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 Science and Engineering Flow in an artificial heart Flow patterns in a tube University of Cambridge (2009)

Motivation Noise 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

Limitations Feature Destruction

Limitations Feature Destruction

Random Walks on the Graph Feature

Previous Work Smolka et al Random Walk for Image Enhancement

Previous Work Sun et al Mesh Denoising

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

How to build the graph

Feature Functions Direction Magnitude

Feature Functions Direction Magnitude Other feature functions in the paper!

Probabilities is the neighborhood of vector i Probability from vector i to vector j

Time to walk A B

A B

A B

A B

A B

- the probability of going from node A to node B after n steps A B

Random Walk Filtering Weighted Average of Random Walk Probabilities

Feature-preserving Discontinuity

Simple Example

Granular Flow

Gaussian FilteringRandom Walk Filtering

Particle Image Velocimetry

GaussianRandom Walk Particle Image Velocimetry

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