Converting a Gaussian Markov random field

In summary, the conversation is about a paper discussing depth reconstruction from a single image using a gaussian multiscale markov random field. The model is trained in a supervised context and converted into a standard multivariate gaussian. The individual is seeking more detailed explanations for this conversion and is referred to another paper discussing image generation using Markov random fields.
  • #1
mort.motes
2
0
Hi I am currently reading:

http://www.cs.cornell.edu/~asaxena/learningdepth/saxena_ijcv07_learningdepth.pdf

which deals with reconstructing depth from a single still image.

A gaussian multiscale markov random field is trained in a supervised context where the model is shown below:

http://img534.imageshack.us/img534/1259/combineda.jpg

now this model is converted into a standard multivariate gaussian (indicated by the arrow) but how is that conversion possible? I have read that it basically is a matter of completing the square but is there some more detailed explanation for this somewhere besides:

http://en.wikipedia.org/wiki/Completing_the_square

which don't really describe the techniques used on markov random fields.
 
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  • #2
I'm not really familiar with image generation using Markov random fields. The following paper discusses approaches using a Bayesian approach. Perhaps it will be useful to you.

http://www.scss.tcd.ie/JiWon.Yoon/papers/MRF/Image%20segmentation%20image.pdf
 
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1. What is a Gaussian Markov random field (GMRF)?

A Gaussian Markov random field is a statistical model that is used to represent spatial or temporal data. It is a type of random field where each data point is normally distributed and is dependent on its neighboring data points.

2. Why would someone want to convert a GMRF?

Converting a GMRF may be necessary in order to use different statistical methods or models that are not compatible with a GMRF. It may also be done to simplify the data and make it more easily interpretable.

3. How is a GMRF converted?

The exact process for converting a GMRF may vary depending on the specific data and desired outcome. In general, it involves transforming the data into a different statistical model or format that is better suited for the desired analysis.

4. What are some common methods for converting a GMRF?

Some common methods for converting a GMRF include using log transformations, taking differences or ratios, or using a different type of random field model such as a Gaussian process or autoregressive model.

5. What are some potential challenges or limitations when converting a GMRF?

Converting a GMRF may result in the loss of important information or introduce biases into the data. It may also be difficult to find an appropriate method for conversion or to interpret the results of the converted data.

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