How to find vertices of triangle approximated from binary image

The purpose is to analyse uniformity of images like below(The shape changes slightly based on device parameters).

I need to find the areas of 3 sub regions drawn by connecting centroid to 3 vertices.

The movement of centroid and variation in these sub areas are required for further analysis(with different device parameters).

For this, cordinates of vertices are required.

(Centroid is obtained from regionprop/blob analysis)

I know that this image is not in actual triangle shape. But is there any method to find the 3 vertices by any approximation method?

I could not find a solution with bounding box, bwboundaries...

Answer 1

[Image Analyst]

You can find the centroid, then the distance of the perimeter to the centroid and then call findpeaks on that distance to find the 3 vertexes. I do that in my attached demo.

[Kiran K]

This method was helpful to find the vertices.

In the attached image case, as the triangle edges are not sharp, all of the peaks on the distance array do not have high prominence. By adjusting the MinPeakProminence, it is able to identify the peaks.

Answer 2

[KSSV]

I = imread('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1239812/image.png') ;

[y,x] = find(I) ; 

mx = mean(x) ; my = mean(y) ; 

d = sqrt((mx-x).^2+(my-y).^2) ; 
idx = isoutlier(d) ; 
x(idx) =[] ; y(idx) =[] ; 


idx = convhull(x,y) ;
x = x(idx) ; y = y(idx) ; 

imshow(I)
hold on
plot(x,y,'.-r')