Improve Ellipse Fit around a Binary Image

Hello all,

The attached image shows a binary edge detection of a bean (shown in white.) In red is an ellipse for which I have attempted to fit to this bean.

My goal is to more precisely fit this ellipse to the bean, instead of the ellipse poorly encompassing the bean. How can I do this? Are there any lines that I can edit to improve this?

The code for which I am applying the ellipse is as follows (where the variable, isolatedBean is used as the binary image input):

    s = regionprops      (isolatedBean, 'Orientation', 'MajorAxisLength','MinorAxisLength', 'Eccentricity', 'Centroid');
hold on
    phi = linspace(0,2*pi,50);
    cosphi = cos(phi);
    sinphi = sin(phi);

    for k = 1:length(s)
        xbar = s(k).Centroid(1);
        ybar = s(k).Centroid(2);

        a = s(k).MajorAxisLength/2;
        b = s(k).MinorAxisLength/2;

        theta = pi*s(k).Orientation/180;
        R = [ cos(theta)   sin(theta)
            -sin(theta)   cos(theta)];

        xy = [a*cosphi; b*sinphi];
        xy = R*xy;

        x = xy(1,:) + xbar;
        y = xy(2,:) + ybar;

        plot(x,y,'r','LineWidth',2);
    end

Thanks for your help!

[Priya Natarajan]

Try edge-based active contour model.... it worked for me... the source code could be found at http://www.mathworks.de/matlabcentral/fileexchange/12711-level-set-for-image-segmentation/all_files

Answer 1

[Image Analyst]

Why not just take the convex hull?

If you really want an true ellipse fit, it's not so easy. But there is a paper on it:

"Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola"

by Sung Joon Ahn*, Wolfgang Rauh, Hans-JuK rgen Warnecke,

Fraunhofer Institute for Manufacturing Engineering and Automation (IPA), Nobelstr. 12, 70569 Stuttgart, Germany Fraunhofer Society, Leonrodstr. 54, 80636 Munich, Germany Received 16 June 2000; accepted 12 September 2000

Pattern Recognition 34 (2001) 2283}2303

http://www.sciencedirect.com/science/article/pii/S0031320300001527

and a FAQ entry: http://matlab.wikia.com/wiki/FAQ#Can_you_program_up_the_algorithm_in_this_article_for_me_and_explain_it_to_me.3F

[N.B.]

My end goal is to graph the different radii of each bean. Can I extract radius data from the bwconvhull function?

Answer 2

[Matt Kindig]

To build on Image Analyst's point, you can do something like this.

outline = bwmorph( isolatedBean, 'skel');   %convert to thin borderline
[r,c]=find(outline);  %find locations where outline=1 (i.e. outline of bean)

I would then use one of the ellipse fitting functions on the File Exchange, such as http://www.mathworks.com/matlabcentral/fileexchange/15125-fitellipse-m to actually fit the ellipse.

[Image Analyst]

Seems like an excellent plan.