Image Restoration using Graphical Models Anna Grim ...Ising Model murphyk/Papers/intro_gm.pdf Local...
Transcript of Image Restoration using Graphical Models Anna Grim ...Ising Model murphyk/Papers/intro_gm.pdf Local...
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Image Restoration usingGraphical Models
Margaret ThorenAnna Grim
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Problem: Image Restoration
https://www.smapip.is.tohoku.ac.jp/~kazu/SMAPIP-KazuKazu/Summary/index-e.html
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Introduction
https://blog.statsbot.co/probabilistic-graphical-models-tutorial-and-solutions-e4f1d72af189
Def: A graphical model consists of a collection of random variables corresponding to some graph.
Example:(1) Random Variables
(2) Graph
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Converting an Image into a Graph
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Ising Model
https://www.cs.ubc.ca/~murphyk/Papers/intro_gm.pdf
Local Energy:
Pairwise Energy:
● We associate a random variable with each pixel;
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Ising Model
● The joint pdf corresponding to the random variables is energy based and defined to be
● Maximizing the probability is equivalent to minimizing the energy
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Overview
https://slideplayer.com/slide/8088915https://www.slideshare.net/zukun/02-probabilistic-inference-in-graphical-models
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Gibbs Sampling
https://slideplayer.com/slide/8141891/
Main Idea: Restoring pixels to values close to original observation and close to neighboring observations
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Formulas for Gibbs Sampling
Restore image by drawing samples from the following distribution
Goal:
● Using properties of Markov Random Fields, we can simplify this distribution such that
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Gibbs Sampling Algorithm(1) Initialization
(2) Sampling
(3) Check for Convergence
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Coding in MATLAB
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Belief Propagation
Main Idea: Message passing algorithm that approximates the marginal probability distribution where pixels take on values based on messages they receive from neighbors
http://ssg.mit.edu/nbp/
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Formulas for Belief Propagation
Messages from node i to node j:
Belief at node j:
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Intuition of Belief Propagation Formulas
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Belief Propagation Algorithm(1) Initialization
(2) Update Messages
(3) Check for convergence
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Messages to Restoration
•Once the messages have converged, we restore the
image by computing
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Convergence
https://en.wikipedia.org/wiki/Tree_(graph_theory)
https://slideplayer.com/slide/5090395/
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Belief Propagation Results
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Conclusions
Belief Propagation Gibbs Sampling