Ellipsoid

[tibuch]

I am improving the geometric 2d feature tests in imagej-ops imagej/imagej-ops#449. Since I couldn't verify the major- and minor-axis numbers I took a closer look at the implementation. Currently ImageJ1 code which is adapted to work with a Polygon is used to find the fitting ellipse from which major- and minor-axis are extracted.

Since I couldn't verify the numbers I opened this discussion imagej/imagej-ops#452 which ended up in this PR imagej/imagej-ops#453 which would decouple the fitting ellipse implementation from the major- and minor-axis implementation and could be tested against a matlab-implementation.

This is not the best solution, because this implementation is based on the deprecated ellipse implementation. In discussion with @tpietzsch and @dietzc I found other implementations of HyperEllipsoids and fitting ellipse algorithms.

What do we have:

• Minor-Major-Axis implementation in imagej-ops which I can't verify and would like to replace.
• The currently used ellipse implementation in imagej-ops is deprecated.
• @axtimwalde has an open issue about HyperEllipsoid HyperEllipsoid imglib2-algorithm#23
• @tpietzsch has an implementation of Hyperellipsoid and some functionality https://github.com/imglib/imglib2-algorithm/compare/ellipsoid-fitting
• @haesleinhuepf has a PR which includes an n-dimensional ellipsoid Added n-dimensional elipsoid and rectangle ROIs, as well as binary operations for ROIs (union, intersection,...) #25
• my PR of a fitting ellipsoid implementation, which is based on the deprecated ellipsoid Fitting ellipse to point set imagej/imagej-ops#453

What I would suggest:

• An ellipse implementation on imglib2 side.
• A fitting ellipse implementation on imglib2 side or on imagej-ops side.

I am happy to contribute, the question is just where to continue.

[maierl]

There's another 3D Ellipsoid implementation available as ImageJ plugin: https://github.com/mcib3d/mcib3d-plugins/blob/master/src/main/java/mcib_plugins/Ellipsoids_3D.java

[tibuch]

I was able to verify the major-minor-axis implementation.

The best fitting ellipse in the major-minor-axis case, is the one with the "same" area. which is different from the referenced implementations which fit an ellipse to a point cloud.

Also ellipse is part of this discussion: http://forum.imagej.net/t/implementation-plan-for-imglib2-rois-2d/2531/1