geometry processing using markov random fields - vision day · 3 geometry processing using mrf...
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Geometry processing using Markov Random Fields
Vedrana Andersen, DTU Informatics
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OVERVIEW
Presentation consists of…
Geometry processing using Markov Random Fields
Bonus slides: Geometry texture processing
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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)
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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)
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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)?
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GEOMETRY PROCESSING USING MRF
Bayesian approach
Likelihood:distance measure
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GEOMETRY PROCESSING USING MRF
MRF priors
Markovianity (local property) – local potential
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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
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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
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GEOMETRY PROCESSING USING MRF
Optimization
Simulated annealing!
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GEOMETRY PROCESSING USING MRF
Results
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GEOMETRY PROCESSING USING MRF
Nice results
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GEOMETRY PROCESSING USING MRF
Very nice results
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GEOMETRY PROCESSING USING MRF
Very nice results
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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
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GEOMETRIC TEXTURE ANALYSIS
Basic idea…
Surface = basic shape + superimposed texture
Extract, analyze, represent, synthesize
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GEOMETRIC TEXTURE ANALYSIS
Ring histograms
2D histograms,
Inspired by SPIN descriptor
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GEOMETRIC TEXTURE ANALYSIS
Another idea…
Texture as a height field
Vector displacement:
pseudo-height
tilt
Not only a height field!
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GEOMETRIC TEXTURE ANALYSIS
Editing
Thank you!
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