Connect two objects to a single blob

Here is an example image of 2 objects. I want to fill the gap between those two to get a single blob. I tried with different morphological closing but could not get a smooth result as drawn in red.

Any help would be much appreciated.

Original Image:

Desired mask:

Answer 1

[Walter Roberson]

If you find() on the image to get the row and column coordinates, then you can use boundary() to get a list of indices into the row and columns that together, taken in order, give an outline that includes all of the points.

[Kamu]

Thanks Walter for your reply. Could you explain it a bit further? I know those functions but did not understand your approach.

[Walter Roberson]

[y, x] = find(YourImage);
K = boundary(x, y);
boundary_x = x(K);
boundary_y = y(K);

mask = poly2mask( boundary_x, boundary_y, size(YourImage,1), size(YourImage,2) );

mask is now an ROI that is 1 for everywhere inside the combined object. Or you can

plot(boundary_x, boundary_y, 'r', 'linewidth', 4)

if what you care about is just drawing the outline rather than figuring out which points are inside of it.