How to create a line that goes through a specific point?

Hello everybody, I have a binary image of edges of a shape, a closed shape and I would like to find the minimum and maximum diameter of that shape. meaning the max and min line (from edge to edge) but it has to go through the point of center of mass. so I have found this point but now I have to draw lines that go through this point and find the min and max. I hope this makes sense... Help someone?? Tnx, Hadas

[Matt J]

Is it a convex shape?

Answer 1

[Matt J]

If the shape is convex, one thing you could is fill in the edges to get a binary image of the whole shape

Image=imfill(Image,'holes');

Then, use radon to get the lengths of lines through the shape and find the min/max, over rays passing through the center of mass.

[Hadas]

HI tnx for you tip. the thing is that the shapes are not necessarily convex and the center of mass will not always be the center of the shape. I am attaching an example for one of the image I have. so the light gray + dark gray area is actually one shape and then the second shape includes also the white area. I think the radon will work but the point of the axis will be the center pixel no? tnx again!

[Matt J]

Not sure what "point of the axis" means. Each column R(:,j) of

 [R,d]=radon(Image,theta)

will give the intersection lengths of many lines angled by theta(j), not just the line passing through the center. In fact R(i,j) will correspond to the line angled by theta(j) and at displacement d(i) from the center. You must find the d(i) of the line passing through the center of mass, for each theta(j).

If your shape is not convex, though, several things in your problem become ambiguously defined. The line passing through the center of mass can intersect the shape in multiple chords, meaning that the diameter line is not a single line segment. You are gambling that your shape is close enough to convex to prevent this from happening.

[Matt J]

Are you sure you shouldn't be defining the max diameter as the smallest circle (centered at the center of mass) that can enclose the shape? And the minimum diameter as the largest circle that can be inscribed inside the shape?

[Hadas]

actually your way is much better! I think I will go with it. but then I will have to take into account the edge of each shape, right? so if we take the example above and I can create an edge image (attached) so how can I find the circles for min and max diameter for each shape? probably the minimum diameter will be easier to find using the largest circle that can be inscribed inside the shape as you suggested but how can I find the smallest circle (centered at the center of mass) that can enclose the shape? for each shape? tnx!!!! Hadas

[Matt J]

You have to isolate the outer edges of the shape, but if you can do that and if (ic,jc) is the coordinate of the center of mass, then it is just

   [I,J]=find(edges);

   Distances=sqrt((I-ic).^2+(J-jc).^2);

   maxDiameter=2*max(Distances);
   minDiameter=2*min(Distances);