Problem on detect ellipse in the image with many shapes inside

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Excuse me again. I have adapted the code from Shape Recognition because I also want to detect the ellipse shape
But the result is not satisfied since the program can detect ellipse but it also detected other shape as ellipse and stop detecting rectangle and square. I write new condition based on bounding box and extent. So I want to know why the program detect other shape as ellipse and how to fix that. Is there any condition of ellipse that I missed?
Thank you in advanced
hold on
for i = 1 : length(STATS)
W(i) = uint8(abs(STATS(i).BoundingBox(3)-STATS(i).BoundingBox(4)) < 0.1); %%If width and height of bounding box are equal, W(i)=1, otherwise W(i)=0
W(i) = W(i) + 2 * uint8((STATS(i).Extent - 1) == 0 ); % Extent =1 case; If circle/ellipse, back term=0, rec/sqr back term =2
W(i) = W(i) + 4 * uint8((STATS(i).Extent - 1) <= 0.7854); %Extent = pi/4 case ellipse/circle
centroid = STATS(i).Centroid;
switch W(i)
case 5
case 2
case 3
case 4

Accepted Answer

DGM on 31 Oct 2022
Edited: DGM on 31 Oct 2022
The answers on this post by ImageAnalyst and myself include attempts to identify ellipses.
The example I gave seems fine identifying squares, rectangles, circles, ellipses, but is not very reliable at identifying general irregular polygons when the image is this small. See the comment on my answer.

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