How to fit rectangles on blobs on binary image

I have this binary image:

I need to find 2 rectangles that fit around the two blobs as best as possible. What's the best method to apply?

Thanks for any help!

Answer 1

[Image Analyst]

John D'Errico's function will give you the minimal bounding rectangle, even if it would be tilted:

https://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects?s_tid=srchtitle

regionprops() will only give you bounding boxes that are aligned with the edges of the image.

Answer 2

[Matt J]

regionprops(BW, 'BoundingBox')