D vector field denoising algorithm
Thank you for your attention
