Random Walks for Vector Field Denoising João Paixão, Marcos Lage, Fabiano Petronetto, Alex Laier,...
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Transcript of Random Walks for Vector Field Denoising João Paixão, Marcos Lage, Fabiano Petronetto, Alex Laier,...
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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
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MotivationVector Fields inScience and Engineering
Flow in an artificial heart
Flow patterns in a tubeUniversity of Cambridge (2009)
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MotivationNoise in vector data-acquisition
Flow around a live swimming fish (Yoshida et al 2004)
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Problem
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Problem:Noise
Denoising
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Gaussian Filtering
E.g. 5x5 Gaussian Filter
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LimitationsFeature Destruction
Gaussian FilteringOriginal Original + Noise
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LimitationsFeature Destruction
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Random Walks on the Graph
Feature
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Previous WorkSmolka et al. 2001 Random Walk for Image
Enhancement
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Previous Work Sun et al. 2007 Mesh Denoising
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Random Walks for Vector FieldsWhat we want-Meshless-Feature-preserving
What do we need- Graph- Probabilities that avoid crossing features
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How to build the graph
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Feature Functions
||||)(
)(
i
i
viF
iF
Direction
Magnitude
i
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Feature Functions
||||)(
)(
i
i
viF
iF
Direction
Magnitude
Other feature functions in the paper!
i
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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
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Time to walk
A
B
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Time to walk
A
B
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Time to walk
A
B
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Time to walk
A
B
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Time to walk
A
B
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Time to walk
- the probability of going from node A to node B after n stepsnBAp ,
A
B
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Random Walk Filtering
Weighted Average of Random Walk Probabilities
Fjj
njii vpv ,
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Feature-preserving
Discontinuity
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Simple Example
Original Original + Noise
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Simple Example
Gaussian Random Walk
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Granular Flow
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Granular Flow
Gaussian Filtering Random Walk Filtering
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Particle Image Velocimetry
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Gaussian Random Walk
Particle Image Velocimetry
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Landslide
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Landslide
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Landslide
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Landslide
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Landslide
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Summary-Feature Preserving-Meshless-Interpretative-Flexible-Easy to implement
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Limitations-Number of parameters-Dependency in them
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Future Works- 3D vector field denoising algorithm
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Thank you for your attention