How can I locate typical points in a image?

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how can I locate those two red points that their tangent line is normal to the x_axis in the image?

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Image Analyst
Image Analyst 2017-8-16
Use find to scan the image line by line getting the first and last place in the line that's not 255. Then with those right and left coordinates, call diff() to find out when the column doesn't change. Then label it and call regionprops() to find the longest such stretch. Let me know if you can't write code for that. A start is
for row = 1 : rows
thisLine = yourImage(row, :);
leftEdge(row) = find(thisLine < 255, 1, 'first');
rightEdge(row) = find(thisLine < 255, 1, 'last');
end
dLeft = diff(leftEdge);
dRight = diff(rightEdge);
and so on. Call bwareafilt() to extract the longest stretch, etc.
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