Best Elliptical Fit for irregular shapes in an image

Question

I have an image with arbitrary regions shape (say objects), let's assume the background pixels are labeled as zeros whereas any object has a unique label (pixels of object 1 are labeled as 1, object 2 pixels are labeled as 2,...). Now for every object, I need to find the best elliptical fit of its pixels. This requires finding the center of the object, the major and minor axis, and the rotation angle. How can I find these?

Thank you;

Answer 1

Principal Component Analysis (PCA) is one way to go. See Wikipedia here.

The centroid is easy enough to find if your shapes are convex - just a weighted average of intensities over the xy positions - and PCA will give you the major and minor axes, hence the orientation.

Once you have the centre and axes, you have the basis for a set of ellipses that cover your shape. Extending the axes - in proportion - and testing each pixel for in/out, you can find the ellipse that just covers your shape. Or if you prefer, you can project each pixel position onto the major and minor axes and find the rough limits in one pass and then test in/out on "corner" cases.

It may help if you post an example image.

Answer 2

As you seem to be using Matlab, you can simply use the regionprops command, given that you have the Image Processing Toolbox.

It can extract all the information you need (and many more properties of image regions) and it will do the PCA for you, if the PCA-based based approach suits your needs.

Doc is here, look for the 'Centroid', 'Orientation', 'MajorAxisLength' and 'MinorAxisLength' parameters specifically.