Find suitable mid point

this is my code

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clear all;

[filename pathname]=uigetfile('*.jpg;*.png;*.tif;*.tiff;*.gif;*.bmp;');

inputimage=imread([pathname filename]);

I=inputimage;

I = rgb2gray(I) ;

[y,x] = find(I) ;

figure

imshow(I)

hold on

plot(x,y,'.b')

plot(x(1),y(1),'*y')

plot(x(end),y(end),'*r')

line([x(1),0],[y(1), 0])

line([x(end),0],[y(end), 0])

figure(1);line([0 1],[0 1]);

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i wana to find the mid point between the yellow point and red point.... the mid poit is that point where the curve become bended........... as shown the point by arrow...

orignal image

ofter code