Add ellipse fitting example

[langestefan]

Draft PR for the ellipse fitting example, will add code.

For this demo I took an image of the cartwheel galaxy captured by the James Webb space telescope:
James Webb Space Telescope images

It's a very general setup and multiple ellipse model definitions, optimization criteria and demo images can be defined.

To efficiently fit the ellipses I need to do some image preprocessing, some filtering and some clustering. For these tasks I used Clustering.jl, Images.jl and DSP.jl. Would it be okay to use these dependencies? I can come up with alternative implementations but it will be more messy.

After fitting the ellipses the final result looks like this:

[odow]

This looks like a super cool (and visual) example.

No problem adding the extra packages. Just ensure they have a compat:

JuMP.jl/docs/Project.toml

Line 42 in 488a0db

[compat]

Also: we need to make sure that the image we use can be redistributed. If possible, find the original source, instead of new scientist?

[langestefan]

Yeah JWST really creates some breathtaking images!

Also: we need to make sure that the image we use can be redistributed. If possible, find the original source, instead of new scientist?

Found the source: https://webbtelescope.org/contents/media/images/2022/039/01G8JXN0K2VBQP112RNSQWTCTH

Unless otherwise stated, all material on the site was produced by NASA and the Space Telescope Science Institute (STScI). Material on this site produced by STScI was created, authored, and/or prepared for NASA under Contract NAS5-03127. Unless otherwise specifically stated, no claim to copyright is being asserted by STScI and material on this site may be freely used as in the public domain in accordance with NASA's contract. However, it is requested that in any subsequent use of this work NASA and STScI be given appropriate acknowledgement.

I'll make sure we add the acknowledgment.

[langestefan]

@odow I tested it locally, it should run.

I have tried to follow the style guide based on other examples but might have missed something.

Maybe good to check if all the MOI calls are correct, and you will probably spot some improvements in JuMP syntax as well.

The final output should look like:

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

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[langestefan]

All comments should be addressed now.