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AliMorty / Markov-Random-Field-Project

This project has two parts. In part one, we use markov random field to denoise an image. In Part two, we use similar model for image segmentation.
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Energy function #1

Closed ir0nt0ad closed 4 years ago

ir0nt0ad commented 4 years ago

Hi, just interested in how you came up with the definition of the energy function. Thank you!

AliMorty commented 4 years ago

Cool! Thank you!

On Fri, 19 Jun 2020, 11:22 pm Roman, notifications@github.com wrote:

Hi, just interested in how you came up with the definition of the energy function. Thank you!

— You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub https://github.com/AliMorty/Markov-Random-Field-Project/issues/1, or unsubscribe https://github.com/notifications/unsubscribe-auth/ADQ452R4Q3HIWAVWFMIOA6TRXOXWJANCNFSM4OC6ZFDQ .

ir0nt0ad commented 4 years ago

Yeah so how did you come up with the formula?

AliMorty commented 4 years ago

Thank you for looking at my project!

This project was a part of PGMs class homework and I remember that we didn't know that much about the theory at that time. We just knew that this formula is effective for capturing the dependencies in this task. I think the first term in the energy function can be related to a logarithm of a normal joint probability distribution for all individual pixels and the second term is used to capture the dependencies between neighbor pixels. (i.e. decrease the probability when two adjacent pixels have different colors.)

I guess this is a Markov network and in this setting, all distributions should have the Gibbs distribution format. this might be a reason why we are expecting the second term to have this format. I am not sure about this sentence at all!)

Because I have done this project in the past, I don't remember the detail right now. Therefore, I have attached the following document for more information about the energy function for this particular task. I hope this helps.

Thank you for your attention and your email.

Bests, Ali

On Sat, 20 Jun 2020, 12:12 am Roman, notifications@github.com wrote:

Yeah so how did you come up with the formula?

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/AliMorty/Markov-Random-Field-Project/issues/1#issuecomment-646833271, or unsubscribe https://github.com/notifications/unsubscribe-auth/ADQ452TQMHBASAIKKBAIEU3RXO5R5ANCNFSM4OC6ZFDQ .

AliMorty commented 4 years ago

In other word, we want to find the probabilty of occurance of any given configuration of pixels. Using this probability, we can find the most likely configuration of unknown pixels. In fact we are using Maximum likelihood estimation to predict the labels for unknown pixels.

Because our model is MRF, we model the dependencies between any two adjacent pixels by a multiplication term (second term in energy funcfion). We also assume that probability distribution for each pixel is a normal distribution.

As a result, we have a the probability distobution for occurance of any particular configuration for pixels. The logarithm of this probability is that energy function that you mentioned.

You can also look at the my previous email and find a document attached to it for more information.

Bests, Ali

On Sat, 20 Jun 2020, 12:37 am Ali Mortazavi, mortazavi.ali1994@gmail.com wrote:

Thank you for looking at my project!

This project was a part of PGMs class homework and I remember that we didn't know that much about the theory at that time. We just knew that this formula is effective for capturing the dependencies in this task. I think the first term in the energy function can be related to a logarithm of a normal joint probability distribution for all individual pixels and the second term is used to capture the dependencies between neighbor pixels. (i.e. decrease the probability when two adjacent pixels have different colors.)

I guess this is a Markov network and in this setting, all distributions should have the Gibbs distribution format. this might be a reason why we are expecting the second term to have this format. I am not sure about this sentence at all!)

Because I have done this project in the past, I don't remember the detail right now. Therefore, I have attached the following document for more information about the energy function for this particular task. I hope this helps.

Thank you for your attention and your email.

Bests, Ali

On Sat, 20 Jun 2020, 12:12 am Roman, notifications@github.com wrote:

Yeah so how did you come up with the formula?

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/AliMorty/Markov-Random-Field-Project/issues/1#issuecomment-646833271, or unsubscribe https://github.com/notifications/unsubscribe-auth/ADQ452TQMHBASAIKKBAIEU3RXO5R5ANCNFSM4OC6ZFDQ .

ir0nt0ad commented 4 years ago

Hey, thanks for the detailed feedback. Unfortunately I can't see the document you said you attached.

ir0nt0ad commented 4 years ago

Great, thanks again!