How to detect triangles, ellipses, and circles in binary image?

I have this binary image, and I need to classify between triangles, ellipses, circles, and rectangles. I already done the rectangle classification part. Apart from thresholding circularity, extent, boundingbox values (which works), how to classify the triangle (it always gets detected as circle using algorithms), classify ellipses vs circles (there is 1 circle in image)?

Answer 1

[Image Analyst]

A good way is to find the centroid and boundaries, then use findpeaks() to find the number of vertices. See my attached shape analysis demos.