How to connect non-continuous boundary and fill the object in binary image

I have a binary image that contains the boundary of the object. The plots of boundary are not continuous, how can I connect those points? Moreover, how can I fill value in this object?

Answer 1

[KSSV]

An vague attempt....it can be further refined or a more legant solution would be possible.

I = imread('m.png') ;

I1 = rgb2gray(I) ;
I1 = imcrop(I1) ;

[y,x] = find(I1) ;

imshow(I1) ;
hold on
% plot(x,y,'.r')

[nx,ny] = size(I1) ;

P1 = [x(x<=nx/2) y(x<=nx/2)] ;
P2 = [x(x>nx/2) y(x>nx/2)] ;

P = P1'; % coordinates / points
c = mean(P,2); % mean/ central point
d = P-c ; % vectors connecting the central point and the given points
th = atan2(d(2,:),d(1,:)); % angle above x axis
[th, idx] = sort(th);   % sorting the angles
P = P(:,idx); % sorting the given points
P = [P P(:,1)]; % add the first at the end to close the polygon
plot( P(1,:), P(2,:), 'r');

P = P2'; % coordinates / points
c = mean(P,2); % mean/ central point
d = P-c ; % vectors connecting the central point and the given points
th = atan2(d(2,:),d(1,:)); % angle above x axis
[th, idx] = sort(th);   % sorting the angles
P = P(:,idx); % sorting the given points
P = [P P(:,1)]; % add the first at the end to close the polygon
plot( P(1,:), P(2,:), 'b');

[AniCnx]

Thank you for your help. But the code was obstructed on the ' idx1 = boundary(P1)' by undefined function boundary. Once I deleated this command, the obstruct went to 'd=P-c' by disagree of the dimension.

Ani

[KSSV]

YOu need not to use boundary.......edited the code.

[AniCnx]

Thank you very much. I sorted it out.