How to make binary image more rounded, closer to ellipsoid shape?

Given: I have following binary image:

Want: I want to make it more rounded, (but not bigger than original bounding box) as follows.

Currently done:

I have tried 'imdilate'

    close all; clear all;clc;
    o_circ = imread('to_round.jpg');
    bw_circ = im2bw(o_circ, graythresh(o_circ));
    bw_circ_2 = imdilate(bw_circ, strel('disk',30));
    figure(1);imshow(bw_circ_2);

But it did't work as I wanted.

Needed: So what I actually need is to make original shape, as close a possible to ellipsoid shape. I guess I could use the regionprops, but I'm quite sure how to use all the values to plot an ellipse...

st = regionprops(bw_circ,'Centroid','MajorAxisLength','MinorAxisLength','Eccentricity');

[MATLAB version]

R2014a

Answer 1

[Walter Roberson]

http://www.mathworks.com/matlabcentral/fileexchange/289-ellipse-m

Answer 2

[Image Analyst]

You could try imclose() to do a morphological closing operation.

Or you could call imconvhull() to get the convex hull of each region.