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Geometry processing using Markov Random Fields Vedrana Andersen, DTU Informatics

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Page 1: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

Geometry processing using Markov Random Fields

Vedrana Andersen, DTU Informatics

Page 2: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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OVERVIEW

Presentation consists of…

Geometry processing using Markov Random Fields

Bonus slides: Geometry texture processing

Page 3: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Basic Idea

Aim: To investigate the use of Markov Random Fields (MRF) for formulating priors on 3D surfaces represented as triangle meshes

Focus on: Mesh smoothing, feature-preserving mesh smoothing (preserving surface ridges)

Page 4: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Motivation, why MRF?

Image analysis -> Geometry processing Easy modeling (Markov property) Flexible, decouples prior and likelihood

(Bayes)

Page 5: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Bayesian approach

How far do we believe the true position of the vertex is the measured position?

What do we know about the surface (e.g. how smooth should it be)?

Page 6: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Bayesian approach

Likelihood:distance measure

Page 7: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

MRF priors

Markovianity (local property) – local potential

Page 8: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

MRF priors

Markov-Gibbs equivalence – a joint probability in a simple form

Meshes: topology, irregularity

Markovianity (local property) – local potential

Page 9: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Feature preservation prior

Smoothness prior

Ridge detection edge sharpness neighborhood support

Smoothing, but not over the detected ridges

Page 10: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Optimization

Simulated annealing!

Page 11: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Results

Page 12: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Nice results

Page 13: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Very nice results

Page 14: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Very nice results

Page 15: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRY PROCESSING USING MRF

Possible improvements

Optimization? Larger neighborhood for edge labeling Mesh optimization (badly shaped

triangles, topology changes)

Future work: Piecewise-quadratic surfaces

Page 16: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRIC TEXTURE ANALYSIS

Basic idea…

Surface = basic shape + superimposed texture

Extract, analyze, represent, synthesize

Page 17: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRIC TEXTURE ANALYSIS

Ring histograms

2D histograms,

Inspired by SPIN descriptor

Page 18: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRIC TEXTURE ANALYSIS

Another idea…

Texture as a height field

Vector displacement:

pseudo-height

tilt

Not only a height field!

Page 19: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

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GEOMETRIC TEXTURE ANALYSIS

Editing

Page 20: Geometry processing using Markov Random Fields - Vision Day · 3 GEOMETRY PROCESSING USING MRF Basic Idea Aim: To investigate the use of Markov Random Fields (MRF) for formulating

Thank you!


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