How can I differentiate different polygon shapes in image

I want to write some code which can help me to classify images according to the polygon shape it contains, such as an image contains a triangle, then system should return "Triangle", if it contains a square then it should return "Square", one image contains only one polygon shape. I have a basic idea of coding, but I am not sure how can I implement those functions, this is the coding structure I came up with:

containSquare = false;
containTriangle = false;
containPentagon = false;

function checkForSquare ()
  %if there is square
      containSquare = true;
end

function checkForTriangle ()
  %if there is Triangle
      containTriangle = true;
end

function checkForPentagon ()
  %if there is Pentagon
      containPentagon = true;
end

return result

and this is a sample image:

any help would be appreciated.

[Walter Roberson]

Please do not close Questions that have an Answer.

Answer 1

[Image Analyst]

That's exactly what my demos do. Basically you find the centroid and make a profile of the radius as you go around the shape. Then count the number of peaks. The number of peaks will be the number of vertices and from that you know the polygon type.

[Alex kew]

thanks for your reply. I noticed that you used circularities of blobs to determine the shape, here is your code:

      % Determine the shape.
  if circularities(blobNumber) < 1.2
    % Theoretical value for a circle is 1.
    message = sprintf('For object #%d,\nthe perimeter = %.3f,\nthe area = %.3f,\nthe circularity = %.3f,\nso the object is a circle',...
      blobNumber, perimeters(blobNumber), areas(blobNumber), circularities(blobNumber));
    shape = 'circle';
  elseif circularities(blobNumber) < 1.5
    % Theoretical value for a square is (4d)^2 / (4*pi*d^2) = 4/pi = 1.273
    message = sprintf('For object #%d,\nthe perimeter = %.3f,\nthe area = %.3f,\nthe circularity = %.3f,\nso the object is a square',...
      blobNumber, perimeters(blobNumber), areas(blobNumber), circularities(blobNumber));
    shape = 'square';
  elseif circularities(blobNumber) > 1.5 && circularities(blobNumber) < 1.8
    % Theoretical value for an isosceles triangle is (3d)^2 / (4 * pi * 0.5 * d * d * sind(60)) = 9/(4 * pi * 0.5*sind(60)) = 1.6539
    message = sprintf('For object #%d,\nthe perimeter = %.3f,\nthe area = %.3f,\nthe circularity = %.3f,\nso the object is an isosceles triangle',...
      blobNumber, perimeters(blobNumber), areas(blobNumber), circularities(blobNumber));
    shape = 'triangle';
  else
    message = sprintf('The circularity of object #%d is %.3f,\nso the object is something else.',...
      blobNumber, circularities(blobNumber));
    shape = 'something else';
  end

if I want to find pentagon and hexagon, what circularities values should I use?

[Image Analyst]

Circularity is not such a good method when the polygons start to become more rounded. I suggest you use the peak finding method instead.