find out the orientation, length and radius of curved rectangular object

I have a image as shown as fig.1.I am trying to fit this binary image with a curved rectangular (fig.2)to figure out:

1. the orientation (the angle between the long axis and the horizontal axis of the curved rectangle)

2. the length (l) and radius (R) of the object. What is the best way to do it?

My very naive idea is using least square fit to fit the boundary of the object and find out these information. However it turns out there is no equation for capped rectangle. In matlab there is a function called rectangle can create the capped rectangle perfectly however it seems just for the plot purpose and can not be implanted into the least square fit. Any help or clue is greatly appreciated.

fig.1: http://i.stack.imgur.com/aRIhm.png

fig.2: http://i.stack.imgur.com/eXzSk.png

Thanks for the help.

Answer 1

[Ryan]

Have you looked at MF regionprops()?

[Walter Roberson]

That can give major and minor axes, and eccentricity equivalent to an ellipse, but an ellipse is not what is desired in this situation.

[Tai-Yen Chen]

Yes, Walter is right. I do check the regionprops but did not meet my purpose.

Answer 2

[Image Analyst]

John D'Errico's File Exchange http://www.mathworks.com/matlabcentral/fileexchange/?term=authorid%3A679 has a minimum bounding rectangle function http://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects. The rectangle can be at any angle. I think this should give you what you want, or close enough (especially considering the very low resolution of your image).

[Tai-Yen Chen]

Hi image Analyst, This is indeed a great start. But just out of curiosity, if I do have a high resolution image, will you have other suggestion on solving this issue?